% This file was created with JabRef 2.10.
% Encoding: Cp1252

@article{hu2017unifying,
  title={On unifying deep generative models},
  author={Hu, Zhiting and Yang, Zichao and Salakhutdinov, Ruslan and Xing, Eric P},
  journal={arXiv preprint arXiv:1706.00550},
  year={2017}
}

% -- Bishop
@book{bishop2006a,
  title = {Pattern recognition and machine learning},
  language = {eng},
  publisher = {Springer,},
  pages = {738 s.},
  year = {2006},
  isbn = {0387310738, 9780387310732},
  author = {Bishop, Christopher M.}
}

% -- NMF maximum likelihood
@article{fevotte2011algorithms,
  title={Algorithms for nonnegative matrix factorization with the $\beta$-divergence},
  author={F{\'e}votte, C{\'e}dric and Idier, J{\'e}r{\^o}me},
  journal={Neural computation},
  volume={23},
  number={9},
  pages={2421--2456},
  year={2011},
  publisher={MIT Press}
}

@article{cichocki2009fast,
  title={Fast local algorithms for large scale nonnegative matrix and tensor factorizations},
  author={Cichocki, Andrzej and Phan, Anh-Huy},
  journal={IEICE transactions on fundamentals of electronics, communications and computer sciences},
  volume={92},
  number={3},
  pages={708--721},
  year={2009},
  publisher={The Institute of Electronics, Information and Communication Engineers}
}


% -- NMF and music

@inproceedings{abdallah4polyphonic,
  title={Polyphonic music transcription by non-negative sparse coding of power spectra},
  author={Abdallah, Samer and Plumbley, Mark},
  booktitle={Proceedings of the Fifth International Conference on Music Information Retrieval (ISMIR’04)},
  pages={10--14}
}

@article{fevotte2009nonnegative,
  title={Nonnegative matrix factorization with the Itakura-Saito divergence: With application to music analysis},
  author={F{\'e}votte, C{\'e}dric and Bertin, Nancy and Durrieu, Jean-Louis},
  journal={Neural computation},
  volume={21},
  number={3},
  pages={793--830},
  year={2009},
  publisher={MIT Press}
}

@article{ozerov2010multichannel,
  title={Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation},
  author={Ozerov, Alexey and F{\'e}votte, C{\'e}dric},
  journal={IEEE Transactions on Audio, Speech, and Language Processing},
  volume={18},
  number={3},
  pages={550--563},
  year={2010},
  publisher={IEEE}
}

@inproceedings{smaragdis2003non,
  title={Non-negative matrix factorization for polyphonic music transcription},
  author={Smaragdis, Paris and Brown, Judith C},
  booktitle={Applications of Signal Processing to Audio and Acoustics, 2003 IEEE Workshop on.},
  pages={177--180},
  year={2003},
  organization={IEEE}
}

@article{virtanen2007monaural,
  title={Monaural sound source separation by nonnegative matrix factorization with temporal continuity and sparseness criteria},
  author={Virtanen, Tuomas},
  journal={IEEE transactions on audio, speech, and language processing},
  volume={15},
  number={3},
  pages={1066--1074},
  year={2007},
  publisher={IEEE}
}

% -- NMF - document clustering

@inproceedings{xu2003document,
  title={Document clustering based on non-negative matrix factorization},
  author={Xu, Wei and Liu, Xin and Gong, Yihong},
  booktitle={Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval},
  pages={267--273},
  year={2003},
  organization={ACM}
}

@article{shahnaz2006document,
  title={Document clustering using nonnegative matrix factorization},
  author={Shahnaz, Farial and Berry, Michael W and Pauca, V Paul and Plemmons, Robert J},
  journal={Information Processing \& Management},
  volume={42},
  number={2},
  pages={373--386},
  year={2006},
  publisher={Elsevier}
}


% -- NMF - neuroinformatics

@article{morup2007erpwavelab,
  title={ERPWAVELAB: A toolbox for multi-channel analysis of time--frequency transformed event related potentials},
  author={M{\o}rup, Morten and Hansen, Lars Kai and Arnfred, Sidse M},
  journal={Journal of neuroscience methods},
  volume={161},
  number={2},
  pages={361--368},
  year={2007},
  publisher={Elsevier}
}

% -- NMF - bioinfomatics

@inproceedings{del2016breast,
  title={Breast cancer’s microarray data: pattern discovery using nonnegative matrix factorizations},
  author={Del Buono, Nicoletta and Esposito, Flavia and Fumarola, Fabio and Boccarelli, Angelina and Coluccia, Mauro},
  booktitle={International Workshop on Machine Learning, Optimization and Big Data},
  pages={281--292},
  year={2016},
  organization={Springer}
}

@article{brunet2004metagenes,
  title={Metagenes and molecular pattern discovery using matrix factorization},
  author={Brunet, Jean-Philippe and Tamayo, Pablo and Golub, Todd R and Mesirov, Jill P},
  journal={Proceedings of the national academy of sciences},
  volume={101},
  number={12},
  pages={4164--4169},
  year={2004},
  publisher={National Acad Sciences}
}

% -- NMF & MAP + ARD

@inproceedings{morup2009tuning,
  title={Tuning pruning in sparse non-negative matrix factorization},
  author={M{\o}rup, Morten and Hansen, Lars Kai},
  booktitle={Signal Processing Conference, 2009 17th European},
  pages={1923--1927},
  year={2009},
  organization={IEEE}
}

@inproceedings{tan2009automatic,
  title={Automatic relevance determination in nonnegative matrix factorization},
  author={Tan, Vincent YF and F{\'e}votte, C{\'e}dric},
  booktitle={SPARS'09-Signal Processing with Adaptive Sparse Structured Representations},
  year={2009}
}


% -- NMF

@article{hinrich2018a,
  title = {Probabilistic sparse non-negative matrix factorization},
  language = {eng},
  publisher = {Springer Verlag},
  editor = {Yannick Deville, Sharon Gannot, Russell Mason, Mark D. Plumbley, Dominic Ward},
  journal = {Lecture Notes in Computer Science},
  volume = {10891},
  pages = {488-498},
  year = {2018},
  issn = {16113349, 03029743},
  isbn = {9783319937632, 9783319937649},
  abstract = {In this paper, we propose a probabilistic sparse non-negative
                  matrix factorization model that extends a recently proposed
                  variational Bayesian non-negative matrix factorization model
                  to explicitly account for sparsity. We assess the influence of
                  imposing sparsity within a probabilistic framework on either
                  the loading matrix, score matrix, or both and further contrast
                  the influence of imposing an exponential or truncated normal
                  distribution as prior. The probabilistic methods are compared
                  to conventional maximum likelihood based NMF and sparse NMF on
                  three image datasets; (1) A (synthetic) swimmer dataset, (2)
                  The CBCL face dataset, and (3) The MNIST handwritten digits
                  dataset. We find that the probabilistic sparse NMF is able to
                  automatically learn the level of sparsity and find that the
                  existing probabilistic NMF as well as the proposed
                  probabilistic sparse NMF prunes inactive components and
                  thereby automatically learns a suitable number of components.
                  We further find that accounting for sparsity can provide more
                  part based representations but for the probabilistic modeling
                  the choice of priors and how sparsity is imposed can have a
                  strong influence on the extracted representations.},
  doi = {10.1007/978-3-319-93764-9_45},
  author = {Hinrich, Jesper Løve and Mørup, Morten}
}

@article{hoyer2004non,
  title={Non-negative matrix factorization with sparseness constraints},
  author={Hoyer, Patrik O},
  journal={Journal of machine learning research},
  volume={5},
  number={Nov},
  pages={1457--1469},
  year={2004}
}

@article{paatero1994a,
	title = {Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values},
	language = {eng},
	journal = {Environmetrics},
	volume = {5},
	number = {2},
	pages = {111-126},
	year = {1994},
	issn = {1099095x, 11804009},
	doi = {10.1002/env.3170050203, 10.1002/(ISSN)1099-095X},
	author = {Paatero, Pentti and Tapper, Unto}
}

@article{lee1999a,
	title = {Learning the parts of objects by non-negative matrix factorization},
	language = {eng},
	publisher = {NATURE PUBLISHING GROUP},
	journal = {Nature},
	volume = {401},
	number = {6755},
	pages = {788-791},
	year = {1999},
	issn = {14764687, 00280836},
	abstract = {Is perception of the whole based on perception of its parts? There
                  is psychological(1) and physiological(2,3) evidence for
                  parts-based representations in the brain, and certain
                  computational theories of object recognition rely on such
                  representations(4,5). But little is known about how brains or
                  computers might learn the parts of objects. Here we
                  demonstrate an algorithm for non-negative matrix factorization
                  that is able to learn parts of faces and semantic features of
                  text. This is in contrast to other methods, such as principal
                  components analysis and vector quantization, that learn
                  holistic, not parts-based, representations. Non-negative
                  matrix factorization is distinguished from the other methods
                  by its use of non-negativity constraints. These constraints
                  lead to a parts-based representation because they allow only
                  additive, not subtractive, combinations. When non-negative
                  matrix factorization is implemented as a neural network,
                  parts-based representations emerge by virtue of two
                  properties: the firing rates of neurons are never negative and
                  synaptic strengths do not change sign.},
	doi = {10.1038/44565},
	author = {Lee, DD and Seung, HS}
}

@article{lee2001a,
  title = {Algorithms for non-negative matrix factorization},
  language = {eng},
  publisher = {M I T PRESS},
  journal = {Advances in Neural Information Processing Systems},
  volume = {13},
  pages = {556-562},
  year = {2001},
  issn = {10495258},
  isbn = {0262122413},
  abstract = {Non-negative matrix factorization (NMF) has previously been shown
                  to be a useful decomposition for multivariate data. Two
                  different multiplicative algorithms for NMF are analyzed. They
                  differ only slightly in the multiplicative factor used in the
                  update rules. One algorithm can be shown to minimize the
                  conventional least squares error while the other minimizes the
                  generalized Kullback-Leibler divergence. The monotonic
                  convergence of both algorithms can be proven using an
                  auxiliary function analogous to that used for proving
                  convergence of the Expectation-Maximization algorithm. The
                  algorithms can also be interpreted as diagonally resealed
                  gradient descent, where the resealing factor is optimally
                  chosen to ensure convergence.},
  author = {Lee, DD and Seung, HS}
}

@article{schmidt2009a,
  title = {Bayesian non-negative matrix factorization},
  language = {eng},
  publisher = {Springer},
  journal = {Proceedings of the International Conference on Independent Component Analysis and Signal Separation},
  volume = {5441},
  pages = {540-547},
  year = {2009},
  issn = {16113349, 03029743},
  isbn = {3642005985},
  abstract = {Abstract. We present a Bayesian treatment of non-negative matrix
                  factorization (NMF), based on a normal likelihood and
                  exponential priors, and derive an efficient Gibbs sampler to
                  approximate the posterior density of the NMF factors. On a
                  chemical brain imaging data set, we show that this improves
                  interpretability by providing uncertainty estimates. We
                  discuss how the Gibbs sampler can be used for model order
                  selection by estimating the marginal likelihood, and compare
                  with the Bayesian information criterion. For computing the
                  maximum a posteriori estimate we present an iterated
                  conditional modes algorithm that rivals existing
                  state-of-the-art NMF algorithms on an image feature extraction
                  problem. Â© Springer-Verlag Berlin Heidelberg 2009.},
  doi = {10.1007/978-3-642-00599-2_68},
  author = {Schmidt, Mikkel Nørgaard and Winther, Ole and Hansen, Lars Kai}
}

@article{brouwer2017a,
	title = {Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation},
	language = {eng},
	publisher = {Springer Verlag},
	editor = {Ceci, Michelangelo, Hollmén, Jaakko, Todorovski, Ljupčo, Vens, Celine, Džeroski, Sašo},
	journal = {Lecture Notes in Computer Science (including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {10534},
	pages = {513-529},
	year = {2017},
	issn = {16113349, 03029743},
	isbn = {9783319712499, 9783319712482},
	abstract = {In this paper, we study the trade-offs of different inference
                  approaches for Bayesian matrix factorisation methods, which
                  are commonly used for predicting missing values, and for
                  finding patterns in the data. In particular, we consider
                  Bayesian nonnegative variants of matrix factorisation and
                  tri-factorisation, and compare non-probabilistic inference,
                  Gibbs sampling, variational Bayesian inference, and a
                  maximum-a-posteriori approach. The variational approach is new
                  for the Bayesian nonnegative models. We compare their
                  convergence, and robustness to noise and sparsity of the data,
                  on both synthetic and real-world datasets. Furthermore, we
                  extend the models with the Bayesian automatic relevance
                  determination prior, allowing the models to perform automatic
                  model selection, and demonstrate its efficiency. Code and data
                  related to this chapter are availabe at:
                  https://github.com/ThomasBrouwer/BNMTF_ARD.},
	doi = {10.1007/978-3-319-71249-9_31},
	author = {Brouwer, Thomas and Frellsen, Jes and Li{{\'{o}}}, Pietro}
}

@article{laurberg2008a,
	title = {Theorems on Positive Data: On the Uniqueness of NMF},
	language = {eng},
	publisher = {Computational Intelligence and Neuroscience},
	year = {2008},
	abstract = {We investigate the conditions for which nonnegative matrix
                  factorization (NMF) is unique and introduce several theorems
                  which can determine whether the decomposition is in fact
                  unique or not. The theorems are illustrated by several
                  examples showing the use of the theorems and their
                  limitations. We have shown that corruption of a unique NMF
                  matrix by additive noise leads to a noisy estimation of the
                  noise-free unique solution. Finally, we use a stochastic view
                  of NMF to analyze which characterization of the underlying
                  model will result in an NMF with small estimation errors.},
	author = {Laurberg, Hans and Gr{{\ae}}sb{{\o}}ll Christensen, Mads and D. Plumbley, Mark and Kai Hansen, Lars and Holdt Jensen, S{{\o}}ren}
}



@article{schmidt2010a,
	title = {INFINITE NON-NEGATIVE MATRIX FACTORIZATION},
	language = {eng},
	publisher = {EUROPEAN ASSOC SIGNAL SPEECH & IMAGE PROCESSING-EURASIP},
	journal = {Signal Processing Conference (eusipco), European},
	pages = {905-909},
	year = {2010},
	issn = {20761465},
	abstract = {We propose the infinite non-negative matrix factorization (INMF)
                  which assumes a potentially unbounded number of components in
                  the Bayesian NMF model. We devise an inference scheme based on
                  Gibbs sampling in conjunction with Metropolis-Hastings moves
                  that admits cross-dimensional exploration of the posterior
                  density. The approach can effectively establish the model
                  order for NMF at a less computational cost than existing
                  approaches such as thermodynamic integration and existing
                  reversible jump Markov chain Monte Carlo sampling schemes. On
                  synthetic and real data we demonstrate the success of (INMF).},
	author = {Schmidt, Mikkel N. and M{{\o}}rup, Morten}
}

@article{m2009a,
	title = {Automatic Relevance Determination for multi-way models},
	language = {eng},
	publisher = {JOHN WILEY & SONS LTD},
	journal = {Journal of Chemometrics},
	volume = {23},
	number = {7-8},
	pages = {352-363},
	year = {2009},
	issn = {1099128x, 08869383},
	abstract = {Estimating the adequate number of components is an important yet
                  difficult problem in multi-way modelling. We demonstrate how a
                  Bayesian framework for model selection based on Automatic
                  Relevance Determination (ARD) can be adapted to the Tucker and
                  CP models. By assigning priors for the model parameters and
                  learning the hyperparameters of these priors the method is
                  able to turn off excess components and simplify the core
                  structure at a computational cost of fitting the conventional
                  Tucker/CP model. To investigate the impact of the choice of
                  priors we based the ARD on both Laplace and Gaussian priors
                  corresponding to regularization by the sparsity promoting
                  L1-norm and the conventional L2-norm, respectively. While the
                  form of the priors had limited effect on the results obtained
                  the ARD approach turned out to form a useful, simple, and
                  efficient tool for selecting the adequate number of components
                  of data within the Tucker and CP structure. For the Tucker and
                  CP model the approach performs better than heuristics such as
                  the Bayesian Information Criterion, Akaikes Information
                  Criterion, DIFFIT and the numerical convex hull (NumConvHull)
                  while operating only at the cost of estimating an ordinary
                  CP/Tucker model. For the CP model the ARD approach performs
                  almost as well as the core consistency diagnostic. Thus, the
                  ARD framework is a simple yet efficient tool for the
                  estimation of the adequate number of components in multi-way
                  models. A Matlab implementation of the proposed algorithm is
                  available for download at www.erpwavelab.org.},
	doi = {10.1002/cem.1223},
	author = {M{{\o}}rup, Morten and Hansen, Lars Kai}
}

@article{bro1997a,
  title = {A fast non-negativity-constrained least squares algorithm},
  language = {eng},
  publisher = {JOHN WILEY & SONS LTD},
  journal = {Journal of Chemometrics},
  volume = {11},
  number = {5},
  pages = {393-401},
  year = {1997},
  issn = {1099128x, 08869383},
  abstract = {In this paper a modification of the standard algorithm for
                  non-negativity-constrained linear least squares regression is
                  proposed. The algorithm is specifically designed for use in
                  multiway decomposition methods such as PARAFAC and N-mode
                  principal component analysis. In those methods the typical
                  situation is that there is a high ratio between the numbers of
                  objects and variables in the regression problems solved.
                  Furthermore, very similar regression problems are solved many
                  times during the iterative procedures used. The algorithm
                  proposed is based on the defacto standard algorithm NNLS by
                  Lawson and Hanson, but modified to take advantage of the
                  special characteristics of iterative algorithms involving
                  repeated use of non-negativity constraints. The principle
                  behind the NNLS algorithm is described in detail and a
                  comparison is made between this standard algorithm and the new
                  algorithm called FNNLS (fast NNLS). (C) 1997 John Wiley &
                  Sons, Ltd.},
  author = {Bro, R and DeJong, S}
}

@article{lin2007a,
  title = {Projected gradient methods for nonnegative matrix factorization},
  language = {eng},
  publisher = {M I T PRESS},
  journal = {Neural Computation},
  volume = {19},
  number = {10},
  pages = {2756-2779},
  year = {2007},
  issn = {1530888x, 08997667},
  abstract = {Nonnegative matrix factorization (NMF) can be formulated as a
                  minimization problem with bound constraints. Although
                  bound-constrained optimization has been studied extensively in
                  both theory and practice, so far no study has formally applied
                  its techniques to NME In this letter, we propose two projected
                  gradient methods for NMF, both of which exhibit strong
                  optimization properties. We discuss efficient implementations
                  and demonstrate that one of the proposed methods converges
                  faster than the popular multiplicative update approach. A
                  simple Matlab code is also provided.},
  doi = {10.1162/neco.2007.19.10.2756},
  author = {Lin, Chih-Jen}
}

