@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{uria2016neural,
  title={Neural autoregressive distribution estimation},
  author={Uria, Benigno and C{\^o}t{\'e}, Marc-Alexandre and Gregor, Karol and Murray, Iain and Larochelle, Hugo},
  journal={The Journal of Machine Learning Research},
  volume={17},
  number={1},
  pages={7184--7220},
  year={2016},
  publisher={JMLR. org}}

@article{rezende2015variational,
  title={Variational inference with normalizing flows},
  author={Rezende, Danilo Jimenez and Mohamed, Shakir},
  journal={arXiv preprint arXiv:1505.05770},
  year={2015}
}

@inproceedings{uria2013rnade,
  title={RNADE: The real-valued neural autoregressive density-estimator},
  author={Uria, Benigno and Murray, Iain and Larochelle, Hugo},
  booktitle={Advances in Neural Information Processing Systems},
  pages={2175--2183},
  year={2013}
}

@article{mathieu2015masked,
  title={Masked Autoencoder for Distribution Estimation},
  author={Mathieu, MADEby},
  year={2015}
}
@article{nalisnick2018deep,
  title={Do deep generative models know what they don't know?},
  author={Nalisnick, Eric and Matsukawa, Akihiro and Teh, Yee Whye and Gorur, Dilan and Lakshminarayanan, Balaji},
  journal={arXiv preprint arXiv:1810.09136},
  year={2018}
}





//BNN literature review

@article{blei2017variational,
  title={Variational inference: A review for statisticians},
  author={Blei, David M and Kucukelbir, Alp and McAuliffe, Jon D},
  journal={Journal of the American statistical Association},
  volume={112},
  number={518},
  pages={859--877},
  year={2017},
  publisher={Taylor \& Francis}
}

@inproceedings{SGHMC_chen2014, author = {Chen, Tianqi and Fox, Emily B. and Guestrin, Carlos}, title = {Stochastic Gradient Hamiltonian Monte Carlo}, year = {2014}, publisher = {JMLR.org}, booktitle = {Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32}, pages = {II–1683–II–1691}, numpages = {9}, location = {Beijing, China}, series = {ICML’14} }

@InProceedings{pearce2018_Bayesian_ensemble,
    title={Uncertainty in Neural Networks: Approximately Bayesian Ensembling},
    author={Tim Pearce and Felix Leibfried and Alexandra Brintrup and Mohamed Zaki and Andy Neely},
    year={2018},
    eprint={1810.05546},
    archivePrefix={arXiv},
    primaryClass={stat.ML}
}

@InProceedings{fort2019_ensemble_explain,
    title={Deep Ensembles: A Loss Landscape Perspective},
    author={Stanislav Fort and Huiyi Hu and Balaji Lakshminarayanan},
    year={2019},
    eprint={1912.02757},
    archivePrefix={arXiv},
    primaryClass={stat.ML}
}

//// 2015
@InProceedings{Blundell_ICML15_BayesByBackProp,
  title = 	 {Weight Uncertainty in Neural Network},
  author = 	 {Charles Blundell and Julien Cornebise and Koray Kavukcuoglu and Daan Wierstra},
  booktitle = 	 {Proceedings of the 32nd International Conference on Machine Learning},
  pages = 	 {1613--1622},
  year = 	 {2015},
  editor = 	 {Francis Bach and David Blei},
  volume = 	 {37},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Lille, France},
  month = 	 {07--09 Jul},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v37/blundell15.pdf},
  url = 	 {http://proceedings.mlr.press/v37/blundell15.html},
  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.}
}

@InProceedings{hernandez-lobatoc_ICML15_PBP,
  title =    {Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks},
  author =   {Jose Miguel Hernandez-Lobato and Ryan Adams},
  booktitle =    {Proceedings of the 32nd International Conference on Machine Learning},
  pages =    {1861--1869},
  year =   {2015},
  editor =   {Francis Bach and David Blei},
  volume =   {37},
  series =   {Proceedings of Machine Learning Research},
  address =    {Lille, France},
  month =    {07--09 Jul},
  publisher =    {PMLR},
  pdf =    {http://proceedings.mlr.press/v37/hernandez-lobatoc15.pdf},
  url =    {http://proceedings.mlr.press/v37/hernandez-lobatoc15.html},
  abstract =   {Large multilayer neural networks trained with backpropagation have recently achieved state-of-the-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic predictions, and a tendency to overfit the training data. In principle, the Bayesian approach to learning neural networks does not have these problems. However, existing Bayesian techniques lack scalability to large dataset and network sizes. In this work we present a novel scalable method for learning Bayesian neural networks, called probabilistic backpropagation (PBP). Similar to classical backpropagation, PBP works by computing a forward propagation of probabilities through the network and then doing a backward computation of gradients. A series of experiments on ten real-world datasets show that PBP is significantly faster than other techniques, while offering competitive predictive abilities. Our experiments also show that PBP provides accurate estimates of the posterior variance on the network weights.}
}


//// 2016

@InProceedings{Gal_ICML16_MC-dropout,
  title = 	 {Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning},
  author = 	 {Yarin Gal and Zoubin Ghahramani},
  booktitle = 	 {Proceedings of The 33rd International Conference on Machine Learning},
  pages = 	 {1050--1059},
  year = 	 {2016},
  editor = 	 {Maria Florina Balcan and Kilian Q. Weinberger},
  volume = 	 {48},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {New York, New York, USA},
  month = 	 {20--22 Jun},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v48/gal16.pdf},
  url = 	 {http://proceedings.mlr.press/v48/gal16.html},
  abstract = 	 {Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs – extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout’s uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout’s uncertainty in deep reinforcement learning.}
}

//// 2017

@incollection{Lakshminarayanan_NIPS17_ensemble,
title = {Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles},
author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
booktitle = {Advances in Neural Information Processing Systems 30},
editor = {I. Guyon and U. V. Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
pages = {6402--6413},
year = {2017},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/7219-simple-and-scalable-predictive-uncertainty-estimation-using-deep-ensembles.pdf}
}


@InProceedings{louizos_ICML17_MNF,
  title =    {Multiplicative Normalizing Flows for Variational {B}ayesian Neural Networks},
  author =   {Christos Louizos and Max Welling},
  booktitle =    {Proceedings of the 34th International Conference on Machine Learning},
  pages =    {2218--2227},
  year =   {2017},
  editor =   {Doina Precup and Yee Whye Teh},
  volume =   {70},
  series =   {Proceedings of Machine Learning Research},
  address =    {International Convention Centre, Sydney, Australia},
  month =    {06--11 Aug},
  publisher =    {PMLR},
  pdf =    {http://proceedings.mlr.press/v70/louizos17a/louizos17a.pdf},
  url =    {http://proceedings.mlr.press/v70/louizos17a.html},
  abstract =   {We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows while still allowing for local reparametrizations and a tractable lower bound. In experiments we show that with this new approximation we can significantly improve upon classical mean field for Bayesian neural networks on both predictive accuracy as well as predictive uncertainty.}
}

@article{Mandt_JMLR17_SGD,
abstract = {Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust the tuning parameters of constant SGD to best match the stationary distribution to a posterior, minimizing the Kullback-Leibler divergence between these two distributions. (2) We demonstrate that constant SGD gives rise to a new variational EM algorithm that optimizes hyperparameters in complex probabilistic models. (3) We also show how to tune SGD with momentum for approximate sampling. (4)We analyze stochastic-gradient MCMC algorithms. For Stochastic-Gradient Langevin Dynamics and Stochastic-Gradient Fisher Scoring, we quantify the approximation errors due to finite learning rates. Finally (5), we use the stochastic process perspective to give a short proof of why Polyak averaging is optimal. Based on this idea, we propose a scalable approximate MCMC algorithm, the Averaged Stochastic Gradient Sampler.},
archivePrefix = {arXiv},
arxivId = {1704.04289},
author = {Mandt, Stephan and {Hof Fman}, Matthew D. and Blei, David M.},
eprint = {1704.04289},
issn = {15337928},
journal = {Journal of Machine Learning Research},
title = {{Stochastic gradient descent as approximate Bayesian inference}},
volume = {18},
year = {2017}
}