@article{cichocki2007a,
  title = {Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization},
  language = {und},
  publisher = {Springer Verlag},
  journal = {Lecture Notes in Computer Science (including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
  volume = {4666 LNCS},
  pages = {169-176},
  year = {2007},
  issn = {16113349, 03029743},
  isbn = {9783540744931},
  abstract = {In the paper we present new Alternating Least Squares (ALS)
                  algorithms for Nonnegative Matrix Factorization (NMF) and
                  their extensions to 3D Nonnegative Tensor Factorization (NTF)
                  that are robust in the presence of noise and have many
                  potential applications, including multi-way Blind Source
                  Separation (BSS), multi-sensory or multi-dimensional data
                  analysis, and nonnegative neural sparse coding. We propose to
                  use local cost functions whose simultaneous or sequential (one
                  by one) minimization leads to a very simple ALS algorithm
                  which works under some sparsity constraints both for an
                  under-determined (a system which has less sensors than
                  sources) and over-determined model. The extensive experimental
                  results confirm the validity and high performance of the
                  developed algorithms, especially with usage of the multi-layer
                  hierarchical NMF. Extension of the proposed algorithm to
                  multidimensional Sparse Component Analysis and Smooth
                  Component Analysis is also proposed. Â© Springer-Verlag Berlin
                  Heidelberg 2007.},
  author = {Cichocki, Andrzej and Zdunek, Rafal and Amari, Shun-Ichi}
}

% -- Swimmer dataset

@article{donoho2004a,
	title = {When does non-negative matrix factorization give a correct decomposition into parts?},
	language = {eng},
	publisher = {M I T PRESS},
	journal = {Advances in Neural Information Processing Systems},
	volume = {16},
	pages = {1141-1148},
	year = {2004},
	abstract = {We interpret non-negative matrix factorization geometrically, as
                  the problem of finding a simplicial cone which contains a
                  cloud of data points and which is contained in the positive
                  orthant. We show that under certain conditions, basically
                  requiring that some of the data are spread across the faces of
                  the positive orthant, there is a unique such simplicial cone.
                  We give examples of synthetic image articulation databases
                  which obey these conditions; these require separated support
                  and factorial sampling. For such databases there is a
                  generative model in terms of 'parts' and NMF correctly
                  identifies the 'parts'. We show that our theoretical results
                  are predictive of the performance of published NMF code, by
                  running the published algorithms on one of our synthetic image
                  articulation databases.},
	author = {Donoho, D and Stodden, V}
}

% ------------ Sleep stage classification -----------------------

% Pools all data from the subject, and uses half of it has training and half of it as testing.
@article{hassan2015a,
  title = {On the Classification of Sleep States By Means of Statistical and Spectral Features from Single Channel Electroencephalogram},
  language = {eng},
  publisher = {IEEE},
  journal = {2015 International Conference on Advances in Computing, Communications and Informatics (icacci)},
  pages = {2238-2243},
  year = {2015},
  isbn = {9781479987917, 9781479987924, 9781479987900},
  abstract = {Traditional sleep scoring based on visual inspection of
                  Electroencephalogram (EEG) signals is onerous for sleep
                  scorers because of the gargantuan volume of data that have to
                  be analyzed per examination. Computer-aided sleep staging can
                  alleviate the onus of the sleep scorers. Again, most of the
                  existing works on automatic sleep staging are multichannel
                  based. Multichannel based sleep scoring is not pragmatic for
                  the implementation of a wearable and portable sleep quality
                  evaluation device. Due to all these factors, automatic sleep
                  scoring based on single channel EEG is garnering increasing
                  attention of sleep researchers. In this work, we propound a
                  single channel based solution to sleep scoring. First, we
                  decompose the EEG signals into segments. We then compute
                  various statistical and spectral features from the signal
                  segments. After performing statistical analyses, we perform
                  classification using artificial neural network. Results of
                  various experiments perspicuously manifest that the proposed
                  scheme is superior to state-of-the-art ones in accuracy.},
  doi = {10.1109/ICACCI.2015.7275950},
  author = {Hassan, Ahnaf Rashik and Bashar, Syed Khairul and Bhuiyan, Mohammed Imamul Hassan}
}


@article{ronzhina2012a,
  title = {Sleep scoring using artificial neural networks},
  language = {eng},
  publisher = {W B SAUNDERS CO LTD},
  journal = {Sleep Medicine Reviews},
  volume = {16},
  number = {3},
  pages = {251-263},
  year = {2012},
  issn = {15322955, 10870792},
  abstract = {Rapid development of computer technologies leads to the intensive
                  automation of many different processes traditionally performed
                  by human experts. One of the spheres characterized by the
                  introduction of new high intelligence technologies
                  substituting analysis performed by humans is sleep scoring.
                  This refers to the classification task and can be solved next
                  to other classification methods by use of artificial neural
                  networks (ANN). ANNs are parallel adaptive systems suitable
                  for solving of nonlinear problems. Using ANN for automatic
                  sleep scoring is especially promising because of new ANN
                  learning algorithms allowing faster classification without
                  decreasing the performance. Both appropriate preparation of
                  training data as well as selection of the ANN model make it
                  possible to perform effective and correct recognizing of
                  relevant sleep stages. Such an approach is highly topical,
                  taking into consideration the fact that there is no automatic
                  scorer utilizing ANN technology available at present. (C) 2011
                  Elsevier Ltd. All rights reserved.},
  doi = {10.1016/j.smrv.2011.06.003},
  author = {Ronzhina, Marina and Janousek, Oto and Kolarova, Jana and Novakova, Marie and Honzik, Petr and Provaznik, Ivo}
}

% -- Multi-tapered spectrograms
@article{prerau2017a,
  title = {Sleep Neurophysiological Dynamics Through the Lens of Multitaper Spectral Analysis},
  language = {eng},
  publisher = {AMER PHYSIOLOGICAL SOC},
  journal = {Physiology},
  volume = {32},
  number = {1},
  pages = {60-92},
  year = {2017},
  issn = {15489221, 15489213},
  abstract = {During sleep, cortical and subcortical structures within the brain
                  engage in highly structured oscillatory dynamics that can be
                  observed in the electroencephalogram (EEG). The ability to
                  accurately describe changes in sleep state from these
                  oscillations has thus been a major goal of sleep medicine.
                  While numerous studies over the past 50 years have shown sleep
                  to be a continuous, multifocal, dynamic process, long-standing
                  clinical practice categorizes sleep EEG into discrete stages
                  through visual inspection of 30-s epochs. By representing
                  sleep as a coarsely discretized progression of stages, vital
                  neurophysiological information on the dynamic interplay
                  between sleep and arousal is lost. However, by using
                  principled timefrequency spectral analysis methods, the rich
                  dynamics of the sleep EEG are immediately visible-elegantly
                  depicted and quantified at time scales ranging from a full
                  night down to individual microevents. In this paper, we review
                  the neurophysiology of sleep through this lens of dynamic
                  spectral analysis. We begin by reviewing spectral estimation
                  techniques traditionally used in sleep EEG analysis and
                  introduce multitaper spectral analysis, a method that makes
                  EEG spectral estimates clearer and more accurate than
                  traditional approaches. Through the lens of the multitaper
                  spectrogram, we review the oscillations and mechanisms
                  underlying the traditional sleep stages. In doing so, we will
                  demonstrate how multitaper spectral analysis makes the
                  oscillatory structure of traditional sleep states
                  instantaneously visible, closely paralleling the traditional
                  hypnogram, but with a richness of information that suggests
                  novel insights into the neural mechanisms of sleep, as well as
                  novel clinical and research applications.},
  doi = {10.1152/physiol.00062.2015},
  author = {Prerau, Michael J. and Brown, Ritchie E. and Bianchi, Matt T. and Ellenbogen, Jeffrey M. and Purdon, Patrick L.}
}

% -- The sleep-edfx database on PhysioNet

@article{kemp2000a,
	title = {Analysis of a sleep-dependent neuronal feedback loop: The slow-wave microcontinuity of the EEG},
	language = {eng},
	publisher = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
	journal = {Ieee Transactions on Biomedical Engineering},
	volume = {47},
	number = {9},
	pages = {1185-1194},
	year = {2000},
	issn = {15582531, 00189294},
	abstract = {Increasing depth of sleep corresponds to an increasing gain in the
                  neuronal feedback loops that generate the low-frequency
                  (slow-wave) electroencephalogram (EEG), We derived the
                  maximum-likelihood estimator of the feedback gain and applied
                  it to quantify sleep depth, The estimator computes the
                  fraction (0$\%$-100$\%$) of the current slow wave which
                  continues in the near-future (0.02 s later) EEG, Therefore,
                  this percentage was dubbed slow-wave microcontinuity (SW). It
                  is not affected by anatomical parameters such as skull
                  thickness, which can considerably bias the commonly used
                  slow-wave power (SWP).In our study, both of the estimators SW
                  and SWP were monitored throughout two nights in 22 subjects,
                  Each subject took temazepam (a benzodiazepine) on one of the
                  two nights, Both estimators detected the effects of age,
                  temazepam, and time of night on sleep. Females were found to
                  have twice the SWP of males, but no gender effect on SW was
                  found. This confirms earlier reports that gender affects SWP
                  but not sleep depth. Subjectively assessed differences in
                  sleep quality between the nights were correlated to
                  differences in SW, not in SWP.These results demonstrate that
                  slow-wave microcontinuity, being based on a physiological
                  model of sleep, reflects sleep depth more closely than SWP
                  does.},
	doi = {10.1109/10.867928},
	author = {Kemp, B and Zwinderman, AH and Tuk, B and Kamphuisen, HAC and Oberye, JJL}
}


% -- Variational inference

@article{blei2017a,
	title = {Variational Inference: A Review for Statisticians},
	language = {eng},
	publisher = {AMER STATISTICAL ASSOC},
	journal = {Journal of the American Statistical Association},
	volume = {112},
	number = {518},
	pages = {859-877},
	year = {2017},
	issn = {1537274x, 01621459},
	abstract = {One of the core problems of modern statistics is to approximate
                  difficult-to-compute probability densities. This problem is
                  especially important in Bayesian statistics, which frames all
                  inference about unknown quantities as a calculation involving
                  the posterior density. In this article, we review variational
                  inference (VI), a method from machine learning that
                  approximates probability densities through optimization. VI
                  has been used in many applications and tends to be faster than
                  classical methods, such as Markov chain Monte Carlo sampling.
                  The idea behind VI is to first posit a family of densities and
                  then to find a member of that family which is close to the
                  target density. Closeness is measured by KullbackLeibler
                  divergence. We review the ideas behind mean-field variational
                  inference, discuss the special case of VI applied to
                  exponential family models, present a full example with a
                  Bayesian mixture of Gaussians, and derive a variant that uses
                  stochastic optimization to scale up to massive data. We
                  discuss modern research in VI and highlight important open
                  problems. VI is powerful, but it is not yet well understood.
                  Our hope in writing this article is to catalyze statistical
                  research on this class of algorithms. Supplementary materials
                  for this article are available online.},
	doi = {10.1080/01621459.2017.1285773},
	author = {Blei, David M. and Kucukelbir, Alp and McAuliffe, Jon D.}
}

@article{saul1996a,
  title = {Mean field theory for sigmoid belief networks},
  language = {eng},
  publisher = {AI ACCESS FOUNDATION},
  journal = {Journal of Artificial Intelligence Research},
  volume = {4},
  pages = {61-76},
  year = {1996},
  issn = {19435037, 10769757},
  abstract = {We develop a mean field theory for sigmoid belief networks based
                  on ideas from statistical mechanics. Our mean field theory
                  provides a tractable approximation to the true probability
                  distribution in these networks; it also yields a lower bound
                  on the likelihood of evidence. We demonstrate the utility of
                  this framework on a benchmark problem in statistical pattern
                  recognition-the classification of handwritten digits.},
  author = {Saul, LK and Jaakkola, T and Jordan, MI}
}

@article{jaakkola1996a,
  title = {Computing upper and lower bounds on likelihoods in intractable networks},
  language = {eng},
  publisher = {MORGAN KAUFMANN PUB INC},
  editor = {Horvitz, E., Jensen, F.},
  journal = {Uncertainty in Artificial Intelligence},
  pages = {340-348},
  year = {1996},
  isbn = {155860412x},
  abstract = {We present deterministic techniques for computing upper and lower
                  bounds on marginal probabilities in sigmoid and noisy-OR
                  networks. These techniques become useful when the size of the
                  network (or clique size) precludes exact computations. We
                  illustrate the tightness of the bounds by numerical
                  experiments.},
  author = {Jaakkola, TS and Jordan, MI}
}

@article{jordan1999a,
  title = {An introduction to variational methods for graphical models},
  language = {eng},
  publisher = {SPRINGER},
  journal = {Machine Learning},
  volume = {37},
  number = {2},
  pages = {183-233},
  year = {1999},
  issn = {15730565, 08856125},
  abstract = {This paper presents a tutorial introduction to the use of
                  variational methods for inference and learning in graphical
                  models (Bayesian networks and Markov random fields). We
                  present a number of examples of graphical models, including
                  the QMR-DT database, the sigmoid belief network, the Boltzmann
                  machine, and several variants of hidden Markov models, in
                  which it is infeasible to run exact inference algorithms. We
                  then introduce variational methods, which exploit laws of
                  large numbers to transform the original graphical model into a
                  simplified graphical model in which inference is efficient.
                  Inference in the simpified model provides bounds on
                  probabilities of interest in the original model. We describe a
                  general framework for generating variational transformations
                  based on convex duality. Finally we return to the examples and
                  demonstrate how variational algorithms can be formulated in
                  each case.},
  doi = {10.1023/A:1007665907178},
  author = {Jordan, MI and Ghahramani, Z and Jaakkola, TS and Saul, LK}
}

@article{s2016a,
  title = {Ladder variational autoencoders},
  language = {eng},
  publisher = {Curran Associates, Inc.},
  editor = {Lee, D. D., Sugiyama, M., Luxburg, U. V., Guyon, I., Garnett, R.},
  journal = {Advances in Neural Information Processing Systems},
  pages = {3745-3753},
  year = {2016},
  issn = {10495258},
  abstract = {Variational autoencoders are powerful models for unsupervised
                  learning. However deep models with several layers of dependent
                  stochastic variables are difficult to train which limits the
                  improvements obtained using these highly expressive models. We
                  propose a new inference model, the Ladder Variational
                  Autoencoder, that recursively corrects the generative
                  distribution by a data dependent approximate likelihood in a
                  process resembling the recently proposed Ladder Network. We
                  show that this model provides state of the art predictive
                  log-likelihood and tighter log-likelihood lower bound compared
                  to the purely bottom-up inference in layered Variational
                  Autoencoders and other generative models. We provide a
                  detailed analysis of the learned hierarchical latent
                  representation and show that our new inference model is
                  qualitatively different and utilizes a deeper more distributed
                  hierarchy of latent variables. Finally, we observe that
                  batch-normalization and deterministic warm-up (gradually
                  turning on the KL-term) are crucial for training variational
                  models with many stochastic layers.},
  author = {Sønderby, Casper Kaae and Raiko, Tapani and Maaløe, Lars and Sønderby, Søren Kaae and Winther, Ole}
}

@article{blundell2015a,
  title = {Weight uncertainty in neural networks},
  language = {eng},
  publisher = {International Machine Learning Society (IMLS)},
  journal = {32nd International Conference on Machine Learning, Icml 2015},
  volume = {2},
  pages = {1613-1622},
  year = {2015},
  isbn = {9781510810587},
  abstract = {We introduce a new, efficient, principled and
                  backpropagation-compatible algorithm for learning a
                  probability distribution on the weights of a neural network,
                  called Bayes by Backprop. It regularises the weights by
                  minimising a compression cost, known as the variational free
                  energy or the expected lower bound on the marginal likelihood.
                  We show that this principled kind of regularisation yields
                  comparable performance to dropout on MNIST classification. We
                  then demonstrate how the learnt uncertainty in the weights can
                  be used to improve generalisation in non-linear regression
                  problems, and how this weight uncertainty can be used to drive
                  the exploration-exploitation trade-off in reinforcement
                  learning.},
  author = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan}
}

% -- Model selection

@article{akaike1974a,
  title = {A new look at the statistical model identification},
  language = {eng},
  publisher = {IEEE},
  journal = {Ieee Transactions on Automatic Control},
  volume = {AC-19},
  number = {6},
  pages = {716-23, 716-723},
  year = {1974},
  issn = {15582523, 00189286},
  abstract = {The history of the development of statistical hypothesis testing
                  in time series analysis is reviewed briefly and it is pointed
                  out that the hypothesis testing procedure is not adequately
                  defined as the procedure for statistical model identification.
                  The classical maximum likelihood estimation procedure is
                  reviewed and a new estimate minimum information theoretical
                  criterion (AIC) estimate (MAICE) which is designed for the
                  purpose of statistical identification is introduced. When
                  there are several competing models the MAICE is defined by the
                  model and the maximum likelihood estimates of the parameters
                  which give the minimum of AIC defined by AIC=(−2)log (maximum
                  likelihood)+2(number of independently adjusted parameters
                  within the model). The practical utility of MAICE in time
                  series analysis is demonstrated with some numerical examples.},
  doi = {10.1109/TAC.1974.1100705},
  author = {Akaike, H.}
}

@article{schwarz1978a,
  title = {Estimating the Dimension of a Model},
  language = {eng},
  publisher = {Institute of Mathematical Statistics},
  journal = {Annals of Statistics},
  volume = {6},
  number = {2},
  pages = {461-464},
  year = {1978},
  issn = {21688966, 00905364},
  abstract = {The problem of selecting one of a number of models of different
                  dimensions is treated by finding its Bayes solution, and
                  evaluating the leading terms of its asymptotic expansion.
                  These terms are a valid large-sample criterion beyond the
                  Bayesian context, since they do not depend on the a priori
                  distribution.},
  doi = {10.1214/aos/1176344136},
  author = {Schwarz, Gideon}
}

% -- KL-divergence

@article{kullback1951a,
  title = {ON INFORMATION AND SUFFICIENCY},
  language = {eng},
  publisher = {INST MATHEMATICAL STATISTICS},
  journal = {Annals of Mathematical Statistics},
  volume = {22},
  number = {1},
  pages = {79-86},
  year = {1951},
  issn = {21688990, 00034851},
  doi = {10.1214/aoms/1177729694},
  author = {KULLBACK, S and LEIBLER, RA}
}

% -- IBP and inference methods

@article{knowles2007a,
  title = {Infinite sparse factor analysis and infinite independent components analysis},
  language = {eng},
  publisher = {Springer-Verlag},
  editor = {Davies, M. E., James, Christopher, Davies, Mike, Abdallah, Samer, Plumbley, Mark},
  journal = {Independent Component Analysis and Signal Separation. Proceedings 7th International Conference, Ica 2007. (lecture Notes in Computer Science Vol. 4666)},
  pages = {381-8, 381-388},
  year = {2007},
  isbn = {3540744932},
  abstract = {A nonparametric Bayesian extension of independent components
                  analysis (ICA) is proposed where observed data Y is modelled
                  as a linear superposition, G, of a potentially infinite number
                  of hidden sources, X. Whether a given source is active for a
                  specific data point is specified by an infinite binary matrix,
                  Z. The resulting sparse representation allows increased data
                  reduction compared to standard ICA. We define a prior on Z
                  using the Indian buffet process (IBP). We describe four
                  variants of the model, with Gaussian or Laplacian priors on X
                  and the one or two-parameter IBPs. We demonstrate Bayesian
                  inference under these models using a Markov chain Monte Carlo
                  (MCMC) algorithm on synthetic and gene expression data and
                  compare to standard ICA algorithms.},
  author = {Knowles, David and Ghahramani, Zoubin}
}

@article{paisley2009a,
  title = {Nonparametric factor analysis with beta process priors},
  language = {eng},
  publisher = {Association for Computing Machinery},
  journal = {Proceedings of the 26th International Conference on Machine Learning, Icml 2009},
  volume = {382},
  pages = {777-784},
  year = {2009},
  isbn = {9781605585161},
  abstract = {We propose a nonparametric extension to the factor analysis
                  problem using a beta process prior. This beta process factor
                  analysis (BP-FA) model allows for a dataset to be decomposed
                  into a linear combination of a sparse set of factors,
                  providing information on the underlying structure of the
                  observations. As with the Dirichlet process, the beta process
                  is a fully Bayesian conjugate prior, which allows for
                  analytical posterior calculation and straightforward
                  inference. We derive a variational Bayes inference algorithm
                  and demonstrate the model on the MNIST digits and HGDP-CEPH
                  cell line panel datasets.},
  doi = {10.1145/1553374.1553474},
  author = {Paisley, John and Carin, Lawrence}
}


% -- IBP

@article{griffiths2005a,
  title = {Infinite latent feature models and the Indian buffet process},
  language = {eng},
  publisher = {Neural information processing system foundation},
  journal = {Advances in Neural Information Processing Systems},
  pages = {475-482},
  year = {2005},
  issn = {10495258},
  isbn = {9780262232531},
  abstract = {We define a probability distribution over equivalence classes of
                  binary matrices with a finite number of rows and an unbounded
                  number of columns. This distribution is suitable for use as a
                  prior in probabilistic models that represent objects using a
                  potentially infinite array of features. We identify a simple
                  generative process that results in the same distribution over
                  equivalence classes, which we call the Indian buffet process.
                  We illustrate the use of this distribution as a prior in an
                  infinite latent feature model, deriving a Markov chain Monte
                  Carlo algorithm for inference in this model and applying the
                  algorithm to an image dataset.},
  author = {Griffiths, Thomas L. and Ghahramani, Zoubin}
}

@article{griffiths2005alonger,
  title = {Infinite latent feature models and the Indian buffet process},
  publisher = {Gatsby Computational Neuroscience Unit},
  journal = {Technical Report 2005-00},
  year = {2005},
  author = {Griffiths, Thomas L. and Ghahramani, Zoubin}
}

@article{griffiths2011a,
  title = {The Indian buffet process: An introduction and review},
  language = {und},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {12},
  pages = {1185-1224},
  year = {2011},
  issn = {15337928, 15324435},
  abstract = {The Indian buffet process is a stochastic process defining a
                  probability distribution over equivalence classes of sparse
                  binary matrices with a finite number of rows and an unbounded
                  number of columns. This distribution is suitable for use as a
                  prior in probabilistic models that represent objects using a
                  potentially infinite array of features, or that involve
                  bipartite graphs in which the size of at least one class of
                  nodes is unknown. We give a detailed derivation of this
                  distribution, and illustrate its use as a prior in an infinite
                  latent feature model. We then review recent applications of
                  the Indian buffet process in machine learning, discuss its
                  extensions, and summarize its connections to other stochastic
                  processes. Â© 2011 Thomas L. Griffiths and Zoubin Ghahramani.},
  author = {Griffiths, Thomas L. and Ghahramani, Zoubin}
}

@article{ghahramani2007bayesian,
  title={Bayesian nonparametric latent feature models},
  author={Ghahramani, Zoubin and Griffiths, Thomas L and Sollich, Peter},
  year={2007},
  publisher={Oxford University Press}
}

% -- Dirichlet Process

@article{antoniak1974mixtures,
  title={Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems},
  author={Antoniak, Charles E},
  journal={The annals of statistics},
  pages={1152--1174},
  year={1974},
  publisher={JSTOR}
}

@article{ferguson1973a,
    title = {A Bayesian Analysis of Some Nonparametric Problems},
    language = {eng},
    publisher = {The Institute of Mathematical Statistics},
    journal = {Annals of Statistics},
    volume = {1},
    number = {2},
    pages = {209-230},
    year = {1973},
    issn = {21688966, 00905364},
    doi = {10.1214/aos/1176342360},
    author = {Ferguson, Thomas S.}
}

% -- Beta Process

@article{thibaux2007a,
  title = {Hierarchical beta processes and the Indian buffet process},
  language = {eng},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {2},
  pages = {564-571},
  year = {2007},
  issn = {15337928, 15324435},
  abstract = {We show that the beta process is the de Finetti mixing
                  distribution buffet process of [2]. This result shows that the
                  beta process plays the role for the Indian buffet process that
                  the Dirichlet process plays for the Chinese restaurant
                  process, a parallel that guides us in deriving analogs for the
                  beta process of the many known extensions of the Dirichlet
                  process. In particular we define Bayesian hierarchies of beta
                  processes and use the connection to the beta process to
                  develop posterior inference algorithms for the Indian buffet
                  process. We also present an application to document
                  classification, exploring a relationship between the
                  hierarchical beta process and smoothed naive Bayes models.},
  author = {Thibaux, Romain and Jordan, Michael I.}
}
@article{hjort1990a,
  title = {NONPARAMETRIC BAYES ESTIMATORS BASED ON BETA PROCESSES IN MODELS FOR LIFE-HISTORY DATA},
  language = {eng},
  publisher = {INST MATHEMATICAL STATISTICS},
  journal = {Annals of Statistics},
  volume = {18},
  number = {3},
  pages = {1259-1294},
  year = {1990},
  issn = {21688966, 00905364},
  abstract = {Several authors have constructed nonparametric Bayes estimators
                  for a cumulative distribution function based on (possibly
                  right-censored) data. The prior distributions have, for
                  example, been Dirichlet processes or, more generally,
                  processes neutral to the right. The present article studies
                  the related problem of finding Bayes estimators for cumulative
                  hazard rates and related quantities, w.r.t. prior
                  distributions that correspond to cumulative hazard rate
                  processes with nonnegative independent increments. A
                  particular class of prior processes, termed beta processes, is
                  introduced and is shown to constitute a conjugate class. To
                  arrive at these, a nonparametric time-discrete framework for
                  survival data, which has some independent interest, is studied
                  first. An important bonus of the approach based on cumulative
                  hazards is that more complicated models for life history data
                  than the simple life table situation can be treated, for
                  example, time-inhomogeneous Markov chains. We find posterior
                  distributions and derive Bayes estimators in such models and
                  also present a semiparametric Bayesian analysis of the Cox
                  regression model. The Bayes estimators are easy to interpret
                  and easy to compute. In the limiting case of a vague prior the
                  Bayes solution for a cumulative hazard is the Nelson-Aalen
                  estimator and the Bayes solution for a survival probability is
                  the Kaplan-Meier estimator.},
  doi = {10.1214/aos/1176347749},
  author = {HJORT, NL}
}

% -- IBP and BP applications

@article{miller2009a,
  title = {Nonparametric latent feature models for link prediction},
  language = {eng},
  journal = {Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference},
  pages = {1276-1284},
  year = {2009},
  isbn = {9781615679119},
  abstract = {As the availability and importance of relational data-such as the
                  friendships summarized on a social networking
                  website-increases, it becomes increasingly important to have
                  good models for such data. The kinds of latent structure that
                  have been considered for use in predicting links in such
                  networks have been relatively limited. In particular, the
                  machine learning community has focused on latent class models,
                  adapting Bayesian nonparametric methods to jointly infer how
                  many latent classes there are while learning which entities
                  belong to each class. We pursue a similar approach with a
                  richer kind of latent variable-latent features-using a
                  Bayesian nonparametric approach to simultaneously infer the
                  number of features at the same time we learn which entities
                  have each feature. Our model combines these inferred features
                  with known covariates in order to perform link prediction. We
                  demonstrate that the greater expressiveness of this approach
                  allows us to improve performance on three datasets.},
  author = {Miller, Kurt T. and Griffiths, Thomas L. and Jordan, Michael I.}
}

@article{valera2017general,
  title={General Latent Feature Modeling for Data Exploration Tasks},
  author={Valera, Isabel and Pradier, Melanie F and Ghahramani, Zoubin},
  journal={arXiv preprint arXiv:1707.08352},
  year={2017}
}

@article{vellanki2017a,
  title = {Nonparametric discovery and analysis of learning patterns and autism subgroups from therapeutic data},
  language = {eng},
  publisher = {SPRINGER LONDON LTD},
  journal = {Knowledge and Information Systems},
  volume = {51},
  number = {1},
  pages = {127-157},
  year = {2017},
  issn = {02193116, 02191377},
  abstract = {The spectrum nature and heterogeneity within autism spectrum
                  disorders (ASD) pose as a challenge for treatment.
                  Personalisation of syllabus for children with ASD can improve
                  the efficacy of learning by adjusting the number of
                  opportunities and deciding the course of syllabus. We research
                  the data-motivated approach in an attempt to disentangle this
                  heterogeneity for personalisation of syllabus. With the help
                  of technology and a structured syllabus, collecting data while
                  a child with ASD masters the skills is made possible. The
                  performance data collected are, however, growing and contain
                  missing elements based on the pace and the course each child
                  takes while navigating through the syllabus. Bayesian
                  nonparametric methods are known for automatically discovering
                  the number of latent components and their parameters when the
                  model involves higher complexity. We propose a nonparametric
                  Bayesian matrix factorisation model that discovers learning
                  patterns and the way participants associate with them. Our
                  model is built upon the linear Poisson gamma model (LPGM) with
                  an Indian buffet process prior and extended to incorporate
                  data with missing elements. In this paper, for the first time
                  we have presented learning patterns deduced automatically from
                  data mining and machine learning methods using intervention
                  data recorded for over 500 children with ASD. We compare the
                  results with non-negative matrix factorisation and K-means,
                  which being parametric, not only require us to specify the
                  number of learning patterns in advance, but also do not have a
                  principle approach to deal with missing data. The F1 score
                  observed over varying degree of similarity measure (Jaccard
                  Index) suggests that LPGM yields the best outcome. By
                  observing these patterns with additional knowledge regarding
                  the syllabus it may be possible to observe the progress and
                  dynamically modify the syllabus for improved learning.},
  doi = {10.1007/s10115-016-0971-7},
  author = {Vellanki, Pratibha and Duong, T and Gupta, Sunil and Venkatesh, Svetha and Phung, D}
}

% -- IBP Sampling

@article{doshi-velez2009a,
  title = {Accelerated sampling for the Indian buffet process},
  language = {eng},
  publisher = {Association for Computing Machinery},
  journal = {Proceedings of the 26th International Conference on Machine Learning, Icml 2009},
  volume = {382},
  pages = {273-280},
  year = {2009},
  isbn = {9781605585161},
  abstract = {We often seek to identify co-occurring hidden features in a set of
                  observations. The Indian Buffet Process (IBP) provides a
                  non-parametric prior on the features present in each
                  observation, but current inference techniques for the IBP
                  often scale poorly. The collapsed Gibbs sampler for the IBP
                  has a running time cubic in the number of observations, and
                  the uncollapsed Gibbs sampler, while linear, is often slow to
                  mix. We present a new linear-time collapsed Gibbs sampler for
                  conjugate likelihood models and demonstrate its efficacy on
                  large real-world datasets.},
  doi = {10.1145/1553374.1553409},
  author = {Doshi-Velez, Finale and Ghahramani, Zoubin}
}

@article{teh2007a,
  title = {Stick-breaking construction for the Indian buffet process},
  language = {eng},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {2},
  pages = {556-563},
  year = {2007},
  issn = {15337928, 15324435},
  abstract = {The Indian buffet process (IBP) is a Bayesian nonparametric
                  distribution whereby objects are modelled using an unbounded
                  number of latent features. In this paper we derive a
                  stick-breaking representation for the IBP. Based on this new
                  representation, we develop slice samplers for the IBP that are
                  efficient, easy to implement and are more generally applicable
                  than the currently available Gibbs sampler. This
                  representation, along with the work of Thibaux and Jordan
                  [17], also illuminates interesting theoretical connections
                  between the IBP, Chinese restaurant processes, Beta processes
                  and Dirichlet processes.},
  author = {Teh, Yee Whye and G{\"o}r{\"u}r, Dilan and Ghahramani, Zoubin}
}

@article{doshi-velez2009b,
  title = {Variational inference for the Indian buffet process},
  language = {eng},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {5},
  pages = {137-144},
  year = {2009},
  issn = {15337928, 15324435},
  abstract = {The Indian Buffet Process (IBP) is a nonparametric prior for
                  latent feature models in which observations are influenced by
                  a combination of hidden features. For example, images may be
                  composed of several objects and sounds may consist of several
                  notes. Latent feature models seek to infer these unobserved
                  features from a set of observations; the IBP provides a
                  principled prior in situations where the number of hidden
                  features is unknown. Current inference methods for the IBP
                  have all relied on sampling. While these methods are
                  guaranteed to be accurate in the limit, samplers for the IBP
                  tend to mix slowly in practice. We develop a deterministic
                  variational method for inference in the IBP based on a
                  truncated stick-breaking approximation, provide theoretical
                  bounds on the truncation error, and evaluate our method in
                  several data regimes. Â© 2009 by the authors.},
  author = {Doshi-Velez, Finale and Miller, Kurt T. and Gael, Jurgen Van and The, Yee Whye}
}


@article{meeds2007a,
  title = {Modeling dyadic data with binary latent factors},
  language = {eng},
  journal = {Advances in Neural Information Processing Systems},
  pages = {977-984},
  year = {2007},
  issn = {10495258},
  isbn = {9780262195683},
  abstract = {We introduce binary matrix factorization, a novel model for
                  unsupervised matrix decomposition. The decomposition is
                  learned by fitting a non-parametric Bayesian probabilistic
                  model with binary latent variables to a matrix of dyadic data.
                  Unlike bi-clustering models, which assign each row or column
                  to a single cluster based on a categorical hidden feature, our
                  binary feature model reflects the prior belief that items and
                  attributes can be associated with more than one latent cluster
                  at a time. We provide simple learning and inference rules for
                  this new model and show how to extend it to an infinite model
                  in which the number of features is not a priori fixed but is
                  allowed to grow with the size of the data.},
  author = {Meeds, Edward and Ghahramani, Zoubin and Neal, Radford and Roweis, Sam}
}

% -- BP sampling

@article{paisley2010a,
  title = {A stick-breaking construction of the beta process},
  language = {und},
  publisher = {Unavailable},
  journal = {Icml 2010 - Proceedings, 27th International Conference on Machine Learning},
  pages = {847-854},
  year = {2010},
  isbn = {9781605589077},
  abstract = {We present and derive a new stick-breaking construction of the
                  beta process. The construction is closely related to a special
                  case of the stick-breaking construction of the Dirich-let
                  process (Sethuraman, 1994) applied to the beta distribution.
                  We derive an inference procedure that relies on Monte Carlo
                  integration to reduce the number of parameters to be inferred,
                  and present results on synthetic data, the MNIST handwritten
                  digits data set and a time-evolving gene expression data set.
                  Copyright 2010 by the author(s)/owner(s).},
  author = {Paisley, John and Carin, Lawrence and Zaas, Aimee and Woods, Christopher W. and Ginsburg, Geoffrey S.}
}

% -- NMF & nonparametric models

@article{hoffman2010a,
  title = {Bayesian nonparametric matrix factorization for recorded music},
  language = {eng},
  publisher = {Unavailable},
  journal = {Icml 2010 - Proceedings, 27th International Conference on Machine Learning},
  pages = {439-446},
  year = {2010},
  isbn = {9781605589077},
  abstract = {Recent research in machine learning has focused on breaking audio
                  spectrograms into separate sources of sound using latent
                  variable decompositions. These methods require that the number
                  of sources be specified in advance, which is not always
                  possible. To address this problem, we develop Gamma Process
                  Nonnegative Matrix Factorization (GaP-NMF), a Bayesian
                  nonpara-metric approach to decomposing spectrograms. The
                  assumptions behind GaP-NMF are based on research in signal
                  processing regarding the expected distributions of spectrogram
                  data, and GaP-NMF automatically discovers the number of latent
                  sources. We derive a mean-field variational inference
                  algorithm and evaluate GaP-NMF on both synthetic data and
                  recorded music. Copyright 2010 by the author(s)/owner(s).},
  author = {Hoffman, Matthew D. and Blei, David M. and Cook, Perry R.}
}

@inproceedings{liang2013beta,
  title={Beta Process Sparse Nonnegative Matrix Factorization for Music.},
  author={Liang, Dawen and Hoffman, Matthew D and Ellis, Daniel PW},
  booktitle={ISMIR},
  pages={375--380},
  year={2013}
}

@article{ding2010a,
  title = {Nonparametric Bayesian matrix factorization by Power-EP},
  language = {eng},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {9},
  pages = {169-176},
  year = {2010},
  issn = {15337928, 15324435},
  abstract = {Many real-world applications can be modeled by matrix
                  factorization. By approximating an observed data matrix as the
                  product of two latent matrices, matrix factorization can
                  reveal hidden structures embedded in data. A common challenge
                  to use matrix factorization is determining the dimensionality
                  of the latent matrices from data. Indian Buffet Processes
                  (IBPs) enable us to apply the nonparametric Bayesian machinery
                  to address this challenge. However, it remains a difficult
                  task to learn nonparametric Bayesian matrix factorization
                  models. In this paper, we propose a novel variational Bayesian
                  method based on new equivalence classes of infinite matrices
                  for learning these models. Furthermore, inspired by the
                  success of nonnegative matrix factorization on many learning
                  problems, we impose nonnegativity constraints on the latent
                  matrices and mix variational inference with expectation
                  propagation. This mixed inference method is unified in a power
                  expectation propagation framework. Experimental results on
                  image decomposition demonstrate the superior computational
                  efficiency and the higher prediction accuracy of our methods
                  compared to alternative Monte Carlo and variational inference
                  methods for IBP models. We also apply the new methods to
                  collaborative filtering and role mining and show the improved
                  predictive performance over other matrix factorization
                  methods. Copyright 2010 by the authors.},
  author = {Ding, Nan and Qi, Yuan and Xiang, Rongjing and Molloy, Ian and Li, Ninghui}
}