@article{Sun_AISTATS17_MVG,
abstract = {Deep neural networks (DNNs) are increasingly popular in modern machine learning. Bayesian learning affords the opportunity to quantify posterior uncertainty on DNN model parameters. Most existing work adopts independent Gaussian priors on the model weights, ignoring possible structural information. In this paper, we consider the matrix variate Gaussian (MVG) distribution to model structured correlations within the weights of a DNN. To make posterior inference feasible, a reparametrization is proposed for the MVG prior, simplifying the complex MVG-based model to an equivalent yet simpler model with independent Gaussian priors on the transformed weights. Consequently, we develop a scalable Bayesian online inference algorithm by adopting the recently proposed probabilistic backpropagation framework. Experiments on several synthetic and real datasets indicate the superiority of our model, achieving competitive performance in terms of model likelihood and predictive root mean square error. Importantly, it also yields faster convergence speed compared to related Bayesian DNN models.},
author = {Sun, Shengyang and Chen, Changyou and Carin, Lawrence},
file = {:Users/lisha/Library/Application Support/Mendeley Desktop/Downloaded/Sun, Chen, Carin - 2017 - Learning Structured Weight Uncertainty in Bayesian Neural Networks.pdf:pdf},
journal = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {1283--1292},
title = {{Learning Structured Weight Uncertainty in Bayesian Neural Networks}},
url = {http://proceedings.mlr.press/v54/sun17b.html},
volume = {54},
year = {2017}
}


//// 2018

@inproceedings{Wen_ICLR18_flipout,
title={Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches},
author={Yeming Wen and Paul Vicol and Jimmy Ba and Dustin Tran and Roger Grosse},
booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=rJNpifWAb},
}

@inproceedings{Ritter_ICLR18_laplace,
abstract = {We leverage recent insights from second-order optimisation for neural networks to construct a Kronecker factored Laplace approximation to the posterior over the weights of a trained network. Our approximation requires no modification of the training procedure, enabling practitioners to estimate the uncertainty of their models currently used in production without having to retrain them. We extensively compare our method to using Dropout and a diagonal Laplace approximation for estimating the uncertainty of a network. We demonstrate that our Kronecker factored method leads to better uncertainty estimates on out-of-distribution data and is more robust to simple adversarial attacks. Our approach only requires calculating two square curvature factor matrices for each layer. Their size is equal to the respective square of the input and output size of the layer, making the method efficient both computationally and in terms of memory usage. We illustrate its scalability by applying it to a state-of-the-art convolutional network architecture.},
author = {Ritter, Hippolyt and Botev, Aleksandar and Barber, David},
booktitle = {6th International Conference on Learning Representations, ICLR 2018 - Conference Track Proceedings},
title = {{A scalable laplace approximation for neural networks}},
year = {2018}
}



@InProceedings{Ghosh_ICML18_horseshoePrior,
  title =    {Structured Variational Learning of {B}ayesian Neural Networks with Horseshoe Priors},
  author =   {Ghosh, Soumya and Yao, Jiayu and Doshi-Velez, Finale},
  booktitle =    {Proceedings of the 35th International Conference on Machine Learning},
  pages =    {1744--1753},
  year =   {2018},
  editor =   {Dy, Jennifer and Krause, Andreas},
  volume =   {80},
  series =   {Proceedings of Machine Learning Research},
  address =    {Stockholmsmässan, Stockholm Sweden},
  month =    {10--15 Jul},
  publisher =    {PMLR},
  pdf =    {http://proceedings.mlr.press/v80/ghosh18a/ghosh18a.pdf},
  url =    {http://proceedings.mlr.press/v80/ghosh18a.html},
  abstract =   {Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection—even choosing the number of nodes—remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in smaller-sample settings including reinforcement learning.}
}


@InProceedings{Zhang_ICML18_noisyNGVI,
  title =    {Noisy Natural Gradient as Variational Inference},
  author =   {Zhang, Guodong and Sun, Shengyang and Duvenaud, David and Grosse, Roger},
  booktitle =    {Proceedings of the 35th International Conference on Machine Learning},
  pages =    {5852--5861},
  year =   {2018},
  editor =   {Dy, Jennifer and Krause, Andreas},
  volume =   {80},
  series =   {Proceedings of Machine Learning Research},
  address =    {Stockholmsmässan, Stockholm Sweden},
  month =    {10--15 Jul},
  publisher =    {PMLR},
  pdf =    {http://proceedings.mlr.press/v80/zhang18l/zhang18l.pdf},
  url =    {http://proceedings.mlr.press/v80/zhang18l.html},
  abstract =   {Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g. fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo’s predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.}
}


@InProceedings{Teye_ICML18_MC-batchNorm,
  title = 	 {{B}ayesian Uncertainty Estimation for Batch Normalized Deep Networks},
  author = 	 {Teye, Mattias and Azizpour, Hossein and Smith, Kevin},
  booktitle = 	 {Proceedings of the 35th International Conference on Machine Learning},
  pages = 	 {4907--4916},
  year = 	 {2018},
  editor = 	 {Dy, Jennifer and Krause, Andreas},
  volume = 	 {80},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Stockholmsmässan, Stockholm Sweden},
  month = 	 {10--15 Jul},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v80/teye18a/teye18a.pdf},
  url = 	 {http://proceedings.mlr.press/v80/teye18a.html},
  abstract = 	 {We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using conventional architectures, without modifications to the network or the training procedure. Our approach is thoroughly validated by measuring the quality of uncertainty in a series of empirical experiments on different tasks. It outperforms baselines with strong statistical significance, and displays competitive performance with recent Bayesian approaches.}
}



//// 2019

@incollection{Maddox_NIPS19_SWAG,
title = {A Simple Baseline for Bayesian Uncertainty in Deep Learning},
author = {Maddox, Wesley J and Izmailov, Pavel and Garipov, Timur and Vetrov, Dmitry P and Wilson, Andrew Gordon},
booktitle = {Advances in Neural Information Processing Systems 32},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. {e}-Buc and E. Fox and R. Garnett},
pages = {13132--13143},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/9472-a-simple-baseline-for-bayesian-uncertainty-in-deep-learning.pdf}
}

@incollection{Osawa_NIPS19_NGVI,
title = {Practical Deep Learning with Bayesian Principles},
author = {Osawa, Kazuki and Swaroop, Siddharth and Khan, Mohammad Emtiyaz E and Jain, Anirudh and Eschenhagen, Runa and Turner, Richard E and Yokota, Rio},
booktitle = {Advances in Neural Information Processing Systems 32},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. {e}-Buc and E. Fox and R. Garnett},
pages = {4289--4301},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/8681-practical-deep-learning-with-bayesian-principles.pdf}
}


//// previous

@article{Le2005,
abstract = {This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate vari- ance local ly unlike standard Gaussian Pro- cess regression or SVMs. This means that our estimator adapts to the local noise. The problem is cast in the setting of maximum a posteriori estimation in exponential families. Unlike previous work, we obtain a convex op- timization problem which can be solved via Newtons method.},
author = {Le, Quoc and Smola, Alex and Canu, St{\'{e}}phane},
doi = {10.1145/1102351.1102413},
isbn = {1-59593-180-5},
issn = {01697439},
journal = {Proceedings of the 22nd international conference on Machine learning ICML 05},
keywords = {learning,statistics {\&} optimisation},
pages = {489--496},
title = {{Heteroscedastic Gaussian Process Regression}},
url = {http://eprints.pascal-network.org/archive/00002009/},
volume = {227},
year = {2005}
}