@article{xuan2018a,
  title = {Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes},
  language = {eng},
  publisher = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
  journal = {Ieee Transactions on Neural Networks and Learning Systems},
  volume = {29},
  number = {5},
  pages = {1835-1849},
  year = {2018},
  issn = {21622388, 2162237x},
  abstract = {Sparse nonnegative matrix factorization (SNMF) aims to factorize a
                  data matrix into two optimized nonnegative sparse factor
                  matrices, which could benefit many tasks, such as
                  document-word co-clustering. However, the traditional SNMF
                  typically assumes the number of latent factors (i.e.,
                  dimensionality of the factor matrices) to be fixed. This
                  assumption makes it inflexible in practice. In this paper, we
                  propose a doubly sparse nonparametric NMF framework to
                  mitigate this issue by using dependent Indian buffet processes
                  (dIBP). We apply a correlation function for the generation of
                  two stick weights associated with each column pair of factor
                  matrices while still maintaining their respective marginal
                  distribution specified by IBP. As a consequence, the
                  generation of two factor matrices will be columnwise
                  correlated. Under this framework, two classes of correlation
                  function are proposed: 1) using bivariate Beta distribution
                  and 2) using Copula function. Compared with the single
                  IBP-based NMF, this paper jointly makes two factor matrices
                  nonparametric and sparse, which could be applied to broader
                  scenarios, such as co-clustering. This paper is seen to be
                  much more flexible than Gaussian process-based and hierarchial
                  Beta process-based dIBPs in terms of allowing the two
                  corresponding binary matrix columns to have greater variations
                  in their nonzero entries. Our experiments on synthetic data
                  show the merits of this paper compared with the
                  state-of-the-art models in respect of factorization
                  efficiency, sparsity, and flexibility. Experiments on
                  real-world data sets demonstrate the efficiency of this paper
                  in document-word co-clustering tasks.},
  doi = {10.1109/TNNLS.2017.2676817},
  author = {Xuan, Junyu and Lu, Jie and Zhang, Guangquan and Xu, Richard Yi Da and Luo, Xiangfeng}
}


% -- MCMC sampling

@article{hastings1970a,
  title = {Monte Carlo Sampling Methods Using Markov Chains and Their Applications},
  language = {und},
  journal = {Biometrika},
  volume = {57},
  number = {1},
  pages = {97},
  year = {1970},
  issn = {14643510, 00063444},
  doi = {10.2307/2334940},
  author = {Hastings, W. K.}
}

@article{geman1984a,
  title = {Stochastic relaxation, Gibbs distributions, and Bayesian restoration of images},
  language = {eng},
  publisher = {IEEE},
  journal = {Ieee Transactions on Pattern Analysis and Machine Intelligence},
  volume = {PAMI-6},
  number = {6},
  pages = {721-41, 721-741},
  year = {1984},
  issn = {19393539, 01628828},
  abstract = {An analogy is drawn between images and statistical mechanics
                  systems. The authors adopt a Bayesian approach to image
                  restoration and introduce a hierarchical stochastic model for
                  the original image, based on the Gibbs distribution, and a new
                  restoration algorithm, based on stochastic relaxation and
                  annealing, for computing the maximum a posteriori (MAP)
                  estimate of the original image, given the degraded image. This
                  algorithm is highly parallel and exploits and equivalence
                  between Gibbs distributions and Markov random fields. The
                  essence of the approach is a stochastic relaxation algorithm
                  that generates a sequence of images that converges in an
                  appropriate sense to the MAP estimate.},
  doi = {10.1109/TPAMI.1984.4767596},
  author = {Geman, S. and Geman, D.}
}

@book{gelman2013bayesian,
  title={Bayesian data analysis},
  author={Gelman, Andrew and Carlin, John B and Stern, Hal S and Dunson, David B and Vehtari, Aki and Rubin, Donald B},
  year={2013},
  publisher={CRC press},
  edition=3
}

% -- Truncated Normal
@book{johnson1970continuous,
  title={Continuous Univariate Distributions-1},
  author={Johnson, NL and Kotz, Samuel and Balakrishnan, N},
  year={1994},
  publisher={New York: Wiley-interscience},
  edition=2
}

@article{botev2017a,
  title = {The normal law under linear restrictions: simulation and estimation via minimax tilting},
  language = {eng},
  publisher = {WILEY-BLACKWELL},
  journal = {Journal of the Royal Statistical Society Series B-statistical Methodology},
  volume = {79},
  number = {1},
  pages = {125-148},
  year = {2017},
  issn = {14679868, 13697412},
  abstract = {Simulation from the truncated multivariate normal distribution in
                  high dimensions is a recurrent problem in statistical
                  computing and is typically only feasible by using approximate
                  Markov chain Monte Carlo sampling. We propose a minimax
                  tilting method for exact independently and identically
                  distributed data simulation from the truncated multivariate
                  normal distribution. The new methodology provides both a
                  method for simulation and an efficient estimator to hitherto
                  intractable Gaussian integrals. We prove that the estimator
                  has a rare vanishing relative error asymptotic property.
                  Numerical experiments suggest that the scheme proposed is
                  accurate in a wide range of set-ups for which competing
                  estimation schemes fail. We give an application to exact
                  independently and identically distributed data simulation from
                  the Bayesian posterior of the probit regression model.},
  doi = {10.1111/rssb.12162},
  author = {Botev, Z. I.}
}

% -- Simulators

@article{heinecke2014a,
  title = {Petascale High Order Dynamic Rupture Earthquake Simulations on Heterogeneous Supercomputers},
  language = {eng},
  publisher = {IEEE Computer Society},
  journal = {International Conference for High Performance Computing, Networking, Storage and Analysis, Sc},
  volume = {2015-},
  number = {January},
  pages = {7012188, 3-14},
  year = {2014},
  issn = {21674337, 21674329},
  isbn = {9781479955008, 9781479954995},
  abstract = {We present an end-to-end optimization of the innovative Arbitrary
                  high-order DERivative Discontinuous Galerkin (ADER-DG)
                  software SeisSol targeting IntelÂ® Xeon Phi coprocessor
                  platforms, achieving unprecedented earthquake model complexity
                  through coupled simulation of full frictional sliding and
                  seismic wave propagation. SeisSol exploits unstructured meshes
                  to flexibly adapt for complicated geometries in realistic
                  geological models. Seismic wave propagation is solved
                  simultaneously with earthquake faulting in a multiphysical
                  manner leading to a heterogeneous solver structure. Our
                  architecture aware optimizations deliver up to 50\% of peak
                  performance, and introduce an efficient compute-communication
                  overlapping scheme shadowing the multiphysics computations.
                  SeisSol delivers near-optimal weak scaling, reaching 8.6
                  DP-PFLOPS on 8,192 nodes of the Tianhe-2 supercomputer. Our
                  performance model projects reaching 18 - 20 DP-PFLOPS on the
                  full Tianhe-2 machine. Of special relevance to modern civil
                  engineering needs, our pioneering simulation of the 1992
                  Landers earthquake shows highly detailed rupture evolution and
                  ground motion at frequencies up to 10 Hz.},
  doi = {10.1109/SC.2014.6},
  author = {Heinecke, Alexander and Breuer, Alexander and Rettenberger, Sebastian and Bader, Michael and Gabriel, Alice Agnes and Pelties, Christian and Bode, Arndt and Barth, William and Liao, Xiang Ke and Vaidyanathan, Karthikeyan and Smelyanskiy, Mikhail and Dubey, Pradeep}
}

@article{endeve2012a,
  title = {Turbulent magnetic field amplification from spiral SASI modes: Implications for core-collapse supernovae and proto-neutron star magnetization},
  language = {eng},
  publisher = {Institute of Physics Publishing},
  journal = {Astrophysical Journal},
  volume = {751},
  number = {1},
  pages = {26},
  year = {2012},
  issn = {15384357, 0004637x, 15384365, 00670049},
  abstract = {We extend our investigation of magnetic field evolution in
                  three-dimensional flows driven by the stationary accretion
                  shock instability (SASI) with a suite of higher-resolution
                  idealized models of the post-bounce core-collapse supernova
                  environment. Our magnetohydrodynamic simulations vary in
                  initial magnetic field strength, rotation rate, and grid
                  resolution. Vigorous SASI-driven turbulence inside the shock
                  amplifies magnetic fields exponentially; but while the
                  amplified fields reduce the kinetic energy of small-scale
                  flows, they do not seem to affect the global shock dynamics.
                  The growth rate and final magnitude of the magnetic energy are
                  very sensitive to grid resolution, and both are underestimated
                  by the simulations. Nevertheless, our simulations suggest that
                  neutron star magnetic fields exceeding 1014G can result from
                  dynamics driven by the SASI, even for non-rotating
                  progenitors. Â© 2012. The American Astronomical Society. All
                  rights reserved..},
  doi = {10.1088/0004-637X/751/1/26},
  author = {Endeve, Eirik and Cardall, Christian Y. and Budiardja, Reuben D. and Beck, Samuel W. and Bejnood, Alborz and Toedte, Ross J. and Mezzacappa, Anthony and Blondin, John M.}
}

@article{raberto2001a,
  title = {Agent-based simulation of a financial market},
  language = {eng},
  publisher = {ELSEVIER SCIENCE BV},
  editor = {Bouchard, J.P., Marsili, M., Roehner, B.M.},
  journal = {Physica A: Statistical Mechanics and Its Applications},
  volume = {299},
  number = {1-2},
  pages = {319-327},
  year = {2001},
  issn = {18732119, 03784371},
  abstract = {This paper introduces an agent-based artificial financial market
                  in which heterogeneous agents trade one single asset through a
                  realistic trading mechanism for price formation. Agents are
                  initially endowed with a finite amount of cash and a given
                  finite portfolio of assets. There is no money-creation
                  process; the total available cash is conserved in time. In
                  each period, agents make random buy and sell decisions that
                  are constrained by available resources, subject to clustering,
                  and dependent on the volatility of previous periods. The model
                  proposed herein is able to reproduce the leptokurtic shape of
                  the probability density of log price returns and the
                  clustering of volatility. Implemented using extreme
                  programming and object-oriented technology, the simulator is a
                  flexible computational experimental facility that can find
                  applications in both academic and industrial research
                  projects. Â© 2001 Elsevier Science B.V. All rights reserved.},
  doi = {10.1016/S0378-4371(01)00312-0},
  author = {Raberto, Marco and Cincotti, Silvano and Focardi, Sergio M. and Marchesi, Michele}
}

@article{perdikaris2016a,
  title = {Multiscale modeling and simulation of brain blood flow},
  language = {eng},
  publisher = {American Institute of Physics Inc.},
  journal = {Physics of Fluids},
  volume = {28},
  number = {2},
  pages = {021304},
  year = {2016},
  issn = {10897666, 10706631},
  abstract = {The aim of this work is to present an overview of recent advances
                  in multi-scale modeling of brain blood flow. In particular, we
                  present some approaches that enable the in silico study of
                  multi-scale and multi-physics phenomena in the cerebral
                  vasculature. We discuss the formulation of continuum and
                  atomistic modeling approaches, present a consistent framework
                  for their concurrent coupling, and list some of the challenges
                  that one needs to overcome in achieving a seamless and
                  scalable integration of heterogeneous numerical solvers. The
                  effectiveness of the proposed framework is demonstrated in a
                  realistic case involving modeling the thrombus formation
                  process taking place on the wall of a patient-specific
                  cerebral aneurysm. This highlights the ability of multi-scale
                  algorithms to resolve important biophysical processes that
                  span several spatial and temporal scales, potentially yielding
                  new insight into the key aspects of brain blood flow in health
                  and disease. Finally, we discuss open questions in multi-scale
                  modeling and emerging topics of future research.},
  doi = {10.1063/1.4941315},
  author = {Perdikaris, Paris and Grinberg, Leopold and Karniadakis, George Em}
}

@article{veldman2007a,
  title = {The numerical simulation of liquid sloshing on board spacecraft},
  language = {eng},
  publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE},
  journal = {Journal of Computational Physics},
  volume = {224},
  number = {1},
  pages = {82-99},
  year = {2007},
  issn = {10902716, 00219991},
  abstract = {The subject of study is the influence of sloshing liquid on the
                  dynamics of spacecraft. A combined theoretical and
                  experimental approach has been followed. On the one hand, CFD
                  simulations have been carried out to predict the combined
                  liquid/solid body motion. Basically a volume-of-fluid (VOF)
                  approach is followed, however with improvements in the
                  treatment of the free liquid surface: these cover the surface
                  reconstruction and displacement and the calculation of surface
                  tension effects by means of a local height function. Also
                  attention has been paid to the stability of the numerical
                  coupling between solid-body dynamics and liquid dynamics. On
                  the other hand, in-orbit experiments have been carried out
                  with the Sloshsat FLEVO satellite. The paper describes a first
                  comparison between theoretical predictions and experimental
                  findings. Â© 2006 Elsevier Inc. All rights reserved.},
  doi = {10.1016/j.jcp.2006.12.020},
  author = {Veldman, A. E.P. and Gerrits, J. and Luppes, R. and Helder, J. A. and Vreeburg, J. P.B.}
}

% -- Surrogate Modeling for likelihood free inference

@article{lueckmann2018likelihood,
  title={Likelihood-free inference with emulator networks},
  author={Lueckmann, Jan-Matthis and Bassetto, Giacomo and Karaletsos, Theofanis and Macke, Jakob H},
  journal={arXiv preprint arXiv:1805.09294},
  year={2018}
}
% -- Surrogate Modeling

@article{wu2018,
title = "Surrogate modeling for liquid-gas interface determination under microgravity",
journal = "Acta Astronautica",
volume = "152",
pages = "71 - 77",
year = "2018",
issn = "0094-5765",
doi = "https://doi.org/10.1016/j.actaastro.2018.07.001",
url = "http://www.sciencedirect.com/science/article/pii/S0094576518307689",
author = "Zongyu Wu and Yiyong Huang and Xiaoqian Chen and Xiang Zhang and Wen Yao",
keywords = "Liquid-gas interface, Surrogate modeling, Capillary, Microgravity",
abstract = "In recent years the advent of on-orbital refueling technology and
                  the accompanying interest in liquid management in space have
                  rekindled attention to the study of the liquid-gas interface
                  determination. So far, a series of numerical methods, such as
                  the Shooting method, are used to calculate the mathematical
                  model of liquid-gas interface. However, these methods have
                  some drawbacks in common, such as poor convergence, dependence
                  on initial value and instability. As a result, long
                  calculation time and sudden calculation interruption are
                  inevitable. Although satisfactory results can be achieved, it
                  requires human intervention. As an important intermediary of
                  capillary flow and liquid management device design, liquid-gas
                  interface calculations need to be done thousands of times.
                  Therefore, the quickness and robustness of liquid-gas
                  interface calculations are needed. Surrogate modeling method
                  arising with the development of aerospace technology in recent
                  years provides a new way to solve this problem. Combining with
                  the characteristics of liquid-gas interface calculation, a
                  double-layer radial basis function surrogate model is proposed
                  to approximate the mathematical model of liquid-gas interface.
                  This surrogate model is approximately equivalent to the
                  mathematical model of liquid-gas interface but is much easier
                  to solve. Compared with the Shooting method, the efficiency of
                  the surrogate model is improved by 99.46%, and the success
                  rate is increased to 100% from 35%."
}

@article{glaz2010a,
  title = {Reduced-order nonlinear unsteady aerodynamic modeling using a
                  surrogate-based recurrence framework},
  language = {eng},
  publisher = {AMER INST AERONAUT ASTRONAUT},
  journal = {Aiaa Journal},
  volume = {48},
  number = {10},
  pages = {2418-2429},
  year = {2010},
  issn = {1533385x, 00011452},
  abstract = {A reduced-order nonlinear unsteady aerodynamic modeling approach
                  suitable for analyzing pitching/plunging airfoils subject to
                  fixed or time-varying freestream Mach numbers is described.
                  The reduced-order model uses kriging surrogates to account for
                  flow nonlinearities and recurrence solutions to account for
                  time-history effects associated with unsteadiness. The
                  resulting surrogate-based recurrence framework generates
                  time-domain predictions of unsteady lift, moment, and drag
                  that accurately approximate computational fluid dynamics
                  solutions, but at a fraction of the computational cost.
                  Results corresponding to transonic conditions demonstrate that
                  the surrogate-based recurrence framework can mimic
                  computational fluid dynamics predictions of unsteady
                  aerodynamic responses when flow nonlinearities are present.
                  For an unsteady aerodynamic modeling problem considered in
                  this study, an accurate reduced-order model was generated by
                  the surrogate-based recurrence framework approach with
                  significantly fewer computational fluid dynamics evaluations
                  compared to results reported in the literature for a similar
                  problem in which a proper-orthogonal-decomposition-based
                  approach was applied. Furthermore, the results show that the
                  surrogate-based approach can accurately model time-varying
                  freestream Mach number effects and is therefore applicable to
                  rotary-wing applications in addition to fixed-wing
                  applications.},
  doi = {10.2514/1.J050471},
  author = {Glaz, Bryan and Liu, Li and Friedmann, Peretz P.}
}

@article{yamazaki2013a,
  title = {Derivative-enhanced variable fidelity surrogate modeling for aerodynamic functions},
  language = {eng},
  publisher = {AMER INST AERONAUTICS  ASTRONAUTICS},
  journal = {Aiaa Journal},
  volume = {51},
  number = {1},
  pages = {126-137},
  year = {2013},
  issn = {1533385x, 00011452},
  abstract = {In this paper a derivative-enhanced variable-fidelity surrogate
                  model approach is developed based on a cokriging formulation.
                  In this approach the absolute values of a high-fidelity
                  function as well as the trends obtained by lowfidelity
                  function values are utilized to develop an accurate surrogate
                  model. Derivative information of arbitrary fidelity levels can
                  be also utilized to develop a more accurate surrogate model.
                  The efficiencies of the developed approaches are investigated
                  by analytic function-fitting, aerodynamic data modeling and
                  two-dimensional airfoildrag- minimization problems. In the
                  aerodynamic problems low-fidelity levels are defined by a
                  different physical model or coarser computational mesh. The
                  numerical examples show that the developed surrogate-model
                  approach is shown to be useful for efficient aerodynamic data
                  modeling and accurate uncertainty analysis with low
                  computational cost. An efficient aerodynamic shape
                  optimization is also realized with the variable fidelity
                  Kriging model. Faster reduction of an aerodynamic objective
                  function is achieved by utilizing the derivative-enhanced
                  variable-fidelitymodel approach in which low-fidelity
                  information as well as adjoint-derivative information are
                  simultaneously utilized to construct a surrogate model.
                  Copyright Â© 2012 by the American Institute of Aeronautics and
                  Astronautics, Inc. All rights reserved.},
  doi = {10.2514/1.J051633},
  author = {Yamazaki, Wataru and Mavriplis, Dimitri J.}
}

@article{biannic2016surrogate,
  title={Surrogate models for aircraft flight control: some off-line and embedded applications},
  author={Biannic, JM and Hardier, G and Roos, C and Seren, C and Verdier, L},
  journal={AerospaceLab Journal},
  number={12},
  pages={pages--1},
  year={2016}
}

@article{gilmer2017a,
  title = {Neural message passing for quantum chemistry},
  language = {eng},
  publisher = {International Machine Learning Society (IMLS)},
  journal = {34th International Conference on Machine Learning, Icml 2017},
  volume = {3},
  pages = {2053-2070},
  year = {2017},
  isbn = {9781510855144},
  abstract = {Supervised learning on molecules has incredible potential to be
                  useful in chemistry, drug discovery, and materials science.
                  Luckily, several promising and closely related neural network
                  models invariant to molecular symmetries have already been
                  described in the literature. These models learn a message
                  passing algorithm and aggregation procedure to compute a
                  function of their entire input graph. At this point, the next
                  step is to find a particularly effective variant of this
                  general approach and apply it to chemical prediction
                  benchmarks until we either solve them or reach the limits of
                  the approach. In this paper, we reformulate existing models
                  into a single common framework we call Message Passing Neural
                  Networks (MPNNs) and explore additional novel variations
                  within this framework. Using MPNNs we demonstrate state of the
                  art results on an important molecular property prediction
                  benchmark; these results are strong enough that we believe
                  future work should focus on datasets with larger molecules or
                  more accurate ground truth labels.},
  author = {Gilmer, Justin and Schoenholz, Samuel S. and Riley, Patrick F. and Vinyals, Oriol and Dahl, George E.}
}

% -- Surrogate modeling approaches

    % -- ANNs
@article{tompson2017a,
  title = {Accelerating eulerian fluid simulation with convolutional networks},
  language = {eng},
  publisher = {International Machine Learning Society (IMLS)},
  journal = {34th International Conference on Machine Learning, Icml 2017},
  volume = {7},
  pages = {5258-5267},
  year = {2017},
  isbn = {9781510855144},
  abstract = {Efficient simulation of the Navicr-Stokes equations for fluid flow
                  is a long standing problem in applied mathematics, for which
                  state-of-the-art methods require large compute resources. In
                  this work, we propose a data-driven approach that leverages
                  the approximation power of deep-learning with the precision of
                  standard solvers to obtain fast and highly realistic
                  simulations. Our method solves the incompressible Euler
                  equations using the standard operator splitting method, in
                  which a large sparse linear system with many free parameters
                  must be solved. We use a Convolutional Network with a highly
                  tailored architecture, trained using a novel unsupervised
                  learning framework to solve the linear system. We present
                  real-time 2D and 3D simulations that outperform recently
                  proposed data-driven methods; the obtained results are
                  realistic and show good generalization properties.},
  author = {Tompson, Jonathan and Schlachter, Kristofer and Sprechmann, Pablo and Perlin, Ken}
}

@article{alam2004comparison,
  title={A comparison of experimental designs in the development of a neural network simulation metamodel},
  author={Alam, Fasihul M and McNaught, Ken R and Ringrose, Trevor J},
  journal={Simulation Modelling Practice and Theory},
  volume={12},
  number={7-8},
  pages={559--578},
  year={2004},
  publisher={Elsevier}
}

@article{khu2003reduction,
  title={Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling},
  author={Khu, S-T and Werner, Micha GF},
  journal={Hydrology and Earth System Sciences Discussions},
  volume={7},
  number={5},
  pages={680--692},
  year={2003}
}

   % -- Polynomials

@article{fen2009assessing,
  title={Assessing a response surface-based optimization approach for soil vapor extraction system design},
  author={Fen, Chiu-Shia and Chan, Chencha and Cheng, Hsien-Chie},
  journal={Journal of Water Resources Planning and Management},
  volume={135},
  number={3},
  pages={198--207},
  year={2009},
  publisher={American Society of Civil Engineers}
}

@article{hussain2002metamodeling,
  title={Metamodeling: radial basis functions, versus polynomials},
  author={Hussain, Mohammed F and Barton, Russel R and Joshi, Sanjay B},
  journal={European Journal of Operational Research},
  volume={138},
  number={1},
  pages={142--154},
  year={2002},
  publisher={Elsevier}
}

   % -- SVMs

@article{willcox2005fourier,
  title={Fourier series for accurate, stable, reduced-order models in large-scale linear applications},
  author={Willcox, Karen and Megretski, Alexandre},
  journal={SIAM Journal on Scientific Computing},
  volume={26},
  number={3},
  pages={944--962},
  year={2005},
  publisher={SIAM}
}

   % -- RBFs
   
@article{regis2007stochastic,
  title={A stochastic radial basis function method for the global optimization of expensive functions},
  author={Regis, Rommel G and Shoemaker, Christine A},
  journal={INFORMS Journal on Computing},
  volume={19},
  number={4},
  pages={497--509},
  year={2007},
  publisher={INFORMS}
}

@article{mullur2006metamodeling,
  title={Metamodeling using extended radial basis functions: a comparative approach},
  author={Mullur, Anoop A and Messac, Achille},
  journal={Engineering with Computers},
  volume={21},
  number={3},
  pages={203},
  year={2006},
  publisher={Springer}
}

   % -- Reviews 

@article{razavi2012a,
  title = {Review of surrogate modeling in water resources},
  language = {eng},
  publisher = {AMER GEOPHYSICAL UNION},
  journal = {Water Resources Research},
  volume = {48},
  number = {7},
  pages = {W07401},
  year = {2012},
  issn = {19447973, 00431397},
  abstract = {Surrogate modeling, also called metamodeling, has evolved and been
                  extensively used over the past decades. A wide variety of
                  methods and tools have been introduced for surrogate modeling
                  aiming to develop and utilize computationally more efficient
                  surrogates of high-fidelity models mostly in optimization
                  frameworks. This paper reviews, analyzes, and categorizes
                  research efforts on surrogate modeling and applications with
                  an emphasis on the research accomplished in the water
                  resources field. The review analyzes 48 references on
                  surrogate modeling arising from water resources and also
                  screens out more than 100 references from the broader research
                  community. Two broad families of surrogates namely response
                  surface surrogates, which are statistical or empirical
                  data-driven models emulating the high-fidelity model
                  responses, and lower-fidelity physically based surrogates,
                  which are simplified models of the original system, are
                  detailed in this paper. Taxonomies on surrogate modeling
                  frameworks, practical details, advances, challenges, and
                  limitations are outlined. Important observations and some
                  guidance for surrogate modeling decisions are provided along
                  with a list of important future research directions that would
                  benefit the common sampling and search (optimization) analyses
                  found in water resources. Â© 2012. American Geophysical
                  Union.},
  doi = {10.1029/2011WR011527},
  author = {Razavi, Saman and Tolson, Bryan A. and Burn, Donald H.}
}

@article{hu2018a,
  title = {Efficient Global Surrogate Modeling Based on Multi-Layer Sampling},
  language = {eng},
  publisher = {SAE International},
  journal = {Sae Technical Papers},
  volume = {2018-},
  number = {4},
  year = {2018},
  issn = {19463987, 19463979, 01487191},
  abstract = {Global surrogate modeling aims to build a surrogate model with
                  high accuracy covering the entire design domain. A major
                  challenge to achieve this objective is how to reduce the
                  number of function evaluations of the original computer
                  simulation model. To date, the most widely used approach for
                  global surrogate modeling is the adaptive surrogate modeling
                  method. It starts with an initial surrogate model, which is
                  then refined adaptively using the mean square error or by
                  maximizing the minimum distance criteria. It is observed that
                  current methods may not be able to effectively construct a
                  global surrogate model when the underlying black box function
                  is locally highly nonlinear. A new surrogate modeling method
                  which can allocate more training points in regions with high
                  nonlinearity is needed to overcome this challenge. This paper
                  proposes an efficient global surrogate modeling method based
                  on a multi-layer sampling scheme. An initial surrogate model
                  is constructed first with a small group of training points.
                  After that, samples of input variables are generated in
                  multiple layers over the design domain. The generated samples
                  are space-filling over the design domain and across layers.
                  From the generated samples, new training points and candidate
                  training points are identified in different layers by directly
                  minimizing the prediction bias of the surrogate model. This
                  enables us to improve the accuracy of the surrogate model more
                  effectively than current available methods. Several
                  mathematical examples and a vibratory system are used to
                  demonstrate the effectiveness of the proposed global surrogate
                  modeling method. The results show that the proposed method
                  performs better than the most widely used variance
                  minimization method.},
  doi = {10.4271/2018-01-0616},
  author = {Hu, Zhen and Mourelatos, Zissimos}
}

% -- Kriging

@article{sacks1989design,
  title={Design and analysis of computer experiments},
  author={Sacks, Jerome and Welch, William J and Mitchell, Toby J and Wynn, Henry P},
  journal={Statistical science},
  pages={409--423},
  year={1989},
  publisher={JSTOR}
}

@article{simpson2001a,
  title = {Kriging models for global approximation in simulation-based multidisciplinary design optimization},
  language = {eng},
  journal = {Aiaa Journal},
  volume = {39},
  number = {12},
  pages = {2233-2241},
  year = {2001},
  issn = {1533385x, 00011452},
  abstract = {Response surface methods have been used for a variety of
                  applications in aerospace engineering, particularly in
                  multidisciplinary design optimization. We investigate the use
                  of kriging models as alternatives to traditional second-order
                  polynomial response surfaces for constructing global
                  approximations for use in a real aerospace engineering
                  application, namely, the design of an aerospike nozzle. Our
                  objective is to examine the difficulties in building and using
                  kriging models to create accurate global approximations to
                  facilitate multidisciplinary design optimization. Error
                  analysis of the response surface and kriging models is
                  performed, along with a graphical comparison of the
                  approximations. Four optimization problems are also formulated
                  and solved using both sets of approximation models to gain
                  insight into their use for multidisciplinary design
                  optimization. We find that the kriging models, which use only
                  a constant "global" model and a Gaussian correlation function,
                  yield global approximations that are slightly more accurate
                  than the response surface models. Â© 2001 Mary Ann Liebert,
                  Inc.},
  doi = {10.2514/2.1234},
  author = {Simpson, Timothy W. and Mauery, Timothy M. and Korte, John J. and Mistree, Farrokh}
}

% stochastic
@article{hamdia2017stochastic,
  title={Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions},
  author={Hamdia, Khader M and Silani, Mohammad and Zhuang, Xiaoying and He, Pengfei and Rabczuk, Timon},
  journal={International Journal of Fracture},
  volume={206},
  number={2},
  pages={215--227},
  year={2017},
  publisher={Springer}
}


% -- ABC

@article{beaumont2002a,
  title = {Approximate Bayesian computation in population genetics},
  language = {eng},
  publisher = {GENETICS},
  journal = {Genetics},
  volume = {162},
  number = {4},
  pages = {2025-2035},
  year = {2002},
  issn = {19432631, 00166731},
  abstract = {We propose a new method for approximate Bayesian statistical
                  inference on the basis of summary statistics. The method is
                  suited to complex problems that arise in population genetics,
                  extending ideas developed in this setting by earlier authors.
                  Properties of the posterior distribution of a parameter, such
                  as its mean or density curve, are approximated without
                  explicit likelihood calculations. This is achieved by fitting
                  a local-linear regression of simulated parameter values on
                  simulated summary statistics, and then substituting the
                  observed summary statistics into the regression equation. The
                  method combines many of the advantages of Bayesian statistical
                  inference with the computational efficiency of methods based
                  on summary statistics. A key advantage of the method is that
                  the nuisance parameters are automatically integrated out in
                  the simulation step, so that the large numbers of nuisance
                  parameters that arise in population genetics problems can be
                  handled without difficulty. Simulation results indicate
                  computational and statistical efficiency that compares
                  favorably with those of alternative methods previously
                  proposed in the literature. We also compare the relative
                  efficiency of inferences obtained using methods based on
                  summary statistics with those obtained directly from the data
                  using MCMC.},
  author = {Beaumont, Mark A. and Zhang, Wenyang and Balding, David J.}
}

@article{sisson2018a,
  title = {Overview of Approximate Bayesian Computation},
  language = {und},
  year = {2018},
  abstract = {  This Chapter, "Overview of Approximate Bayesian Computation", is to appear as
  the first chapter in the forthcoming Handbook of Approximate Bayesian
  Computation (2018). It details the main ideas and concepts behind ABC methods
  with many examples and illustrations.
  },
  author = {Sisson, S. A. and Fan, Y. and Beaumont, M. A.}
}

@article{blum2013a,
  title = {A comparative review of dimension reduction methods in approximate bayesian computation},
  language = {eng},
  publisher = {INST MATHEMATICAL STATISTICS},
  journal = {Statistical Science},
  volume = {28},
  number = {2},
  pages = {189-208},
  year = {2013},
  issn = {21688745, 08834237},
  abstract = {Approximate Bayesian computation (ABC) methods make use of
                  comparisons between simulated and observed summary statistics
                  to overcome the problem of computationally intractable
                  likelihood functions. As the practical implementation of ABC
                  requires computations based on vectors of summary statistics,
                  rather than full data sets, a central question is how to
                  derive low-dimensional summary statistics from the observed
                  data with minimal loss of information. In this article we
                  provide a comprehensive review and comparison of the
                  performance of the principal methods of dimension reduction
                  proposed in the ABC literature. The methods are split into
                  three nonmutually exclusive classes consisting of best subset
                  selection methods, projection techniques and regularization.
                  In addition, we introduce two new methods of dimension
                  reduction. The first is a best subset selection method based
                  on Akaike and Bayesian information criteria, and the second
                  uses ridge regression as a regularization procedure. We
                  illustrate the performance of these dimension reduction
                  techniques through the analysis of three challenging models
                  and data sets. Â© Institute of Mathematical Statistics, 2013.},
  doi = {10.1214/12-STS406},
  author = {Blum, M. G.B. and Nunes, M. A. and Prangle, D. and Sisson, S. A.}
}

@article{prangle2015a,
  title = {Summary Statistics in Approximate Bayesian Computation},
  language = {und},
  year = {2015},
  abstract = { This document is due to appear as a chapter of the forthcoming
                  Handbook of Approximate Bayesian Computation (ABC) edited by
                  S. Sisson, Y. Fan, and M. Beaumont. Since the earliest work on
                  ABC, it has been recognised that using summary statistics is
                  essential to produce useful inference results. This is because
                  ABC suffers from a curse of dimensionality effect, whereby
                  using high dimensional inputs causes large approximation
                  errors in the output. It is therefore crucial to find low
                  dimensional summaries which are informative about the
                  parameter inference or model choice task at hand. This chapter
                  reviews the methods which have been proposed to select such
                  summaries, extending the previous review paper of Blum et al.
                  (2013) with recent developments. Related theoretical results
                  on the ABC curse of dimensionality and sufficiency are also
                  discussed. },
  author = {Prangle, Dennis}
}

@inproceedings{park2016k2,
  title={K2-ABC: Approximate Bayesian Computation with Kernel Embeddings.},
  author={Park, Mijung and Jitkrittum, Wittawat and Sejdinovic, Dino},
  booktitle={AISTATS},
  pages={398--407},
  year={2016}
}


% -- ABC applications

@article{siegmund2008a,
  title = {Modeling DNA methylation in a population of cancer cells},
  language = {eng},
  publisher = {WALTER DE GRUYTER GMBH},
  journal = {Statistical Applications in Genetics and Molecular Biology},
  volume = {7},
  number = {1},
  pages = {18},
  year = {2008},
  issn = {21946302, 15446115},
  abstract = {Little is known about how human cancers grow because direct
                  observations are impractical. Cancers are clonal populations
                  and the billions of cancer cells present in a visible tumor
                  are progeny of a single transformed cell. Therefore, human
                  cancers can be represented by somatic cell ancestral trees
                  that start from a single transformed cell and end with
                  billions of present day cancer cells. We use a genealogical
                  approach to infer tumor growth from somatic trees, employing
                  haplotype DNA methylation pattern variation, or differences
                  between specific CpG sites or "tags," in the cancer genome.
                  DNA methylation is an epigenetic mark that is copied, with
                  error, during genome replication. At our tags, neutral copy
                  errors in DNA methylation appear to occur at random, and much
                  more frequently than sequence copy errors. To reconstruct a
                  cancer tree, we sample and compare human colorectal genomes
                  within small geographic regions (a cancer fragment), between
                  fragments on the same side of the tumor, and between fragments
                  from opposite tumor halves. The combined information on both
                  physical distance and epigenetic distance informs our model
                  for tumor ancestry. We use approximate Bayesian computation, a
                  simulation-based method, to model tumor growth under a variety
                  of evolutionary scenarios, estimating parameters that fit
                  observed DNA methylation patterns. We conclude that
                  methylation patterns sampled from human cancers are consistent
                  with replication errors and certain simple cancer growth
                  models. The inferred cancer trees are consistent with
                  Gompertzian growth, a well-known cancer growth pattern.
                  Copyright ©2008 The Berkeley Electronic Press. All rights
                  reserved.},
  doi = {10.2202/1544-6115.1374},
  author = {Siegmund, Kimberly D. and Marjoram, Paul and Shibata, Darryl}
}

@article{foll2008a,
  title = {An approximate bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure},
  language = {eng},
  publisher = {GENETICS},
  journal = {Genetics},
  volume = {179},
  number = {2},
  pages = {927-939},
  year = {2008},
  issn = {19432631, 00166731},
  abstract = {There is great interest in using amplified fragment length
                  polymorphism (AFLP) markers because they are inexpensive and
                  easy to produce. It is, therefore, possible to generate a
                  large number of markers that have a wide coverage of species
                  genomes. Several statistical methods have been proposed to
                  study the genetic structure using AFLPs but they assume
                  Hardy-Weinberg equilibrium and do not estimate the inbreeding
                  coefficient, FIS. A Bayesian method has been proposed by
                  Holsinger and colleagues that relaxes these simplifying
                  assumptions but we have identified two sources of bias that
                  can influence estimates based on these markers: (i) the use of
                  a uniform prior on ancestral allele frequencies and (ii) the
                  ascertainment bias of AFLP markers. We present a new Bayesian
                  method that avoids these biases by using an implementation
                  based on the approximate Bayesian computation (ABC) algorithm.
                  This new method estimates population-specific FIS and FST
                  values and offers users the possibility of taking into account
                  the criteria for selecting the markers that are used in the
                  analyses. The software is available at our web site
                  (http://www-leca.ujf-grenoble.fr/logiciels.htm). Finally, we
                  provide advice on how to avoid the effects of ascertainment
                  bias. Copyright Â© 2008 by the Genetics Society of America.},
  doi = {10.1534/genetics.107.084541},
  author = {Foll, Matthieu and Beaumont, Mark A. and Gaggiotti, Oscar}
}

@article{blum2010a,
  title = {HIV with contact tracing: a case study in approximate Bayesian computation},
  language = {eng},
  publisher = {Oxford University Press},
  journal = {Biostatistics},
  volume = {11},
  number = {4},
  pages = {644-660},
  year = {2010},
  issn = {14684357, 14654644},
  abstract = {Missing data is a recurrent issue in epidemiology where the
                  infection process may be partially observed. Approximate
                  Bayesian computation (ABC), an alternative to data imputation
                  methods such as Markov chain Monte Carlo (MCMC) integration,
                  is proposed for making inference in epidemiological models. It
                  is a likelihood-free method that relies exclusively on
                  numerical simulations. ABC consists in computing a distance
                  between simulated and observed summary statistics and
                  weighting the simulations according to this distance. We
                  propose an original extension of ABC to path-valued summary
                  statistics, corresponding to the cumulated number of
                  detections as a function of time. For a standard compartmental
                  model with Suceptible, Infectious and Recovered individuals
                  (SIR), we show that the posterior distributions obtained with
                  ABC and MCMC are similar. In a refined SIR model well suited
                  to the HIV contact–tracing data in Cuba, we perform a
                  comparison between ABC with full and binned detection times.
                  For the Cuban data, we evaluate the efficiency of the
                  detection system and predict the evolution of the HIV-AIDS
                  disease. In particular, the percentage of undetected
                  infectious individuals is found to be of the order of 40%.},
  author = {Blum, Michael G. B. and Tran, Viet Chi}
}