@article{Zhu2017,
abstract = {Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection across millions of metrics. Classical time series models are often used in conjunction with a probabilistic formulation for uncertainty estimation. However, such models are hard to tune, scale, and add exogenous variables to. Motivated by the recent resurgence of Long Short Term Memory networks, we propose a novel end-to-end Bayesian deep model that provides time series prediction along with uncertainty estimation. We provide detailed experiments of the proposed solution on completed trips data, and successfully apply it to large-scale time series anomaly detection at Uber.},
archivePrefix = {arXiv},
arxivId = {1709.01907},
author = {Zhu, Lingxue and Laptev, Nikolay},
doi = {10.1109/ICDMW.2017.19},
eprint = {1709.01907},
file = {:C$\backslash$:/Users/lenovo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhu, Laptev - 2017 - Deep and Confident Prediction for Time Series at Uber.pdf:pdf},
keywords = {anomaly detection,bayesian neural networks,predictive uncertainty,time series},
mendeley-groups = {Ji/confidence},
title = {{Deep and Confident Prediction for Time Series at Uber}},
url = {http://arxiv.org/abs/1709.01907},
year = {2017}
}

@article{Denker1991,
abstract = {(1) The outputs of a typical multi-output classification network do not satisfy the axioms of probability; probabilities should be positive and sum to one. This problem can be solved by treating the trained network as a preprocessor that produces a feature vector that can be further processed, for instance by classical statistical estimation techniques. (2) We present a method for computing the first two moments ofthe probability distribution indicating the range of outputs that are consistent with the input and the training data. It is particularly useful to combine these two ideas: we implement the ideas of section 1 using Parzen windows, where the shape and relative size of each window is computed using the ideas of section 2. This allows us to make contact between important theoretical ideas (e.g. the ensemble formalism) and practical techniques (e.g. back-prop). Our results also shed new light on and generalize the well-known "soft max" scheme.},
archivePrefix = {arXiv},
arxivId = {11359-901120-05},
author = {Denker, John S and LeCun, Yann},
doi = {10.1.1.32.7096},
eprint = {11359-901120-05},
journal = {Advances in Neural Information Processing Systems 3},
pages = {853--859},
title = {{Transforming Neural-Net Output Levels to Probability Distributions}},
url = {http://papers.nips.cc/paper/419-transforming-neural-net-output-levels-to-probability-distributions.pdf{\%}5Cnfiles/4250/Denker ? LeCun - 1991 - Transforming Neural-Net Output Levels to Probabili.pdf{\%}5Cnfiles/4251/419-transforming-neural-net-output-levels-to-},
year = {1991}
}

@article{MacKay1992,
abstract = {A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained.},
author = {MacKay, David J. C.},
doi = {10.1162/neco.1992.4.3.448},
isbn = {0899-7667},
issn = {0899-7667},
journal = {Neural Computation},
number = {3},
pages = {448--472},
title = {{A Practical Bayesian Framework for Backpropagation Networks}},
url = {http://www.mitpressjournals.org/doi/10.1162/neco.1992.4.3.448},
volume = {4},
year = {1992}
}

@article{Warner1997,
abstract = {Two features distinguish the Bayesian approach to learning models from data. First, beliefs derived from background knowledge are used to select a prior probability distribution for the model parameters. Second, predictions of future observations are made by integrating the model's predictions with respect to the posterior parameter distribution obtained by updating this prior to take account of the data. For neural network models, both these aspects present diiculties | the prior over network parameters has no obvious relation to our prior knowledge, and integration over the posterior is computationally very demanding. I address the problem by deening classes of prior distributions for network param-eters that reach sensible limits as the size of the network goes to innnity. In this limit, the properties of these priors can be elucidated. Some priors converge to Gaussian processes, in which functions computed by the network may be smooth, Brownian, or fractionally Brownian. Other priors converge to non-Gaussian stable processes. Interesting eeects are obtained by combining priors of both sorts in networks with more than one hidden layer.},
author = {Warner, Bradley a. and Neal, Radford M.},
doi = {10.2307/2965731},
isbn = {0387947248},
issn = {01621459},
journal = {Journal of the American Statistical Association},
keywords = {Automatic Relevance Detarmination,Gaussian Process,Neal},
pages = {791},
pmid = {3473},
title = {{Bayesian Learning for Neural Networks}},
url = {http://www.jstor.org/stable/2965731?origin=crossref},
volume = {92},
year = {1997}
}

@article{Graves2011,
abstract = {Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.},
author = {Graves, Alex},
isbn = {9781618395993},
journal = {Nips},
pages = {1--9},
title = {{Practical Variational Inference for Neural Networks.}},
url = {https://papers.nips.cc/paper/4329-practical-variational-inference-for-neural-networks.pdf},
year = {2011}
}



@article{Hernandez-Lobato2015,
abstract = {Black-box alpha (BB-$\alpha$) is a new approximate inference method based on the minimization of $\alpha$-divergences. BB-$\alpha$ scales to large datasets because it can be implemented using stochastic gradient descent. BB-$\alpha$ can be applied to com- plex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter$\alpha$, the method is able to interpolate between variational Bayes (VB) ($\alpha$→0) and an algorithm similar to expec- tation propagation (EP) ($\alpha$ = 1). Experiments on probit regression and neural network regression and classification problems show that BB-$\alpha$ with non-standard settings of $\alpha$, such as $\alpha$ = 0.5, usu- ally produces better predictions than with $\alpha$→0 (VB) or $\alpha$ = 1 (EP).},
archivePrefix = {arXiv},
arxivId = {arXiv:1511.03243v1},
author = {Hern{\'{a}}ndez-Lobato, Jos{\'{e}} Miguel and Li, Yingzhen and Hern{\'{a}}ndez-Lobato, Daniel and Bui, Thang and Turner, Richard},
eprint = {arXiv:1511.03243v1},
isbn = {9781510829008},
issn = {1938-7228},
journal = {Black box learning {\&} inference workshop (NIPS)},
pages = {1--5},
title = {{Black-box $\alpha$ divergence Minimization}},
year = {2015}
}



@inproceedings{Gal_ICLR16Workshop_bernoulliVI,
Author = {Yarin Gal and Zoubin Ghahramani},
Title = {Bayesian Convolutional Neural Networks with {B}ernoulli Approximate Variational Inference},
Year = {2016},
booktitle = {4th International Conference on Learning Representations (ICLR) workshop track},
}



@article{Srivastava2014,
abstract = {Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different " thinned " networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.},
archivePrefix = {arXiv},
arxivId = {1102.4807},
author = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
doi = {10.1214/12-AOS1000},
eprint = {1102.4807},
isbn = {1532-4435},
issn = {15337928},
journal = {Journal of Machine Learning Research},
keywords = {deep learning,model combination,neural networks,regularization},
pages = {1929--1958},
pmid = {23285570},
title = {{Dropout: A Simple Way to Prevent Neural Networks from Overfitting}},
volume = {15},
year = {2014}
}


@article{Miyato2016,
abstract = {Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations to numerous entries of the input vector, which is inappropriate for sparse high-dimensional inputs such as one-hot word representations. We extend adversarial and virtual adversarial training to the text domain by applying perturbations to the word embeddings in a recurrent neural network rather than to the original input itself. The proposed method achieves state of the art results on multiple benchmark semi-supervised and purely supervised tasks. We provide visualizations and analysis showing that the learned word embeddings have improved in quality and that while training, the model is less prone to overfitting.},
archivePrefix = {arXiv},
arxivId = {1605.07725},
author = {Miyato, Takeru and Dai, Andrew M. and Goodfellow, Ian},
doi = {10.2507/daaam.scibook.2010.27},
eprint = {1605.07725},
isbn = {2840601737},
issn = {17269687},
journal = {arXiv},
number = {2015},
pages = {1--9},
pmid = {19963286},
title = {{Virtual Adversarial Training for Semi-Supervised Text Classification}},
url = {http://arxiv.org/abs/1605.07725},
year = {2016}
}

// dropout

@article{Hinton2012,
abstract = {When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.},
archivePrefix = {arXiv},
arxivId = {1207.0580},
author = {Hinton, Geoffrey E. and Srivastava, Nitish and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan R.},
doi = {arXiv:1207.0580},
eprint = {1207.0580},
file = {:D$\backslash$:/Lisha/document/reference/confidence/BNN/dropout/1207.0580.pdf:pdf},
isbn = {9781467394673},
issn = {9781467394673},
mendeley-groups = {Ji/confidence/BNN/dropout},
pages = {1--18},
pmid = {1000104337},
title = {{Improving neural networks by preventing co-adaptation of feature detectors}},
url = {http://arxiv.org/abs/1207.0580},
year = {2012}
}




@article{Gal2015dropout,
abstract = {Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.},
archivePrefix = {arXiv},
arxivId = {1506.02142},
author = {Gal, Yarin and Ghahramani, Zoubin},
doi = {10.1109/TKDE.2015.2507132},
eprint = {1506.02142},
file = {:D$\backslash$:/Lisha/document/reference/confidence/BNN/dropout/dropout.pdf:pdf},
isbn = {1506.02142},
issn = {1938-7228},
mendeley-groups = {Ji/confidence/BNN/dropout},
pmid = {88045},
title = {{Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning}},
url = {http://arxiv.org/abs/1506.02142},
volume = {48},
year = {2015}
}



// library

@article{Shi2017zhusuan,
abstract = {In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.},
archivePrefix = {arXiv},
arxivId = {1709.05870},
author = {Shi, Jiaxin and Chen, Jianfei and Zhu, Jun and Sun, Shengyang and Luo, Yucen and Gu, Yihong and Zhou, Yuhao},
eprint = {1709.05870},
file = {:C$\backslash$:/Users/ziheng/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Shi et al. - 2017 - ZhuSuan A Library for Bayesian Deep Learning.pdf:pdf},
keywords = {bayesian inference,deep gen-,deep learning,probabilistic programming},
mendeley-groups = {Ji/confidence/BDL,Ji/confidence/BNN},
pages = {1--29},
title = {{ZhuSuan: A Library for Bayesian Deep Learning}},
url = {http://arxiv.org/abs/1709.05870},
year = {2017}
}

@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}
}

@inproceedings{tran2017edward,
  author = {Dustin Tran and Matthew D. Hoffman and Rif A. Saurous and Eugene Brevdo and Kevin Murphy and David M. Blei},
  title = {Deep probabilistic programming},
  booktitle = {International Conference on Learning Representations},
  year = {2017}
}


@misc{UberPyro,
  author = {Noah Goodman},
  title = {Uber AI Labs Open Sources Pyro, a Deep Probabilistic Programming Language},
  note = {Available at \url{https://eng.uber.com/pyro/}, last access 2018-01-12}
}




// other confidence model literature review



// dataset


// dataset


	@MISC{FAN_model,
	author = {Adrian Bulat and Georgios Tzimiropoulos},
	title = {How far are we from solving the 2D \& 3D Face Alignment problem?
(and a dataset of 230,000 3D facial landmarks)},
	url = {https://adrianbulat.com/face-alignment},
	note = {\url{https://adrianbulat.com/face-alignment}, accessed 02-November-2018},
	}


// accidents

	@MISC{uber-accident,
	author = {Mark Rosenker and Amitai Bin-Nun},
	title = {After tragic self-driving Uber accident, the government needs to set safety standards},
	editor = {USA Today},
	month = {April},
	year = {2018},
	url = {https://www.usatoday.com/story/opinion/2018/03/30/after-tragic-self-driving-uber-accident-government-needs-set-safety-standards-column/460114002/},
	}

	@MISC{Tesla-accident,
	author = {Marco della Cava},
	title = {Tesla Model S was on Autopilot, Utah driver tells police},
	editor = {USA Today},
	month = {May},
	year = {2018},
	url = {https://www.usatoday.com/story/tech/2018/05/14/tesla-model-s-crash-utah-involved-autopilot-distracted-driver/609596002/},
	}
	

// aleatoric uncertainty

	@inproceedings{Nix1994,
	abstract = {Introduces a method that estimates the mean and the variance of the probability distribution of the target as a function of the input, given an assumed target error-distribution model. Through the activation of an auxiliary output unit, this method provides a measure of the uncertainty of the usual network output for each input pattern. The authors derive the cost function and weight-update equations for the example of a Gaussian target error distribution, and demonstrate the feasibility of the network on a synthetic problem where the true input-dependent noise level is known.},
	author = {Nix, D.A. and Weigend, A.S.},
	booktitle = {Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94)},
	doi = {10.1109/ICNN.1994.374138},
	isbn = {0-7803-1901-X},
	pages = {55--60 vol.1},
	title = {{Estimating the mean and variance of the target probability distribution}},
	url = {http://ieeexplore.ieee.org/document/374138/},
	year = {1994}
	}

	@article{Le2005,
	abstract = {This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate vari- ance local ly unlike standard Gaussian Pro- cess regression or SVMs. This means that our estimator adapts to the local noise. The problem is cast in the setting of maximum a posteriori estimation in exponential families. Unlike previous work, we obtain a convex op- timization problem which can be solved via Newtons method.},
	author = {Le, Quoc and Smola, Alex and Canu, St{\'{e}}phane},
	doi = {10.1145/1102351.1102413},
	isbn = {1-59593-180-5},
	issn = {01697439},
	journal = {Proceedings of the 22nd international conference on Machine learning ICML 05},
	keywords = {learning,statistics {\&} optimisation},
	pages = {489--496},
	title = {{Heteroscedastic Gaussian Process Regression}},
	url = {http://eprints.pascal-network.org/archive/00002009/},
	volume = {227},
	year = {2005}
	}

	@book{Goodfellow-et-al-2016,
    title={Deep Learning},
    author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher={MIT Press},
    note={\url{http://www.deeplearningbook.org}},
    year={2016}
	}

	@inproceedings{Ng17Gamma,
	  author    = {Nathan H. Ng and
	               Rodney A. Gabriel and
	               Julian McAuley and
	               Charles Elkan and
	               Zachary C. Lipton},
	  title     = {Predicting Surgery Duration with Neural Heteroscedastic Regression},
	  booktitle = {{MLHC}},
	  series    = {Proceedings of Machine Learning Research},
	  volume    = {68},
	  pages     = {100--111},
	  publisher = {{PMLR}},
	  year      = {2017}
	}

// Epistemic uncertainty



@book{Abu-Mostafa2012,
 author = {Abu-Mostafa, Yaser S. and Magdon-Ismail, Malik and Lin, Hsuan-Tien},
 title = {Learning From Data},
 year = {2012},
 isbn = {1600490069, 9781600490064},
 publisher = {AMLBook},
} 

@book{weiss2006,
  title={A Course in Probability},
  author={Weiss, N.A. and Holmes, P.T. and Hardy, M.},
  isbn={9780201774719},
  lccn={2004051068},
  url={https://books.google.com/books?id=Be9fJwAACAAJ},
  year={2006},
  publisher={Pearson Addison Wesley}
}

@book{Mahler2001,
title={Foundations of Casualty Actuarial Science},
edition={4th},
publisher={Casualty Actuarial Society},
author={Mahler, Howard C. and Dean, Curtis Gary},
year={2001},
isbn={9780962476228},
chapter={8},
pages={525–526}
}


//BNN literature review

@article{Kendall2017,
abstract = {There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks.},
archivePrefix = {arXiv},
arxivId = {1703.04977},
author = {Kendall, Alex and Gal, Yarin},
eprint = {1703.04977},
file = {:D$\backslash$:/Lisha/document/reference/confidence/BNN/what uncertainties do we need.pdf:pdf},
mendeley-groups = {Ji/confidence/BNN/model},
number = {Nips},
title = {{What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?}},
url = {http://arxiv.org/abs/1703.04977},
year = {2017}
}

@article{Lakshminarayanan2016,
abstract = {Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which learn a distribution over weights, are currently the state-of-the-art for estimating predictive uncertainty; however these require significant modifications to the training procedure and are computationally expensive compared to standard (non-Bayesian) NNs. We propose an alternative to Bayesian NNs that is simple to implement, readily parallelizable, requires very little hyperparameter tuning, and yields high quality predictive uncertainty estimates. Through a series of experiments on classification and regression benchmarks, we demonstrate that our method produces well-calibrated uncertainty estimates which are as good or better than approximate Bayesian NNs. To assess robustness to dataset shift, we evaluate the predictive uncertainty on test examples from known and unknown distributions, and show that our method is able to express higher uncertainty on out-of-distribution examples. We demonstrate the scalability of our method by evaluating predictive uncertainty estimates on ImageNet.},
archivePrefix = {arXiv},
arxivId = {1612.01474},
author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
eprint = {1612.01474},
file = {:G$\backslash$:/Ji/reference/confidence/ensemble.pdf:pdf},
mendeley-groups = {Ji/confidence},
title = {{Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles}},
url = {http://arxiv.org/abs/1612.01474},
year = {2016}
}