@article{tanaka2006a,
  title = {Using approximate bayesian computation to estimate tuberculosis transmission parameters from genotype data},
  language = {eng},
  publisher = {GENETICS},
  journal = {Genetics},
  volume = {173},
  number = {3},
  pages = {1511-1520},
  year = {2006},
  issn = {19432631, 00166731},
  abstract = {Tuberculosis can be studied at the population level by genotyping
                  strains of Mycobacterium tuberculosis isolated from patients.
                  We use an approximate Bayesian computational method in
                  combination with a stochastic model of tuberculosis
                  transmission and mutation of a molecular marker to estimate
                  the net transmission rate, the doubling time, and the
                  reproductive value of the pathogen. This method is applied to
                  a published data set from San Francisco of tuberculosis
                  genotypes based on the marker IS6110. The mutation rate of
                  this marker has previously been studied, and we use those
                  estimates to form a prior distribution of mutation rates in
                  the inference procedure. The posterior point estimates of the
                  key parameters of interest for these data are as follows: net
                  transmission rate, 0.69/year [95\% credibility interval (C.I.)
                  0.38, 1.08]; doubling time, 1.08 years (95\% C.I. 0.64, 1.82);
                  and reproductive value 3.4 (95\% C.I. 1.4, 79.7). These
                  figures suggest a rapidly spreading epidemic, consistent with
                  observations of the resurgence of tuberculosis in the United
                  States in the 1980s and 1990s. Copyright © 2006 by the
                  Genetics Society of America.},
  doi = {10.1534/genetics.106.055574},
  author = {Tanaka, Mark M. and Francis, Andrew R. and Luciani, Fabio and Sisson, S. A.}
}

% -- Ratio surrogates

@article{brehmer2018a,
  author =       {Brehmer, Johann and Louppe, Gilles and Pavez, Juan and
                  Cranmer, Kyle},
  title =        {Mining Gold From Implicit Models To Improve Likelihood-Free
                  Inference},
  journal =      {CoRR},
  year =         2018,
  url =          {http://arxiv.org/abs/1805.12244v3},
  abstract =     {Simulators often provide the best description of real-world
                  phenomena. However, they also lead to challenging inverse
                  problems because the density they implicitly define is often
                  intractable. We present a new suite of simulation-based
                  inference techniques that go beyond the traditional
                  Approximate Bayesian Computation approach, which struggles in
                  a high-dimensional setting, and extend methods that use
                  surrogate models based on neural networks. We show that
                  additional information, such as the joint likelihood ratio and
                  the joint score, can often be extracted from simulators and
                  used to augment the training data for these surrogate models.
                  Finally, we demonstrate that these new techniques are more
                  sample efficient and provide higher-fidelity inference than
                  traditional methods.},
  archivePrefix ={arXiv},
  eprint =       {1805.12244v3},
  primaryClass = {stat.ML},
}

@article{stoye2018a,
  title = {Likelihood-free inference with an improved cross-entropy estimator},
  language = {und},
  pages = {8},
  year = {2018},
  abstract = { We extend recent work (Brehmer, et. al., 2018) that use neural
                  networks as surrogate models for likelihood-free inference. As
                  in the previous work, we exploit the fact that the joint
                  likelihood ratio and joint score, conditioned on both observed
                  and latent variables, can often be extracted from an implicit
                  generative model or simulator to augment the training data for
                  these surrogate models. We show how this augmented training
                  data can be used to provide a new cross-entropy estimator,
                  which provides improved sample efficiency compared to previous
                  loss functions exploiting this augmented training data. },
  author = {Stoye, Markus and Brehmer, Johann and Louppe, Gilles and Pavez, Juan and Cranmer, Kyle}
}

% -- Neural Density Estimation

@article{rezende2015a,
  title = {Variational inference with normalizing flows},
  language = {eng},
  publisher = {International Machine Learning Society (IMLS)},
  journal = {32nd International Conference on Machine Learning, Icml 2015},
  volume = {2},
  pages = {1530-1538},
  year = {2015},
  isbn = {9781510810587},
  abstract = {The choice of approximate posterior distribution is one of the
                  core problems in variational inference. Most applications of
                  variational inference employ simple families of posterior
                  approximations in order to allow for efficient inference,
                  focusing on mean-field or other simple structured
                  approximations. This restriction has a significant impact on
                  the quality of inferences made using variational methods. We
                  introduce a new approach for specifying flexible, arbitrarily
                  complex and scalable approximate posterior distributions. Our
                  approximations are distributions constructed through a
                  normalizing flow, whereby a simple initial density is
                  transformed into a more complex one by applying a sequence of
                  invertible transformations until a desired level of complexity
                  is attained. We use this view of normalizing flows to develop
                  categories of finite and infinitesimal flows and provide a
                  unified view of approaches for constructing rich posterior
                  approximations. We demonstrate that the theoretical advantages
                  of having posteriors that better match the true posterior,
                  combined with the scalability of amortized variational
                  approaches, provides a clear improvement in performance and
                  applicability of variational inference.},
  author = {Rezende, Danilo Jimenez and Mohamed, Shakir}
}

@article{papamakarios2017a,
  title = {Masked autoregressive flow for density estimation},
  language = {eng},
  publisher = {Neural information processing systems foundation},
  journal = {Advances in Neural Information Processing Systems},
  volume = {2017-},
  pages = {2339-2348},
  year = {2017},
  issn = {10495258},
  abstract = {Autoregressive models are among the best performing neural density
                  estimators. We describe an approach for increasing the
                  flexibility of an autoregressive model, based on modelling the
                  random numbers that the model uses internally when generating
                  data. By constructing a stack of autoregressive models, each
                  modelling the random numbers of the next model in the stack,
                  we obtain a type of normalizing flow suitable for density
                  estimation, which we call Masked Autoregressive Flow. This
                  type of flow is closely related to Inverse Autoregressive Flow
                  and is a generalization of Real NVP. Masked Autoregressive
                  Flow achieves state-of-the-art performance in a range of
                  general-purpose density estimation tasks.},
  author = {Papamakarios, George and Pavlakou, Theo and Murray, Iain}
}

@article{papamakarios2018sequential,
  title={Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows},
  author={Papamakarios, George and Sterratt, David C and Murray, Iain},
  journal={arXiv preprint arXiv:1805.07226},
  year={2018}
}

@article{paige2016a,
  title = {Inference networks for sequential monte carlo in graphical models},
  language = {eng},
  publisher = {International Machine Learning Society (IMLS)},
  journal = {33rd International Conference on Machine Learning, Icml 2016},
  volume = {6},
  pages = {4434-4444},
  year = {2016},
  isbn = {9781510829008},
  abstract = {We introduce a new approach for amortizing inference in directed
                  graphical models by learning heuristic approximations to
                  stochastic inverses, designed specifically for use as proposal
                  distributions in sequential Monte Carlo methods. We describe a
                  procedure for constructing and learning a structured neural
                  network which represents an inverse factorization of the
                  graphical model, resulting in a conditional density estimator
                  that takes as input particular values of the observed random
                  variables, and returns an approximation to the distribution of
                  the latent variables. This recognition model can be learned
                  offline, independent from any particular dataset, prior to
                  performing inference. The output of these networks can be used
                  as automatically-learned high-quality proposal distributions
                  to accelerate sequential Monte Carlo across a diverse range of
                  problem settings.},
  author = {Paige, Brooks and Wood, Frank}
}

@article{uria2016a,
  title = {Neural autoregressive distribution estimation},
  language = {eng},
  publisher = {Microtome Publishing},
  journal = {Journal of Machine Learning Research},
  volume = {17},
  pages = {1-37},
  year = {2016},
  issn = {15337928, 15324435},
  abstract = {We present Neural Autoregressive Distribution Estimation (NADE)
                  models, which are neural network architectures applied to the
                  problem of unsupervised distribution and density estimation.
                  They leverage the probability product rule and a weight
                  sharing scheme inspired from restricted Boltzmann machines, to
                  yield an estimator that is both tractable and has good
                  generalization performance. We discuss how they achieve
                  competitive performance in modeling both binary and
                  real-valued observations. We also present how deep NADE models
                  can be trained to be agnostic to the ordering of input
                  dimensions used by the autoregressive product rule
                  decomposition. Finally, we also show how to exploit the
                  topological structure of pixels in images using a deep
                  convolutional architecture for NADE.},
  author = {Uria, Benigno and Cote, Marc Alexandre and Gregor, Karol and Murray, Iain and Larochelle, Hugo}
}

@article{papamakarios2016a,
  title = {Fast e-free inference of simulation models with Bayesian conditional density estimation},
  language = {eng},
  publisher = {Neural information processing systems foundation},
  journal = {Advances in Neural Information Processing Systems},
  pages = {1036-1044},
  year = {2016},
  issn = {10495258},
  abstract = {Many statistical models can be simulated forwards but have
                  intractable likelihoods. Approximate Bayesian Computation
                  (ABC) methods are used to infer properties of these models
                  from data. Traditionally these methods approximate the
                  posterior over parameters by conditioning on data being inside
                  an â-ball around the observed data, which is only
                  correct in the limit ââ0. Monte Carlo methods
                  can then draw samples from the approximate posterior to
                  approximate predictions or error bars on parameters. These
                  algorithms critically slow down as â â 0, and
                  in practice draw samples from a broader distribution than the
                  posterior. We propose a new approach to likelihood-free
                  inference based on Bayesian conditional density estimation.
                  Preliminary inferences based on limited simulation data are
                  used to guide later simulations. In some cases, learning an
                  accurate parametric representation of the entire true
                  posterior distribution requires fewer model simulations than
                  Monte Carlo ABC methods need to produce a single sample from
                  an approximate posterior.},
  author = {Papamakarios, George and Murray, Iain}
}

@article{cranmer2016a,
  title = {Approximating Likelihood Ratios with Calibrated Discriminative
    Classifiers},
  language = {und},
  pages = {35},
  year = {2016},
  abstract = { In many fields of science, generalized likelihood ratio tests are
                  established tools for statistical inference. At the same time,
                  it has become increasingly common that a simulator (or
                  generative model) is used to describe complex processes that
                  tie parameters $\theta$ of an underlying theory and
                  measurement apparatus to high-dimensional observations
                  $\mathbf{x}\in \mathbb{R}^p$. However, simulator often do not
                  provide a way to evaluate the likelihood function for a given
                  observation $\mathbf{x}$, which motivates a new class of
                  likelihood-free inference algorithms. In this paper, we show
                  that likelihood ratios are invariant under a specific class of
                  dimensionality reduction maps $\mathbb{R}^p \mapsto
                  \mathbb{R}$. As a direct consequence, we show that
                  discriminative classifiers can be used to approximate the
                  generalized likelihood ratio statistic when only a generative
                  model for the data is available. This leads to a new machine
                  learning-based approach to likelihood-free inference that is
                  complementary to Approximate Bayesian Computation, and which
                  does not require a prior on the model parameters. Experimental
                  results on artificial problems with known exact likelihoods
                  illustrate the potential of the proposed method. },
  author = {Cranmer, Kyle and Pavez, Juan and Louppe, Gilles}
}

@article{dinh2016density,
  title={Density estimation using real nvp},
  author={Dinh, Laurent and Sohl-Dickstein, Jascha and Bengio, Samy},
  journal={arXiv preprint arXiv:1605.08803},
  year={2016}
}

@article{dinh2015a,
  title = {NICE: Non-linear Independent Components Estimation},
  language = {und},
  pages = {11},
  year = {2015},
  abstract = { We propose a deep learning framework for modeling complex
                  high-dimensional densities called Non-linear Independent
                  Component Estimation (NICE). It is based on the idea that a
                  good representation is one in which the data has a
                  distribution that is easy to model. For this purpose, a
                  non-linear deterministic transformation of the data is learned
                  that maps it to a latent space so as to make the transformed
                  data conform to a factorized distribution, i.e., resulting in
                  independent latent variables. We parametrize this
                  transformation so that computing the Jacobian determinant and
                  inverse transform is trivial, yet we maintain the ability to
                  learn complex non-linear transformations, via a composition of
                  simple building blocks, each based on a deep neural network.
                  The training criterion is simply the exact log-likelihood,
                  which is tractable. Unbiased ancestral sampling is also easy.
                  We show that this approach yields good generative models on
                  four image datasets and can be used for inpainting. },
  author = {Dinh, Laurent and Krueger, David and Bengio, Yoshua}
}

@article{fan2013a,
  title = {Approximate Bayesian computation via regression density estimation},
  language = {eng},
  publisher = {Wiley-Blackwell Publishing Ltd},
  journal = {Stat},
  volume = {2},
  number = {1},
  pages = {34-48},
  year = {2013},
  issn = {20491573},
  abstract = {Approximate Bayesian computation (ABC) methods, which are
                  applicable when the likelihood is difficult or impossible to
                  calculate, are an active topic of current research. Most
                  current ABC algorithms directly approximate the posterior
                  distribution, but an alternative, less common strategy is to
                  approximate the likelihood function. This has several
                  advantages. First, in some problems, it is easier to
                  approximate the likelihood than to approximate the posterior.
                  Second, an approximation to the likelihood allows reference
                  analyses to be constructed based solely on the likelihood.
                  Third, it is straightforward to perform sensitivity analyses
                  for several different choices of prior once an approximation
                  to the likelihood is constructed, which needs to be done only
                  once. The contribution of the present paper is to consider
                  regression density estimation techniques to approximate the
                  likelihood in the ABC setting. Our likelihood approximations
                  build on recently developed marginal adaptation density
                  estimators by extending them for conditional density
                  estimation. Our approach facilitates reference Bayesian
                  inference, as well as frequentist inference. The method is
                  demonstrated via a challenging problem of inference for
                  stereological extremes, where we perform both frequentist and
                  Bayesian inference.},
  doi = {10.1002/sta4.15},
  author = {Fan, Yanan and Nott, David J. and Sisson, Scott A.}
}


% -- Reinforcement Learning

@article{levine18_reinf_learn_contr_as_probab_infer,
  author =       {Levine, Sergey},
  title =        {Reinforcement Learning and Control As Probabilistic Inference:
                  Tutorial and Review},
  journal =      {CoRR},
  year =         2018,
  url =          {http://arxiv.org/abs/1805.00909v3},
  abstract =     {The framework of reinforcement learning or optimal control
                  provides a mathematical formalization of intelligent decision
                  making that is powerful and broadly applicable. While the
                  general form of the reinforcement learning problem enables
                  effective reasoning about uncertainty, the connection between
                  reinforcement learning and inference in probabilistic models
                  is not immediately obvious. However, such a connection has
                  considerable value when it comes to algorithm design:
                  formalizing a problem as probabilistic inference in principle
                  allows us to bring to bear a wide array of approximate
                  inference tools, extend the model in flexible and powerful
                  ways, and reason about compositionality and partial
                  observability. In this article, we will discuss how a
                  generalization of the reinforcement learning or optimal
                  control problem, which is sometimes termed maximum entropy
                  reinforcement learning, is equivalent to exact probabilistic
                  inference in the case of deterministic dynamics, and
                  variational inference in the case of stochastic dynamics. We
                  will present a detailed derivation of this framework, overview
                  prior work that has drawn on this and related ideas to propose
                  new reinforcement learning and control algorithms, and
                  describe perspectives on future research.},
  archivePrefix ={arXiv},
  eprint =       {1805.00909v3},
  primaryClass = {cs.LG},
}

% -- Machine Learning Theory

@article{shalev-shwartz2013a,
  title = {Understanding machine learning: From theory to algorithms},
  language = {eng},
  publisher = {Cambridge University Press},
  journal = {Understanding Machine Learning: From Theory To Algorithms},
  volume = {9781107057135},
  pages = {1-397},
  year = {2013},
  isbn = {9781107298019, 9781107057135},
  abstract = {Machine learning is one of the fastest growing areas of computer
                  science, with far-reaching applications. The aim of this
                  textbook is to introduce machine learning, and the algorithmic
                  paradigms it offers, in a principled way. The book provides an
                  extensive theoretical account of the fundamental ideas
                  underlying machine learning and the mathematical derivations
                  that transform these principles into practical algorithms.
                  Following a presentation of the basics of the field, the book
                  covers a wide array of central topics that have not been
                  addressed by previous textbooks. These include a discussion of
                  the computational complexity of learning and the concepts of
                  convexity and stability; important algorithmic paradigms
                  including stochastic gradient descent, neural networks, and
                  structured output learning; and emerging theoretical concepts
                  such as the PAC-Bayes approach and compression-based bounds.
                  Designed for an advanced undergraduate or beginning graduate
                  course, the text makes the fundamentals and algorithms of
                  machine learning accessible to students and non-expert readers
                  in statistics, computer science, mathematics, and
                  engineering.},
  doi = {10.1017/CBO9781107298019},
  author = {Shalev-Shwartz, Shai and Ben-David, Shai}
}


% -- GANs

@article{goodfellow2014a,
  title = {Generative Adversarial Nets},
  language = {eng},
  publisher = {NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)},
  journal = {Advances in Neural Information Processing Systems 27 (nips 2014)},
  volume = {27},
  number = {January},
  pages = {2672-2680},
  year = {2014},
  issn = {10495258},
  abstract = { We propose a new framework for estimating generative models via
                  an adversarial process, in which we simultaneously train two
                  models: a generative model G that captures the data
                  distribution, and a discriminative model D that estimates the
                  probability that a sample came from the training data rather
                  than G. The training procedure for G is to maximize the
                  probability of D making a mistake. This framework corresponds
                  to a minimax two-player game. In the space of arbitrary
                  functions G and D, a unique solution exists, with G recovering
                  the training data distribution and D equal to 1/2 everywhere.
                  In the case where G and D are defined by multilayer
                  perceptrons, the entire system can be trained with
                  backpropagation. There is no need for any Markov chains or
                  unrolled approximate inference networks during either training
                  or generation of samples. Experiments demonstrate the
                  potential of the framework through qualitative and
                  quantitative evaluation of the generated samples.},
  author = {Goodfellow, Ian J. and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua}
}