@article{Zhu2017,
abstract = {Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection across millions of metrics. Classical time series models are often used in conjunction with a probabilistic formulation for uncertainty estimation. However, such models are hard to tune, scale, and add exogenous variables to. Motivated by the recent resurgence of Long Short Term Memory networks, we propose a novel end-to-end Bayesian deep model that provides time series prediction along with uncertainty estimation. We provide detailed experiments of the proposed solution on completed trips data, and successfully apply it to large-scale time series anomaly detection at Uber.},
archivePrefix = {arXiv},
arxivId = {1709.01907},
author = {Zhu, Lingxue and Laptev, Nikolay},
doi = {10.1109/ICDMW.2017.19},
eprint = {1709.01907},
file = {:C$\backslash$:/Users/lenovo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhu, Laptev - 2017 - Deep and Confident Prediction for Time Series at Uber.pdf:pdf},
keywords = {anomaly detection,bayesian neural networks,predictive uncertainty,time series},
mendeley-groups = {Ji/confidence},
title = {{Deep and Confident Prediction for Time Series at Uber}},
url = {http://arxiv.org/abs/1709.01907},
year = {2017}
}

@article{Denker1991,
abstract = {(1) The outputs of a typical multi-output classification network do not satisfy the axioms of probability; probabilities should be positive and sum to one. This problem can be solved by treating the trained network as a preprocessor that produces a feature vector that can be further processed, for instance by classical statistical estimation techniques. (2) We present a method for computing the first two moments ofthe probability distribution indicating the range of outputs that are consistent with the input and the training data. It is particularly useful to combine these two ideas: we implement the ideas of section 1 using Parzen windows, where the shape and relative size of each window is computed using the ideas of section 2. This allows us to make contact between important theoretical ideas (e.g. the ensemble formalism) and practical techniques (e.g. back-prop). Our results also shed new light on and generalize the well-known "soft max" scheme.},
archivePrefix = {arXiv},
arxivId = {11359-901120-05},
author = {Denker, John S and LeCun, Yann},
doi = {10.1.1.32.7096},
eprint = {11359-901120-05},
journal = {Advances in Neural Information Processing Systems 3},
pages = {853--859},
title = {{Transforming Neural-Net Output Levels to Probability Distributions}},
url = {http://papers.nips.cc/paper/419-transforming-neural-net-output-levels-to-probability-distributions.pdf{\%}5Cnfiles/4250/Denker ? LeCun - 1991 - Transforming Neural-Net Output Levels to Probabili.pdf{\%}5Cnfiles/4251/419-transforming-neural-net-output-levels-to-},
year = {1991}
}

@article{Warner1997,
abstract = {Two features distinguish the Bayesian approach to learning models from data. First, beliefs derived from background knowledge are used to select a prior probability distribution for the model parameters. Second, predictions of future observations are made by integrating the model's predictions with respect to the posterior parameter distribution obtained by updating this prior to take account of the data. For neural network models, both these aspects present diiculties | the prior over network parameters has no obvious relation to our prior knowledge, and integration over the posterior is computationally very demanding. I address the problem by deening classes of prior distributions for network param-eters that reach sensible limits as the size of the network goes to innnity. In this limit, the properties of these priors can be elucidated. Some priors converge to Gaussian processes, in which functions computed by the network may be smooth, Brownian, or fractionally Brownian. Other priors converge to non-Gaussian stable processes. Interesting eeects are obtained by combining priors of both sorts in networks with more than one hidden layer.},
author = {Warner, Bradley a. and Neal, Radford M.},
doi = {10.2307/2965731},
isbn = {0387947248},
issn = {01621459},
journal = {Journal of the American Statistical Association},
keywords = {Automatic Relevance Detarmination,Gaussian Process,Neal},
pages = {791},
pmid = {3473},
title = {{Bayesian Learning for Neural Networks}},
url = {http://www.jstor.org/stable/2965731?origin=crossref},
volume = {92},
year = {1997}
}

@article{Graves2011,
abstract = {Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.},
author = {Graves, Alex},
isbn = {9781618395993},
journal = {Nips},
pages = {1--9},
title = {{Practical Variational Inference for Neural Networks.}},
url = {https://papers.nips.cc/paper/4329-practical-variational-inference-for-neural-networks.pdf},
year = {2011}
}


@article{Blundell2015,
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.},
archivePrefix = {arXiv},
arxivId = {1505.05424},
author = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
eprint = {1505.05424},
file = {:C$\backslash$:/Users/lenovo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Blundell et al. - 2015 - Weight Uncertainty in Neural Networks.pdf:pdf},
isbn = {9781510810587},
mendeley-groups = {Ji/confidence},
title = {{Weight Uncertainty in Neural Networks}},
url = {http://arxiv.org/abs/1505.05424},
volume = {37},
year = {2015}
}




@article{Hernandez-Lobato2015,
abstract = {Black-box alpha (BB-$\alpha$) is a new approximate inference method based on the minimization of $\alpha$-divergences. BB-$\alpha$ scales to large datasets because it can be implemented using stochastic gradient descent. BB-$\alpha$ can be applied to com- plex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be eas- ily obtained using automatic differentiation. By changing the divergence parameter$\alpha$, the method is able to interpolate between variational Bayes (VB) ($\alpha$→0) and an algorithm similar to expec- tation propagation (EP) ($\alpha$ = 1). Experiments on probit regression and neural network regression and classification problems show that BB-$\alpha$ with non-standard settings of $\alpha$, such as $\alpha$ = 0.5, usu- ally produces better predictions than with $\alpha$→0 (VB) or $\alpha$ = 1 (EP).},
archivePrefix = {arXiv},
arxivId = {arXiv:1511.03243v1},
author = {Hern{\'{a}}ndez-Lobato, Jos{\'{e}} Miguel and Li, Yingzhen and Hern{\'{a}}ndez-Lobato, Daniel and Bui, Thang and Turner, Richard},
eprint = {arXiv:1511.03243v1},
isbn = {9781510829008},
issn = {1938-7228},
journal = {Black box learning {\&} inference workshop (NIPS)},
pages = {1--5},
title = {{Black-box $\alpha$ divergence Minimization}},
year = {2015}
}



@article{Gal2015,
abstract = {Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10.},
archivePrefix = {arXiv},
arxivId = {1506.02158},
author = {Gal, Yarin and Ghahramani, Zoubin},
doi = {10.1029/2003JD002581},
eprint = {1506.02158},
file = {:G$\backslash$:/Ji/reference/confidence/1506.02158.pdf:pdf},
isbn = {9781611970685},
issn = {0004-6361},
mendeley-groups = {Ji/confidence},
pages = {1--12},
pmid = {23459267},
title = {{Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference}},
url = {http://arxiv.org/abs/1506.02158},
year = {2015}
}



@article{Srivastava2014,
abstract = {Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different " thinned " networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.},
archivePrefix = {arXiv},
arxivId = {1102.4807},
author = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
doi = {10.1214/12-AOS1000},
eprint = {1102.4807},
isbn = {1532-4435},
issn = {15337928},
journal = {Journal of Machine Learning Research},
keywords = {deep learning,model combination,neural networks,regularization},
pages = {1929--1958},
pmid = {23285570},
title = {{Dropout: A Simple Way to Prevent Neural Networks from Overfitting}},
volume = {15},
year = {2014}
}