@article{mohamed16_learn_implic_gener_model,
  author =       {Mohamed, Shakir and Lakshminarayanan, Balaji},
  title =        {Learning in Implicit Generative Models},
  journal =      {CoRR},
  year =         2016,
  url =          {http://arxiv.org/abs/1610.03483v4},
  abstract =     {Generative adversarial networks (GANs) provide an algorithmic
                  framework for constructing generative models with several
                  appealing properties: they do not require a likelihood
                  function to be specified, only a generating procedure; they
                  provide samples that are sharp and compelling; and they allow
                  us to harness our knowledge of building highly accurate neural
                  network classifiers. Here, we develop our understanding of
                  GANs with the aim of forming a rich view of this growing area
                  of machine learning---to build connections to the diverse set
                  of statistical thinking on this topic, of which much can be
                  gained by a mutual exchange of ideas. We frame GANs within the
                  wider landscape of algorithms for learning in implicit
                  generative models--models that only specify a stochastic
                  procedure with which to generate data--and relate these ideas
                  to modelling problems in related fields, such as econometrics
                  and approximate Bayesian computation. We develop
                  likelihood-free inference methods and highlight hypothesis
                  testing as a principle for learning in implicit generative
                  models, using which we are able to derive the objective
                  function used by GANs, and many other related objectives. The
                  testing viewpoint directs our focus to the general problem of
                  density ratio estimation. There are four approaches for
                  density ratio estimation, one of which is a solution using
                  classifiers to distinguish real from generated data. Other
                  approaches such as divergence minimisation and moment matching
                  have also been explored in the GAN literature, and we
                  synthesise these views to form an understanding in terms of
                  the relationships between them and the wider literature,
                  highlighting avenues for future exploration and
                  cross-pollination.},
  archivePrefix ={arXiv},
  eprint =       {1610.03483},
  primaryClass = {stat.ML},
}

@article{dumoulin2016adversarially,
  title={Adversarially learned inference},
  author={Dumoulin, Vincent and Belghazi, Ishmael and Poole, Ben and Mastropietro, Olivier and Lamb, Alex and Arjovsky, Martin and Courville, Aaron},
  journal={arXiv preprint arXiv:1606.00704},
  year={2016}
}


% -- VAEs and reparameterization trick

@article{kingma2014a,
  title = {Auto-Encoding Variational Bayes},
  language = {und},
  year = {2014},
  abstract = {How can we perform efficient inference and learning in directed
                  probabilistic models, in the presence of continuous latent
                  variables with intractable posterior distributions, and large
                  datasets? We introduce a stochastic variational inference and
                  learning algorithm that scales to large datasets and, under
                  some mild differentiability conditions, even works in the
                  intractable case. Our contributions is two-fold. First, we
                  show that a reparameterization of the variational lower bound
                  yields a lower bound estimator that can be straightforwardly
                  optimized using standard stochastic gradient methods. Second,
                  we show that for i.i.d. datasets with continuous latent
                  variables per datapoint, posterior inference can be made
                  especially efficient by fitting an approximate inference model
                  (also called a recognition model) to the intractable posterior
                  using the proposed lower bound estimator. Theoretical
                  advantages are reflected in experimental results.},
  author = {Kingma, Diederik P and Welling, Max}
}


% -- Inference compilation

@inproceedings{le2017inference,
  author = {Le, Tuan Anh and Baydin, At{\i}l{\i}m G{\"u}ne{\c s} and Wood, Frank},
  booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
  title = {Inference Compilation and Universal Probabilistic Programming},
  year = {2017},
  volume = {54},
  pages = {1338--1348},
  series = {Proceedings of Machine Learning Research},
  address = {Fort Lauderdale, FL, USA},
  publisher = {PMLR},
  file = {../assets/pdf/le2017inference.pdf},
  link = {http://proceedings.mlr.press/v54/},
  arxiv = {https://arxiv.org/abs/1610.09900}
}

% -- Wake-Sleep

@article{hinton1995wake,
  title={The" wake-sleep" algorithm for unsupervised neural networks},
  author={Hinton, Geoffrey E and Dayan, Peter and Frey, Brendan J and Neal, Radford M},
  journal={Science},
  volume={268},
  number={5214},
  pages={1158--1161},
  year={1995},
  publisher={American Association for the Advancement of Science}
}

@article{bornschein2014reweighted,
  title={Reweighted wake-sleep},
  author={Bornschein, J{\"o}rg and Bengio, Yoshua},
  journal={arXiv preprint arXiv:1406.2751},
  year={2014}
}

@article{le2018revisiting,
  title={Revisiting reweighted wake-sleep},
  author={Le, Tuan Anh and Kosiorek, Adam R and Siddharth, N and Teh, Yee Whye and Wood, Frank},
  journal={arXiv preprint arXiv:1805.10469},
  year={2018}
}

% -- REBAR and Reinforce

@article{tucker2017a,
  title = {REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models},
  language = {eng},
  publisher = {NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)},
  journal = {Advances in Neural Information Processing Systems 30 (nips 2017)},
  volume = {30},
  year = {2017},
  issn = {10495258},
  abstract = { Learning in models with discrete latent variables is challenging
                  due to high variance gradient estimators. Generally,
                  approaches have relied on control variates to reduce the
                  variance of the REINFORCE estimator. Recent work (Jang et al.,
                  2016; Maddison et al., 2016) has taken a different approach,
                  introducing a continuous relaxation of discrete variables to
                  produce low-variance, but biased, gradient estimates. In this
                  work, we combine the two approaches through a novel control
                  variate that produces low-variance, unbiased gradient
                  estimates. Then, we introduce a modification to the continuous
                  relaxation and show that the tightness of the relaxation can
                  be adapted online, removing it as a hyperparameter. We show
                  state-of-the-art variance reduction on several benchmark
                  generative modeling tasks, generally leading to faster
                  convergence to a better final log-likelihood.},
  author = {Tucker, George and Mnih, Andriy and Maddison, Chris J. and Lawson, Dieterich and Sohl-Dickstein, Jascha}
}


@article{glynn1990a,
  title = {LIKELIHOOD RATIO GRADIENT ESTIMATION FOR STOCHASTIC-SYSTEMS},
  language = {eng},
  publisher = {ASSOC COMPUTING MACHINERY},
  journal = {Communications of the Acm},
  volume = {33},
  number = {10},
  pages = {75-84},
  year = {1990},
  issn = {15577317, 00010782},
  abstract = {Efficient Monte Carlo gradient estimation is an important
                  ingredient of simulation-based optimization algorithms. The
                  author's goal is to describe one efficient method for
                  estimating gradients in the Monte Carlo setting, namely the
                  likelihood ratio method (also known as the efficient score
                  method). He describes two important problems which motivates
                  his study of efficient gradient estimation algorithms. He
                  presents the likelihood ratio gradient estimator in a general
                  setting in which the essential idea is most transparent. The
                  author then specializes the estimator to discrete-time
                  stochastic processes. He derives likelihood-ratio-gradient
                  estimators for both time-homogeneous and non-time homogeneous
                  discrete-time Markov chains. He discusses likelihood ratio
                  gradient estimation in continuous time. As examples of the
                  analysis, he presents the gradient estimators for
                  time-homogeneous continuous-time Markov chains, non-time
                  homogeneous continuous-time Markov chains, semi-Markov
                  processes; and generalized semi-Markov processes.},
  doi = {10.1145/84537.84552},
  author = {GLYNN, PW}
}

% -- pyprob

@misc{pyprob,
  title={\textit{pyprob}},
  howpublished={https://github.com/probprog/pyprob},
  author={Baydin, Atilim Gunes and Le, Tuan Anh},
  publisher={GitHub},
  year={2018}
  }

% -- pyprob

@misc{ppx,
 title={\textit{ppx}},
 howpublished={https://github.com/pyprob/ppx},
 author={Baydin, Atilim Gunes and Le, Tuan Anh and Heinrich, Lukas and Bhimji, Wahid and Cranmer, Kyle and Wood, Frank},
 publisher={GitHub},
 year={2018}
 }
 
% -- Probabilistic Programming


@article{bingham2018pyro,
author = {Bingham, Eli and Chen, Jonathan P. and Jankowiak, Martin and Obermeyer, Fritz and
          Pradhan, Neeraj and Karaletsos, Theofanis and Singh, Rohit and Szerlip, Paul and
          Horsfall, Paul and Goodman, Noah D.},
title = {Pyro: Deep Universal Probabilistic Programming},
journal = {Journal of Machine Learning Research},
year = {2018}
}
                
@article{van2018introduction,
  title={An Introduction to Probabilistic Programming},
  author={van de Meent, Jan-Willem and Paige, Brooks and Yang, Hongseok and Wood, Frank},
  journal={arXiv preprint arXiv:1809.10756},
  year={2018}
}

@article{gordon2014a,
  title = {Probabilistic programming},
  language = {eng},
  publisher = {Association for Computing Machinery, Inc},
  journal = {Future of Software Engineering, Fose 2014 - Proceedings},
  pages = {167-181},
  year = {2014},
  isbn = {9781450328654},
  abstract = {Probabilistic programs are usual functional or imperative programs
                  with two added constructs: (1) the ability to draw values at
                  random from distributions, and (2) the ability to condition
                  values of variables in a program via observations. Models from
                  diverse application areas such as computer vision, coding
                  theory, cryptographic protocols, biology and reliability
                  analysis can be written as probabilistic programs.
                  Probabilistic inference is the problem of computing an
                  explicit representation of the probability distribution
                  implicitly specified by a probabilistic program. Depending on
                  the application, the desired output from inference may vary-we
                  may want to estimate the expected value of some function f
                  with respect to the distribution, or the mode of the
                  distribution, or simply a set of samples drawn from the
                  distribution. In this paper, we describe connections this
                  research area called \Probabilistic Programming" has with
                  programming languages and software engineering, and this
                  includes language design, and the static and dynamic analysis
                  of programs. We survey current state of the art and speculate
                  on promising directions for future research.},
  doi = {10.1145/2593882.2593900},
  author = {Gordon, Andrew D. and Henzinger, Thomas A. and Nori, Aditya V. and Rajamani, Sriram K.}
}

@article{tran2016edward,
  author = {Dustin Tran and Alp Kucukelbir and Adji B. Dieng and Maja Rudolph and Dawen Liang and David M. Blei},
  title = {{Edward: A library for probabilistic modeling, inference, and criticism}},
  journal = {arXiv preprint arXiv:1610.09787},
  year = {2016}
}

@article{lunn2009bugs,
  title={The BUGS project: Evolution, critique and future directions},
  author={Lunn, David and Spiegelhalter, David and Thomas, Andrew and Best, Nicky},
  journal={Statistics in medicine},
  volume={28},
  number={25},
  pages={3049--3067},
  year={2009},
  publisher={Wiley Online Library}
}

@misc{dippl,
  title={{The Design and Implementation of Probabilistic Programming Languages}},
  author={Goodman, Noah D and Stuhlm\"{u}ller, Andreas},
  year={2014},
  howpublished={http://dippl.org}
}

@article{carpenter2017stan,
  title={Stan: A probabilistic programming language},
  author={Carpenter, Bob and Gelman, Andrew and Hoffman, Matthew D and Lee, Daniel and Goodrich, Ben and Betancourt, Michael and Brubaker, Marcus and Guo, Jiqiang and Li, Peter and Riddell, Allen},
  journal={Journal of statistical software},
  volume={76},
  number={1},
  year={2017},
  publisher={Columbia Univ., New York, NY (United States); Harvard Univ., Cambridge, MA~…}
}


@article{goodman2008a,
  title = {Church: A language for generative models},
  language = {eng},
  publisher = {AUAI Press},
  journal = {Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, Uai 2008},
  pages = {220-229},
  year = {2008},
  isbn = {0974903949, 9780974903941},
  abstract = {Formal languages for probabilistic modeling enable re-use,
                  modularity, and descriptive clarity, and can foster generic
                  inference techniques. We introduce Church, a universal
                  language for describing stochastic generative processes.
                  Church is based on the Lisp model of lambda calculus,
                  containing a pure Lisp as its deterministic subset. The
                  semantics of Church is defined in terms of evaluation
                  histories and conditional distributions on such histories.
                  Church also includes a novel language construct, the
                  stochastic memoizer, which enables simple description of many
                  complex non-parametric models. We illustrate language features
                  through several examples, including: a generalized Bayes net
                  in which parameters cluster over trials, infinite PCFGs,
                  planning by inference, and various non-parametric clustering
                  models. Finally, we show how to implement query on any Church
                  program, exactly and approximately, using Monte Carlo
                  techniques.},
  author = {Goodman, Noah D. and Mansinghka, Vikash K. and Roy, Daniel and Bonawitz, Keith and Tenenbaum, Joshua B.}
}

@article{milch2005a,
  title = {BLOG: Probabilistic models with unknown objects},
  language = {eng},
  publisher = {International Joint Conferences on Artificial Intelligence},
  journal = {Ijcai International Joint Conference on Artificial Intelligence},
  pages = {1352-1359},
  year = {2005},
  issn = {10450823},
  abstract = {This paper introduces and illustrates BLOG, a formal language for
                  defining probability models over worlds with unknown objects
                  and identity uncertainty. BLOG unifies and extends several
                  existing approaches. Subject to certain acyclicity
                  constraints, every BLOG model specifies a unique probability
                  distribution over first-order model structures that can
                  contain varying and unbounded numbers of objects. Furthermore,
                  complete inference algorithms exist for a large fragment of
                  the language. We also introduce a probabilistic form of
                  Skolemization for handling evidence.},
  author = {Milch, Brian and Marthi, Bhaskara and Russell, Stuart and Sontag, David and Ong, Daniel L. and Kolobov, Andrey}
}

@misc{InferNET18,
author = "Minka, T. and Winn, J.M. and Guiver, J.P. and Zaykov, Y. and Fabian, D. and Bronskill, J.",
title = {/{Infer.NET 0.3}},
year = 2018,
note = {Microsoft Research Cambridge. http://dotnet.github.io/infer}
}

@article{pfeffer2009figaro,
  title={Figaro: An object-oriented probabilistic programming language},
  author={Pfeffer, Avi},
  journal={Charles River Analytics Technical Report},
  volume={137},
  pages={96},
  year={2009}
}

@article{mansinghka2014a,
  title = {Venture: a higher-order probabilistic programming platform with
                  programmable inference},
  language = {und},
  pages = {78},
  year = {2014},
  abstract = { We describe Venture, an interactive virtual machine for
                  probabilistic programming that aims to be sufficiently
                  expressive, extensible, and efficient for general-purpose use.
                  Like Church, probabilistic models and inference problems in
                  Venture are specified via a Turing-complete, higher-order
                  probabilistic language descended from Lisp. Unlike Church,
                  Venture also provides a compositional language for custom
                  inference strategies built out of scalable exact and
                  approximate techniques. We also describe four key aspects of
                  Venture's implementation that build on ideas from
                  probabilistic graphical models. First, we describe the
                  stochastic procedure interface (SPI) that specifies and
                  encapsulates primitive random variables. The SPI supports
                  custom control flow, higher-order probabilistic procedures,
                  partially exchangeable sequences and ``likelihood-free''
                  stochastic simulators. It also supports external models that
                  do inference over latent variables hidden from Venture.
                  Second, we describe probabilistic execution traces (PETs),
                  which represent execution histories of Venture programs. PETs
                  capture conditional dependencies, existential dependencies and
                  exchangeable coupling. Third, we describe partitions of
                  execution histories called scaffolds that factor global
                  inference problems into coherent sub-problems. Finally, we
                  describe a family of stochastic regeneration algorithms for
                  efficiently modifying PET fragments contained within
                  scaffolds. Stochastic regeneration linear runtime scaling in
                  cases where many previous approaches scaled quadratically. We
                  show how to use stochastic regeneration and the SPI to
                  implement general-purpose inference strategies such as
                  Metropolis-Hastings, Gibbs sampling, and blocked proposals
                  based on particle Markov chain Monte Carlo and mean-field
                  variational inference techniques. },
  author = {Mansinghka, Vikash and Selsam, Daniel and Perov, Yura}
}

@inproceedings{wood2014new,
  title={A new approach to probabilistic programming inference},
  author={Wood, Frank and Meent, Jan Willem and Mansinghka, Vikash},
  booktitle={Artificial Intelligence and Statistics},
  pages={1024--1032},
  year={2014}
}

@inproceedings{kulkarni2015picture,
  title={Picture: A probabilistic programming language for scene perception},
  author={Kulkarni, Tejas D and Kohli, Pushmeet and Tenenbaum, Joshua B and Mansinghka, Vikash},
  booktitle={Proceedings of the ieee conference on computer vision and pattern recognition},
  pages={4390--4399},
  year={2015}
}

% -- sequential importance sampling

@article{arulampalam2002a,
  title = {A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking},
  language = {eng},
  publisher = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
  journal = {Ieee Transactions on Signal Processing},
  volume = {50},
  number = {2},
  pages = {174-188},
  year = {2002},
  issn = {19410476, 1053587x},
  abstract = {Increasingly, for many application areas, it is becoming important
                  to include elements of nonlinearity and non-Gaussianity in
                  order to model accurately the underlying dynamics of a
                  physical system: Moreover, it is typically crucial to process
                  data on-line as it arrives, both from the point of view of
                  storage costs as well as for rapid adaptation to changing
                  signal characteristics. In this paper, we review both optimal
                  and suboptimal Bayesian algorithms for nonlinear/non-Gaussian
                  tracking problems, with a focus on particle filters. Particle
                  filters are sequential Monte Carlo methods based on point mass
                  (or "particle") representations of probability densities,
                  which can be applied to any state-space model and which
                  generalize the traditional Kalman filtering methods:. Several
                  variants of the particle filter such as SIR, ASIR; and RPF are
                  introduced within a generic framework of the sequential
                  importance sampling (SIS) algorithm. These are discussed and
                  compared with the standard EKF through an illustrative
                  example.},
  doi = {10.1109/78.978374},
  author = {Arulampalam, MS and Maskell, S and Gordon, N and Clapp, T}
}

@article{doucet2009tutorial,
  title={A tutorial on particle filtering and smoothing: Fifteen years later},
  author={Doucet, Arnaud and Johansen, Adam M},
  journal={Handbook of nonlinear filtering},
  volume={12},
  number={656-704},
  pages={3},
  year={2009}
}

% -- ADAM
@inproceedings{kingma2015method,
author = {Kingma, Diederik and Ba, Jimmy},
year = {2014},
month = {12},
pages = {},
title = {Adam: A Method for Stochastic Optimization},
journal = {International Conference on Learning Representations}
}

% -- electric circuits simulator

@misc{ahkab,
  title={\textit{ahkab}},
  url={https://github.com/ahkab/ahkab/},
  author={Venturini, Giuseppe and Daniher, Ian and Crowther, Rob and KOLANICH},
  publisher={GitHub},
  year={2017},
  commit={c41a5859131ed755aefa744b195c2144b402c260}
  }


% -- smc
 
 @article{del2006sequential,
  title={Sequential monte carlo samplers},
  author={Del Moral, Pierre and Doucet, Arnaud and Jasra, Ajay},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={68},
  number={3},
  pages={411--436},
  year={2006},
  publisher={Wiley Online Library}
}  

% -- HMC

@article{duane1987hybrid,
  title={Hybrid monte carlo},
  author={Duane, Simon and Kennedy, Anthony D and Pendleton, Brian J and Roweth, Duncan},
  journal={Physics letters B},
  volume={195},
  number={2},
  pages={216--222},
  year={1987},
  publisher={Elsevier}
}
  
% -- lmh
 
 @article{wingate2011a,
 title = {Lightweight implementations of probabilistic programming languages via transformational compilation},
 language = {eng},
 publisher = {Microtome Publishing},
 journal = {Journal of Machine Learning Research},
 volume = {15},
 pages = {770-778},
 year = {2011},
 issn = {15337928, 15324435},
 abstract = {We describe a general method of transforming arbitrary programming
                  languages into probabilistic programming languages with
                  straightforward MCMC inference engines. Random choices in the
                  program are "named" with information about their position in
                  an execution trace; these names are used in conjunction with a
                  database holding values of random variables to implement MCMC
                  inference in the space of execution traces. We encode naming
                  information using lightweight source-to-source compilers. Our
                  method enables us to reuse existing infrastructure (compilers,
                  profilers, etc.) with minimal additional code, implying fast
                  models with low development overhead. We illustrate the
                  technique on two languages, one functional and one imperative:
                  Bher, a compiled version of the Church language which
                  eliminates interpretive overhead of the original MIT-Church
                  implementation, and Stochastic Matlab, a new open-source
                  language. Copyright 2011 by the authors.},
 author = {Wingate, David and Stuhlm{\"u}ller, Andreas and Goodman, Noah D.}
}

% -- Physics inference

@article{gleisberg2009event,
  title={Event generation with SHERPA 1.1},
  author={Gleisberg, Tanju and H{\"o}che, Stefan and Krauss, F and Sch{\"o}nherr, M and Schumann, S and Siegert, F and Winter, J},
  journal={Journal of High Energy Physics},
  volume={2009},
  number={02},
  pages={007},
  year={2009},
  publisher={IOP Publishing}
}

@inproceedings{baydin2019etalumis,
  title = {Etalumis: Bringing Probabilistic Programming to Scientific Simulators at Scale},
  shorttitle = {Etalumis},
  booktitle = {Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis},
  author = {Baydin, Atilim G{\"u}ne{\c s} and Shao, Lei and Bhimji, Wahid and Heinrich, Lukas and Meadows, Lawrence and Liu, Jialin and Munk, Andreas and Naderiparizi, Saeid and {Gram-Hansen}, Bradley and Louppe, Gilles and Ma, Mingfei and Zhao, Xiaohui and Torr, Philip and Lee, Victor and Cranmer, Kyle and Prabhat and Wood, Frank},
  year = {2019},
  month = nov,
  pages = {1--24},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  doi = {10.1145/3295500.3356180},
  copyright = {All rights reserved},
  isbn = {978-1-4503-6229-0},
  keywords = {deep learning,inference,probabilistic programming,simulation},
  series = {SC '19}
}

@incollection{baydin2019efficient,
  title = {Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model},
  booktitle = {Advances in Neural Information Processing Systems 32},
  author = {Baydin, Atilim Gunes and Shao, Lei and Bhimji, Wahid and Heinrich, Lukas and Naderiparizi, Saeid and Munk, Andreas and Liu, Jialin and {Gram-Hansen}, Bradley and Louppe, Gilles and Meadows, Lawrence and Torr, Philip and Lee, Victor and Cranmer, Kyle and Prabhat, Mr. and Wood, Frank},
  year = {2019},
  pages = {5459--5472},
  publisher = {Curran Associates, Inc.},
  copyright = {All rights reserved},
  selected = {true},
  abbr = {NeurIPS}
}

% -- LSTMS

@article{hochreiter1997a,
  title = {Long short-term memory},
  language = {eng},
  publisher = {M I T PRESS},
  journal = {Neural Computation},
  volume = {9},
  number = {8},
  pages = {1735-1780},
  year = {1997},
  issn = {1530888x, 08997667},
  abstract = {Learning to store information over extended time intervals by
                  recurrent backpropagation takes a very long time, mostly
                  because of insufficient, decaying error backflow. We briefly
                  review Hochreiter's (1991) analysis of this problem, then
                  address it by introducing a novel, efficient, gradient-based
                  method called long short-term memory (LSTM). Truncating the
                  gradient where this does not do harm, LSTM can learn to bridge
                  minimal time lags in excess of 1000 discrete-time steps by
                  enforcing constant error now through constant error carousels
                  within special units. Multiplicative gate units learn to open
                  and close access to the constant error flow. LSTM is local in
                  space and time; its computational complexity per time step and
                  weight is O(1). Our experiments with artificial data involve
                  local, distributed, real-valued, and noisy pattern
                  representations. In comparisons with real-time recurrent
                  learning, back propagation through time, recurrent cascade
                  correlation, Elman nets, and neural sequence chunking, LSTM
                  leads to many more successful runs, and learns much faster.
                  LSTM also solves complex, artificial long-time-lag tasks that
                  have never been solved by previous recurrent network
                  algorithms.},
  author = {Hochreiter, S and Schmidhuber, J}
}

@article{hochreiter1998a,
  title = {The vanishing gradient problem during learning recurrent neural nets and problem solutions},
  language = {eng},
  publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD},
  journal = {International Journal of Uncertainty Fuzziness and Knowledge-based Systems},
  volume = {6},
  number = {2},
  pages = {107-116},
  year = {1998},
  issn = {17936411, 02184885},
  abstract = {Recurrent nets are in principle capable to store past inputs to
                  produce the currently desired output. Because of this property
                  recurrent nets are used in time series prediction and process
                  control. Practical applications involve temporal dependencies
                  spanning many time steps, e.g. between relevant inputs and
                  desired outputs. In this case, however, gradient based
                  learning methods take too much time. The extremely increased
                  learning time arises because the error vanishes as it gets
                  propagated back. In this article the decaying error flow is
                  theoretically analyzed. Then methods trying to overcome
                  vanishing gradients are briefly discussed. Finally,
                  experiments comparing conventional algorithms and alternative
                  methods are presented. With advanced methods long time lag
                  problems can be solved in reasonable time.},
  doi = {10.1142/S0218488598000094},
  author = {Hochreiter, S}
}

@misc{hochreiter2001gradient,
  title={Gradient flow in recurrent nets: the difficulty of learning long-term dependencies},
  author={Hochreiter, Sepp and Bengio, Yoshua and Frasconi, Paolo and Schmidhuber, J{\"u}rgen and others},
  year={2001},
  publisher={A field guide to dynamical recurrent neural networks. IEEE Press}
}

% -- amortized inference

@inproceedings{gershman2014amortized,
  title={Amortized inference in probabilistic reasoning},
  author={Gershman, Samuel and Goodman, Noah},
  booktitle={Proceedings of the Annual Meeting of the Cognitive Science Society},
  volume={36},
  number={36},
  year={2014}
}

% -- CDF
@misc{openfoam,
  title={\textit{OpenFoam}},
  url={https://openfoam.com/},
  year={2018}
  }

% -- Carla

@inproceedings{Dosovitskiy17,
  title = { {CARLA}: {An} Open Urban Driving Simulator},
  author = {Alexey Dosovitskiy and German Ros and Felipe Codevilla and Antonio Lopez and Vladlen Koltun},
  booktitle = {Proceedings of the 1st Annual Conference on Robot Learning},
  pages = {1--16},
  year = {2017}
}


% -- Attention


@article{harvey2019attention,
  title={Attention for inference compilation},
  author={Harvey, William and Munk, Andreas and Baydin, At{\i}l{\i}m G{\"u}ne{\c{s}} and Bergholm, Alexander and Wood, Frank},
  journal={arXiv preprint arXiv:1910.11961},
  year={2019}
}

@inproceedings{vaswani2017attention,
  title={Attention is all you need},
  author={Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser, {\L}ukasz and Polosukhin, Illia},
  booktitle={Advances in Neural Information Processing Systems},
  pages={5998--6008},
  year={2017}
}

@article{jabot2009inferring,
  title={Inferring the parameters of the neutral theory of biodiversity using phylogenetic information and implications for tropical forests},
  author={Jabot, Franck and Chave, J{\'e}r{\^o}me},
  journal={Ecology letters},
  volume={12},
  number={3},
  pages={239--248},
  year={2009},
  publisher={Wiley Online Library}
}

@article{jeong2005efficient,
  title={Efficient optimization design method using kriging model},
  author={Jeong, Shinkyu and Murayama, Mitsuhiro and Yamamoto, Kazuomi},
  journal={Journal of aircraft},
  volume={42},
  number={2},
  pages={413--420},
  year={2005}
}

@article{rikards2004surrogate,
  title={Surrogate models for optimum design of stiffened composite shells},
  author={Rikards, Rolands and Abramovich, Haim and Auzins, J and Korjakins, Aleksandrs and Ozolinsh, O and Kalnins, K and Green, Tony},
  journal={Composite Structures},
  volume={63},
  number={2},
  pages={243--251},
  year={2004},
  publisher={Elsevier}
}


% -- Physics modeling

@book{tuttle2003structural,
  title={Structural analysis of polymeric composite materials},
  author={Tuttle, Mark E},
  year={2003},
  publisher={Crc Press}
}

@book{pascault2002thermosetting,
  title={Thermosetting polymers},
  author={Pascault, Jean-Pierre and Sautereau, Henry and Verdu, Jacques and Williams, Roberto JJ},
  volume={477},
  year={2002},
  publisher={Marcel Dekker New York}
}

@techreport{HexcelComposites2010,
abstract = {HexPly{\textregistered} 8552 is a high performance tough epoxy matrix for use in primary aerospace structures. It exhibits good impact resistance and damage tolerance for a wide range of applications. HexPly{\textregistered} 8552 is an amine cured, toughened epoxy resin system supplied with unidirectional or woven carbon or glass fibres. HexPly{\textregistered} 8552 was developed as a controlled flow system to operate in environments up to 121{\textordmasculine}C (250{\textordmasculine}F).},
address = {Stamford},
author = {{Hexcel Composites}},
title = {{HexPly 8552 product data}},
year = {2010}
}

@techreport{Technologies2019,
address = {Vancouver},
author = {{Convergent Manufacturing Technologies}},
title = {{RAVEN Simulation Software}},
year = {2019}
}

@article{Zobeiry2018,
abstract = {The manufacture of large complex aircraft structures made of advanced composites is done by heating the parts on complex, thermally massive tools using convective heating inside autoclaves. In recent years, numerical simulation of the process has shown great value, but lack of knowledge of the convective heat transfer boundary conditions remains a major obstacle to widespread adoption. An infrared thermography method is presented, suitable for evaluating the thermal response of these processing conditions. The method is based on increasing the emissivity of a tool surface with a painted vacuum bag before thermal imaging. Accurate readings with an average temperature difference of 1.1℃ compared to thermocouple data were achieved. The benefit of the thermography method is the highly detailed surface temperature map. Three tools with very similar geometries but made of Invar, aluminum and carbon fibre composite, respectively, were tested, and results interpreted using analytical solutions for the different tooling feature and convective boundary condition combinations. Analytical simulations, which were validated by comparison to numerical models, explain well the effect of autoclave airflow, tooling material and sub-structure variation on the temperature profiles measured by this infrared thermography method.},
author = {Zobeiry, Navid and Park, John and Poursartip, Anoush},
doi = {10.1177/0021998318798444},
issn = {0021-9983},
journal = {Journal of Composite Materials},
keywords = {advanced composites,autoclave processing,background and introduction,designs,given the promise of,infrared imaging,lighter and more efficient,out-of-autoclave processing,tooling},
mendeley-groups = {TGML},
pages = {002199831879844},
title = {{An infrared thermography-based method for the evaluation of the thermal response of tooling for composites manufacturing}},
url = {http://journals.sagepub.com/doi/10.1177/0021998318798444},
year = {2018}
}

@article{Rasekh2004,
abstract = {The modelling of the processing of composite structures is now relatively well established, and it has been shown that it is possible to predict the thermal behaviour of a composite structure during the manufacturing process. One requires the thermo-chemical response of the resin as well as the thermal properties of the fibre, the tooling, cores and inserts, etc.,. All of this information can be plugged into a finite element description of the thermo-chemical problem, including the heat transfer characteristics of the autoclave or oven. Predictions of the behaviour can then be made, and these predictions are of great value in selecting a cure cycle that is fast yet does not lead to an exotherm or otherwise violate process requirements. The above approach works well, but it is complicated and time-consuming to perform. In addition, it is difficult to get easy insight into the generality of the material behaviour, even when many computer runs are performed. In this paper, we present simple equations and diagrams, which enable one to estimate the thermal lag and then exotherm for typical cure cycles and structure/tooling/autoclave or oven combinations. The benefit of these equations and diagrams, which are based on and therefore consistent with more complex finite element modelling, is that they are simple to use, and provide great insight at very low cost and effort. Copyright 2004 by The University of British Columbia.},
author = {Rasekh, Ali and Vaziri, Reza and Poursartip, Anoush},
file = {:/cmt-files/Users/andrew/Papers/2004/2004 - Rasekh, Vaziri, Poursartip - Simple Techniques for Thermal Analysis of the Processing of Composite Structures.pdf:pdf},
journal = {36th International SAMPE Technical Conference},
keywords = {cure,materials,modeling,process,resins,simulation,thermal analysis},
pages = {11},
title = {{Simple Techniques for Thermal Analysis of the Processing of Composite Structures}},
year = {2004}
}

% -- Reinforce Trick

@article{williams1992simple,
  title={Simple statistical gradient-following algorithms for connectionist reinforcement learning},
  author={Williams, Ronald J},
  journal={Machine learning},
  volume={8},
  number={3-4},
  pages={229--256},
  year={1992},
  publisher={Springer}
}

% -- Gumbel Softmax

@article{jang2016categorical,
  title={Categorical reparameterization with gumbel-softmax},
  author={Jang, Eric and Gu, Shixiang and Poole, Ben},
  journal={arXiv preprint arXiv:1611.01144},
  year={2016}
}

% -- Rejection sampling

@article{neumann1950,
author = {Neumann, Von},
year = {1950},
month = {11},
pages = {36-38},
title = {Various techniques used in connection with random digits},
volume = {12},
journal = {National Bureau of Standards, Applied Math Series}
}

% -- learning execution traces

@article{reed2015neural,
  title={Neural programmer-interpreters},
  author={Reed, Scott and De Freitas, Nando},
  journal={arXiv preprint arXiv:1511.06279},
  year={2015}
}

% -- Computer Science

@inproceedings{barner2002combining,
  title={Combining symmetry reduction and under-approximation for symbolic model checking},
  author={Barner, Sharon and Grumberg, Orna},
  booktitle={International Conference on Computer Aided Verification},
  pages={93--106},
  year={2002},
  organization={Springer}
}

@inproceedings{takisaka2018ranking,
  title={Ranking and repulsing supermartingales for reachability in probabilistic programs},
  author={Takisaka, Toru and Oyabu, Yuichiro and Urabe, Natsuki and Hasuo, Ichiro},
  booktitle={International Symposium on Automated Technology for Verification and Analysis},
  pages={476--493},
  year={2018},
  organization={Springer}
}

@inproceedings{paszke2019pytorch,
  title={PyTorch: An imperative style, high-performance deep learning library},
  author={Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and others},
  booktitle={Advances in Neural Information Processing Systems},
  pages={8024--8035},
  year={2019}
}

@article{advani2003process,
  title={Process modeling in composites manufacturing},
  author={Advani, Suresh G and Sozer, E Murat and Mishnaevsky Jr, L},
  journal={Appl. Mech. Rev.},
  volume={56},
  number={5},
  pages={B69--B70},
  year={2003}
}

@article{cranmer2020frontier,
  title={The frontier of simulation-based inference},
  author={Cranmer, Kyle and Brehmer, Johann and Louppe, Gilles},
  journal={Proceedings of the National Academy of Sciences},
  year={2020},
  publisher={National Acad Sciences}
}

% surrogate for inference

@misc{himes2020accurate,
    title={Accurate Machine Learning Atmospheric Retrieval via a Neural Network Surrogate Model for Radiative Transfer},
    author={Michael D. Himes and Joseph Harrington and Adam D. Cobb and Atilim Gunes Baydin and Frank Soboczenski and Molly D. O'Beirne and Simone Zorzan and David C. Wright and Zacchaeus Scheffer and Shawn D. Domagal-Goldman and Giada N. Arney},
    year={2020},
    eprint={2003.02430},
    archivePrefix={arXiv},
    primaryClass={astro-ph.IM}
}

@incollection{aldous1985exchangeability,
  title={Exchangeability and related topics},
  author={Aldous, David J},
  booktitle={{\'E}cole d'{\'E}t{\'e} de Probabilit{\'e}s de Saint-Flour XIII—1983},
  pages={1--198},
  year={1985},
  publisher={Springer}
}


%CARLA simulator
@inproceedings{Dosovitskiy17,
  title = { {CARLA}: {An} Open Urban Driving Simulator},
  author = {Alexey Dosovitskiy and German Ros and Felipe Codevilla and Antonio Lopez and Vladlen Koltun},
  booktitle = {Proceedings of the 1st Annual Conference on Robot Learning},
  pages = {1--16},
  year = {2017}
}

@inproceedings{weiss2018practical,
  title={On the Practical Computational Power of Finite Precision RNNs for Language Recognition},
  author={Weiss, Gail and Goldberg, Yoav and Yahav, Eran},
  booktitle={Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)},
  pages={740--745},
  year={2018}
}

@article{siegelmann1995computational,
  title={On the computational power of neural nets},
  author={Siegelmann, Hava T and Sontag, Eduardo D},
  journal={Journal of computer and system sciences},
  volume={50},
  number={1},
  pages={132--150},
  year={1995},
  publisher={Elsevier}
}

@article{siegelmann1994analog,
  title={Analog computation via neural networks},
  author={Siegelmann, Hava T and Sontag, Eduardo D},
  journal={Theoretical Computer Science},
  volume={131},
  number={2},
  pages={331--360},
  year={1994},
  publisher={Elsevier}
}

@book{siegelmann1998neural,
  title={Neural Networks and Analog Computation: Beyond the Turing Limit},
  author={Siegelmann, Hava},
  year={1998},
  publisher={Springer Science \& Business Media}
}

@inproceedings{chen2018recurrent,
  title={Recurrent Neural Networks as Weighted Language Recognizers},
  author={Chen, Yining and Gilroy, Sorcha and Maletti, Andreas and May, Jonathan and Knight, Kevin},
  booktitle={Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)},
  pages={2261--2271},
  year={2018}
}

@article{graves2016hybrid,
  title={Hybrid computing using a neural network with dynamic external memory},
  author={Graves, Alex and Wayne, Greg and Reynolds, Malcolm and Harley, Tim and Danihelka, Ivo and Grabska-Barwi{\'n}ska, Agnieszka and Colmenarejo, Sergio G{\'o}mez and Grefenstette, Edward and Ramalho, Tiago and Agapiou, John and others},
  journal={Nature},
  volume={538},
  number={7626},
  pages={471--476},
  year={2016},
  publisher={Nature Publishing Group}
}