@article{Miyato2016,
abstract = {Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations to numerous entries of the input vector, which is inappropriate for sparse high-dimensional inputs such as one-hot word representations. We extend adversarial and virtual adversarial training to the text domain by applying perturbations to the word embeddings in a recurrent neural network rather than to the original input itself. The proposed method achieves state of the art results on multiple benchmark semi-supervised and purely supervised tasks. We provide visualizations and analysis showing that the learned word embeddings have improved in quality and that while training, the model is less prone to overfitting.},
archivePrefix = {arXiv},
arxivId = {1605.07725},
author = {Miyato, Takeru and Dai, Andrew M. and Goodfellow, Ian},
doi = {10.2507/daaam.scibook.2010.27},
eprint = {1605.07725},
isbn = {2840601737},
issn = {17269687},
journal = {arXiv},
number = {2015},
pages = {1--9},
pmid = {19963286},
title = {{Virtual Adversarial Training for Semi-Supervised Text Classification}},
url = {http://arxiv.org/abs/1605.07725},
year = {2016}
}

// dropout

@article{Hinton2012,
abstract = {When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.},
archivePrefix = {arXiv},
arxivId = {1207.0580},
author = {Hinton, Geoffrey E. and Srivastava, Nitish and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan R.},
doi = {arXiv:1207.0580},
eprint = {1207.0580},
file = {:D$\backslash$:/Lisha/document/reference/confidence/BNN/dropout/1207.0580.pdf:pdf},
isbn = {9781467394673},
issn = {9781467394673},
mendeley-groups = {Ji/confidence/BNN/dropout},
pages = {1--18},
pmid = {1000104337},
title = {{Improving neural networks by preventing co-adaptation of feature detectors}},
url = {http://arxiv.org/abs/1207.0580},
year = {2012}
}







// mix density

@inproceedings{Nowozin2018MixdensityPose,
  author    = {Sergey Prokudin and
               Peter V. Gehler and
               Sebastian Nowozin},
  title     = {Deep Directional Statistics: Pose Estimation with Uncertainty Quantification},
  booktitle = {Computer Vision - {ECCV} 2018 - 15th European Conference, Munich, Germany, September 8-14, 2018, Proceedings, Part {IX}},
  pages     = {542--559},
  year      = {2018},
  crossref  = {DBLP:conf/eccv/2018-9},
  url       = {https://doi.org/10.1007/978-3-030-01240-3\_33},
  doi       = {10.1007/978-3-030-01240-3\_33},
  timestamp = {Mon, 08 Oct 2018 17:08:07 +0200},
  biburl    = {https://dblp.org/rec/bib/conf/eccv/ProkudinGN18},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

@TECHREPORT{Bishop94mixturedensity,
    author = {Christopher M. Bishop},
    title = {Mixture density networks},
    institution = {},
    year = {1994}
}

// kde

@TECHREPORT{Bishop94mixturedensity,
    author = {Christopher M. Bishop},
    title = {Mixture density networks},
    institution = {},
    year = {1994}
}

@BOOK{kde96,
  TITLE = {Smoothing Methods in Statistics},
  AUTHOR = {Jeffrey S. Simonoff},
  YEAR = {1996},
  PUBLISHER = {Springer},
  ISBN={0-387-94716-7}
}



// face alignment


SDM
@inproceedings{Xiong13SDM,
author = {Xuehan Xiong and Fernando De la Torre Frade},
title = {Supervised Descent Method and its Applications to Face Alignment},
booktitle = {IEEE International Conference on Computer Vision and Pattern Recognition (CVPR)},
year = {2013},
month = {May},
keywords = {tracking, face alignment, facial feature detection, nonlinear least squares},
}

@inproceedings{Xiong15cascade_GSDM,
  author    = {Xuehan Xiong and
               Fernando De la Torre},
  title     = {Global supervised descent method},
  booktitle = {{CVPR}},
  pages     = {2664--2673},
  publisher = {{IEEE} Computer Society},
  year      = {2015}
}

////ASM

@inproceedings{Milborrow08ASM_LFF,
 author = {Milborrow, Stephen and Nicolls, Fred},
 title = {Locating Facial Features with an Extended Active Shape Model},
 booktitle = {Proceedings of the 10th European Conference on Computer Vision: Part IV},
 series = {ECCV '08},
 year = {2008},
 isbn = {978-3-540-88692-1},
 location = {Marseille, France},
 pages = {504--513},
 numpages = {10},
 url = {http://dx.doi.org/10.1007/978-3-540-88693-8_37},
 doi = {10.1007/978-3-540-88693-8_37},
 acmid = {1478275},
 publisher = {Springer-Verlag},
 address = {Berlin, Heidelberg},
} 

//// AAM

@InProceedings{Cootes98AAM,
author="Cootes, T. F.
and Edwards, G. J.
and Taylor, C. J.",
editor="Burkhardt, Hans
and Neumann, Bernd",
title="Active appearance models",
booktitle="Computer Vision --- ECCV'98",
year="1998",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="484--498",
}

@ARTICLE{Kahraman10AAM,
    author       = "F. Kahraman and G. Muhitin and S. Darkner and R. Larsen",
    title        = "An Active Illumination and Appearance Model for Face Alignment",
    year         = "2010",
    pages        = "677-692",
    journal      = "Turkish Journal of  Electrical Engineering and Computer Science",
    volume       = "18",
    editor       = "",
    number       = "4",
    publisher    = "",
    url          = "http://www2.imm.dtu.dk/pubdb/p.php?6179",
}
 
@Article{Matthews04AAM,
author="Matthews, Iain and Baker, Simon",
title="Active Appearance Models Revisited",
journal="International Journal of Computer Vision",
year="2004",
month="Nov",
day="01",
volume="60",
number="2",
pages="135--164",
issn="1573-1405",
doi="10.1023/B:VISI.0000029666.37597.d3",
url="https://doi.org/10.1023/B:VISI.0000029666.37597.d3"
}


@inproceedings{Saragih07AAM,
 author = {Saragih, J. and Goecke, R.},
 booktitle = {2007 IEEE 11th International Conference on Computer Vision},
 doi = {10.1109/iccv.2007.4409106},
 keywords = {Psychology},
 note = {Exported from https://app.dimensions.ai on 2018/11/15},
 pages = {1-8},
 title = {A Nonlinear Discriminative Approach to AAM Fitting},
 url = {https://app.dimensions.ai/details/publication/pub.1094990039 and http://users.rsise.anu.edu.au/~roland/Publications/SaragihGoecke_ICCV2007.pdf},
 year = {2007}
}

//// CLM

@InProceedings{Neeraj08CLM_facetracer,
author = {Neeraj Kumar and Peter N. Belhumeur and Shree K. Nayar},
title = {FaceTracer: A Search Engine for Large Collections of Images with Faces},
booktitle = {The 10th European Conference on Computer Vision (ECCV)},
month = {October},
year = {2008}
}

@Article{Saragih11CLM,
author="Saragih, Jason M.
and Lucey, Simon
and Cohn, Jeffrey F.",
title="Deformable Model Fitting by Regularized Landmark Mean-Shift",
journal="International Journal of Computer Vision",
year="2011",
month="Jan",
day="01",
volume="91",
number="2",
pages="200--215",
issn="1573-1405",
doi="10.1007/s11263-010-0380-4",
url="https://doi.org/10.1007/s11263-010-0380-4"
}

//// cascade

@inproceedings{Burgos-Artizzu13cascade_COFW,
 author = {Burgos-Artizzu, Xavier P. and Perona, Pietro and Doll\'{a}r, Piotr},
 title = {Robust Face Landmark Estimation Under Occlusion},
 booktitle = {Proceedings of the 2013 IEEE International Conference on Computer Vision},
 series = {ICCV '13},
 year = {2013},
 isbn = {978-1-4799-2840-8},
 pages = {1513--1520},
 numpages = {8},
 url = {http://dx.doi.org/10.1109/ICCV.2013.191},
 doi = {10.1109/ICCV.2013.191},
 acmid = {2587092},
 publisher = {IEEE Computer Society},
 address = {Washington, DC, USA},
 keywords = {Face shape, Face recognition, Landmark estimation, Pose estimation},
} 

@Article{Cao14cascade_ESR,
author="Cao, Xudong
and Wei, Yichen
and Wen, Fang
and Sun, Jian",
title="Face Alignment by Explicit Shape Regression",
journal="International Journal of Computer Vision",
year="2014",
month="Apr",
day="01",
volume="107",
number="2",
pages="177--190",
issn="1573-1405",
doi="10.1007/s11263-013-0667-3",
url="https://doi.org/10.1007/s11263-013-0667-3"
}

@InProceedings{Chen14cascade,
author="Chen, Dong
and Ren, Shaoqing
and Wei, Yichen
and Cao, Xudong
and Sun, Jian",
editor="Fleet, David
and Pajdla, Tomas
and Schiele, Bernt
and Tuytelaars, Tinne",
title="Joint Cascade Face Detection and Alignment",
booktitle="Computer Vision -- ECCV 2014",
year="2014",
publisher="Springer International Publishing",
address="Cham",
pages="109--122",
isbn="978-3-319-10599-4"
}


@article{Zhu16cascade_UnconstrainedFA,
  title={Unconstrained Face Alignment via Cascaded Compositional Learning},
  author={Shizhan Zhu and Cheng Li and Chen Change Loy and Xiaoou Tang},
  journal={2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2016},
  pages={3409-3417}
}

@inproceedings{Zhu15cascade_,
  author = {Zhu, Shizhan and Li, Cheng and Loy, Chen Change and Tang, Xiaoou},
  biburl = {https://www.bibsonomy.org/bibtex/2d9ea0567d383fa93d8960453328f8e77/dblp},
  booktitle = {CVPR},
  crossref = {conf/cvpr/2015},
  ee = {http://doi.ieeecomputersociety.org/10.1109/CVPR.2015.7299134},
  interhash = {6cf867094d546ca548917513f53a53a6},
  intrahash = {d9ea0567d383fa93d8960453328f8e77},
  isbn = {978-1-4673-6964-0},
  keywords = {dblp},
  pages = {4998-5006},
  publisher = {IEEE Computer Society},
  timestamp = {2016-04-29T11:54:14.000+0200},
  title = {Face alignment by coarse-to-fine shape searching.},
  url = {http://dblp.uni-trier.de/db/conf/cvpr/cvpr2015.html#ZhuLLT15},
  year = 2015
}



//// Hour Glass
@inproceedings{Newell16Hourglass,
  author    = {Alejandro Newell and
               Kaiyu Yang and
               Jia Deng},
  title     = {Stacked Hourglass Networks for Human Pose Estimation},
  booktitle = {Computer Vision - {ECCV} 2016 - 14th European Conference, Amsterdam,
               The Netherlands, October 11-14, 2016, Proceedings, Part {VIII}},
  pages     = {483--499},
  year      = {2016},
  crossref  = {DBLP:conf/eccv/2016-8},
  url       = {https://doi.org/10.1007/978-3-319-46484-8\_29},
  doi       = {10.1007/978-3-319-46484-8\_29},
  timestamp = {Fri, 19 May 2017 01:25:55 +0200},
  biburl    = {https://dblp.org/rec/bib/conf/eccv/NewellYD16},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}


//// Fully convolutional network

@inproceedings{Long15FCNN,
  author    = {Jonathan Long and
               Evan Shelhamer and
               Trevor Darrell},
  title     = {Fully convolutional networks for semantic segmentation},
  booktitle = {{IEEE} Conference on Computer Vision and Pattern Recognition, {CVPR}
               2015, Boston, MA, USA, June 7-12, 2015},
  pages     = {3431--3440},
  year      = {2015},
  crossref  = {DBLP:conf/cvpr/2015},
  url       = {https://doi.org/10.1109/CVPR.2015.7298965},
  doi       = {10.1109/CVPR.2015.7298965},
  timestamp = {Thu, 25 May 2017 01:00:00 +0200},
  biburl    = {https://dblp.org/rec/bib/conf/cvpr/LongSD15},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

//// heatmap pose
@inproceedings{Tompson14heatmapPose,
 author = {Tompson, Jonathan and Jain, Arjun and LeCun, Yann and Bregler, Christoph},
 title = {Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation},
 booktitle = {Proceedings of the 27th International Conference on Neural Information Processing Systems - Volume 1},
 series = {NIPS'14},
 year = {2014},
 location = {Montreal, Canada},
 pages = {1799--1807},
 numpages = {9},
 url = {http://dl.acm.org/citation.cfm?id=2968826.2969027},
 acmid = {2969027},
 publisher = {MIT Press},
 address = {Cambridge, MA, USA},
} 

@inproceedings{Wei16openpose,
  author    = {Shih{-}En Wei and
               Varun Ramakrishna and
               Takeo Kanade and
               Yaser Sheikh},
  title     = {Convolutional Pose Machines},
  booktitle = {2016 {IEEE} Conference on Computer Vision and Pattern Recognition,
               {CVPR} 2016, Las Vegas, NV, USA, June 27-30, 2016},
  pages     = {4724--4732},
  year      = {2016},
  crossref  = {DBLP:conf/cvpr/2016},
  url       = {https://doi.org/10.1109/CVPR.2016.511},
  doi       = {10.1109/CVPR.2016.511},
  timestamp = {Thu, 25 May 2017 01:00:00 +0200},
  biburl    = {https://dblp.org/rec/bib/conf/cvpr/WeiRKS16},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}


heatmap regression loss study

@article{sun17integral,
  title={Integral human pose regression},
  author={Sun, Xiao and Xiao, Bin and Liang, Shuang and Wei, Yichen},
  journal={arXiv preprint arXiv:1711.08229},
  year={2017}
}

@article{sun18integral,
  title={An Integral Pose Regression System for the ECCV2018 PoseTrack Challenge},
  author={Sun, Xiao and Li, Chuankang and Lin, Stephen},
  journal={arXiv preprint arXiv:1809.06079},
  year={2018}
}

// softmax
maskrcnn (body joint)
@inproceedings{he17maskrcnn,
	Author    = {Kaiming He and Georgia Gkioxari and
	             Piotr Doll\'{a}r and Ross Girshick},
	Title     = {{Mask R-CNN}},
	Booktitle = {Proceedings of the International
	             Conference on Computer Vision ({ICCV})},
	Year = {2017}}

(face age)

@article{Pan18faceage_meanvarloss,
author = {Pan, Hongyu and Han, Hu and Shan, Shiguang and Chen, Xilin},
doi = {10.1109/CVPR.2018.00554},
file = {:Users/lisha/Library/Application Support/Mendeley Desktop/Downloaded/Pan et al. - Unknown - Mean-Variance Loss for Deep Age Estimation from a Face.pdf:pdf},
journal = {CVPR 2018},
pages = {5285--5294},
title = {{Mean-Variance Loss for Deep Age Estimation from a Face}},
url = {http://openaccess.thecvf.com/content{\_}cvpr{\_}2018/papers/Pan{\_}Mean-Variance{\_}Loss{\_}for{\_}CVPR{\_}2018{\_}paper.pdf}
}


// sigmoid
@article{Papandreou17bodypose_sigmoid,
  title={Towards Accurate Multi-person Pose Estimation in the Wild},
  author={George Papandreou and Tyler Zhu and Nori Kanazawa and Alexander Toshev and Jonathan Tompson and Christoph Bregler and Kevin P. Murphy},
  journal={2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2017},
  pages={3711-3719}
}

@inproceedings{Insafutdinov16bodypose_sigmoid_DeeperCutAD,
  title={DeeperCut: A Deeper, Stronger, and Faster Multi-Person Pose Estimation Model},
  author={Eldar Insafutdinov and Leonid Pishchulin and Bjoern Andres and Mykhaylo Andriluka and Bernt Schiele},
  booktitle={ECCV},
  year={2016}
}

@article{Pishchulin16bodypose_sigmoid_DeepCutJS,
  title={DeepCut: Joint Subset Partition and Labeling for Multi Person Pose Estimation},
  author={Leonid Pishchulin and Eldar Insafutdinov and Siyu Tang and Bjoern Andres and Mykhaylo Andriluka and Peter V. Gehler and Bernt Schiele},
  journal={2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2016},
  pages={4929-4937}
}

//softlb

@inproceedings{Bulat16bodypose_softlb_HumanPE,
  title={Human pose estimation via Convolutional Part Heatmap Regression},
  author={Adrian Bulat and Georgios Tzimiropoulos},
  booktitle={ECCV},
  year={2016}
}

@article{Cao17bodypose_softlb_RealtimeM2,
  title={Realtime Multi-person 2D Pose Estimation Using Part Affinity Fields},
  author={Zhe Cao and Tomas Simon and Shih-En Wei and Yaser Sheikh},
  journal={2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2017},
  pages={1302-1310}
}



@article{Chen17bodypose_softlb_AdversarialPA,
  title={Adversarial PoseNet: A Structure-Aware Convolutional Network for Human Pose Estimation},
  author={Yu Chen and Chunhua Shen and Xiu-Shen Wei and Lingqiao Liu and Jian Yang},
  journal={2017 IEEE International Conference on Computer Vision (ICCV)},
  year={2017},
  pages={1221-1230}
}




//// recent SoA face alignment

////// FAN

@inproceedings{Bulat17FAN,
  title={How far are we from solving the 2D \& 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)},
  author={Bulat, Adrian and Tzimiropoulos, Georgios},
  booktitle={International Conference on Computer Vision},
  year={2017}
}


////// Look at boundary
@inproceedings{wayne2018LAB,
  author = {Wu, Wayne and Qian, Chen and Yang, Shuo and Wang, Quan and Cai, Yici and Zhou, Qiang},
  title = {Look at Boundary: A Boundary-Aware Face Alignment Algorithm},
  booktitle = {CVPR},
  month = June,
  year = {2018}
} 

////// SAN

@inproceedings{Dong2018SAN,
   title={Style Aggregated Network for Facial Landmark Detection},
   author={Dong, Xuanyi and Yan, Yan and Ouyang, Wanli and Yang, Yi},
   booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
   pages={379--388},
   year={2018}
}



////// other deep learning based face alignment
MDM
@inproceedings{Trigeorgis16MDM,
  author    = {George Trigeorgis and
               Patrick Snape and
               Mihalis A. Nicolaou and
               Epameinondas Antonakos and
               Stefanos Zafeiriou},
  title     = {Mnemonic Descent Method: {A} Recurrent Process Applied for End-to-End
               Face Alignment},
  booktitle = {{CVPR}},
  pages     = {4177--4187},
  publisher = {{IEEE} Computer Society},
  year      = {2016}
}

CFSS
@inproceedings{zhu2015CFSS,
  title={Face Alignment by Coarse-to-Fine Shape Searching},
  author={Zhu, Shizhan and Li, Cheng and Loy, Chen Change and Tang, Xiaoou},
  booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},
  pages={4998--5006},
  year={2015}
}

TCDCN
@InProceedings{Zhang14TCDCN,
author="Zhang, Zhanpeng and Luo, Ping and Loy, Chen Change and Tang, Xiaoou",
editor="Fleet, David and Pajdla, Tomas and Schiele, Bernt and Tuytelaars, Tinne",
title="Facial Landmark Detection by Deep Multi-task Learning",
booktitle="Computer Vision -- ECCV 2014",
year="2014",
publisher="Springer International Publishing",
address="Cham",
pages="94--108",
}

DCNNc
@inproceedings{Sun13cnncFaceAlignment,
author = {Sun, Yi and Wang, Xiaogang and Tang, Xiaoou},
title = {Deep Convolutional Network Cascade for Facial Point Detection},
booktitle = {Computer Vision - {CVPR} IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition. . 10.1109/CVPR.2013.446., Proceedings},
pages = {3476--3483},
year = {2013},
}

@article{Deng17JMFA,
  author    = {Jiankang Deng and
               George Trigeorgis and
               Yuxiang Zhou and
               Stefanos Zafeiriou},
  title     = {Joint Multi-view Face Alignment in the Wild},
  journal   = {CoRR},
  volume    = {abs/1708.06023},
  year      = {2017}
}

////// occlusion
@inproceedings{Yue17occlusion,
  author    = {Yue Wu and
               Chao Gou and
               Qiang Ji},
  title     = {Simultaneous Facial Landmark Detection, Pose and Deformation Estimation
               Under Facial Occlusion},
  booktitle = {{CVPR}},
  pages     = {5719--5728},
  publisher = {{IEEE} Computer Society},
  year      = {2017}
}

@inproceedings{Yue15occlusion,
  author    = {Yue Wu and
               Qiang Ji},
  title     = {Robust Facial Landmark Detection Under Significant Head Poses and
               Occlusion},
  booktitle = {{ICCV}},
  pages     = {3658--3666},
  publisher = {{IEEE} Computer Society},
  year      = {2015}
}

@InProceedings{Zhu_19_CVPR_occlusion-adaptive,
author = {Zhu, Meilu and Shi, Daming and Zheng, Mingjie and Sadiq, Muhammad},
title = {Robust Facial Landmark Detection via Occlusion-Adaptive Deep Networks},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2019}
}

@InProceedings{Reddy_19_CVPR_2d3d-occlusion,
author = {Reddy, N. Dinesh and Vo, Minh and Narasimhan, Srinivasa G.},
title = {Occlusion-Net: 2D/3D Occluded Keypoint Localization Using Graph Networks},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2019}
}


// Bayesian propagate
@article{Ozdemir17BayesianCascade,
  author    = {Onur Ozdemir and
               Benjamin Woodward and
               Andrew A. Berlin},
  title     = {Propagating Uncertainty in Multi-Stage Bayesian Convolutional Neural
               Networks with Application to Pulmonary Nodule Detection},
  journal   = {CoRR},
  volume    = {abs/1712.00497},
  year      = {2017},
  url       = {http://arxiv.org/abs/1712.00497},
  archivePrefix = {arXiv},
  eprint    = {1712.00497},
  timestamp = {Mon, 13 Aug 2018 16:47:25 +0200},
  biburl    = {https://dblp.org/rec/bib/journals/corr/abs-1712-00497},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

@inproceedings{Teye18batchnormBayesian,
  author    = {Mattias Teye and
               Hossein Azizpour and
               Kevin Smith},
  title     = {Bayesian Uncertainty Estimation for Batch Normalized Deep Networks},
  booktitle = {{ICML}},
  series    = {{JMLR} Workshop and Conference Proceedings},
  volume    = {80},
  pages     = {4914--4923},
  publisher = {JMLR.org},
  year      = {2018}
}




@incollection{Lakshminarayanan_ensemble_NIPS17,
title = {Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles},
author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
booktitle = {Advances in Neural Information Processing Systems 30},
editor = {I. Guyon and U. V. Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
pages = {6402--6413},
year = {2017},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/7219-simple-and-scalable-predictive-uncertainty-estimation-using-deep-ensembles.pdf}
}


@incollection{Malinin_prior_network_NIPS18,
title = {Predictive Uncertainty Estimation via Prior Networks},
author = {Malinin, Andrey and Gales, Mark},
booktitle = {Advances in Neural Information Processing Systems 31},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {7047--7058},
year = {2018},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/7936-predictive-uncertainty-estimation-via-prior-networks.pdf}
}

\\ old works on occlusion datasets

@article{Feng_CRC_2015,
author = {Feng, Zhenhua and Huber, Patrik and Kittler, Josef and Wu, Xiaojun},
year = {2015},
month = {01},
pages = {76-80},
title = {Random Cascaded-Regression Copse for Robust Facial Landmark Detection},
volume = {22},
journal = {IEEE Signal Processing Letters},
doi = {10.1109/LSP.2014.2347011}
}


@article{Ghiasi_OC_2014,
author = {Ghiasi, Golnaz and Fowlkes, Charless},
year = {2014},
month = {09},
pages = {1899-1906},
title = {Occlusion Coherence: Localizing Occluded Faces with a Hierarchical Deformable Part Model},
journal = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
doi = {10.1109/CVPR.2014.306}
}

@article{Cao_ESR_2014,
 author = {Cao, Xudong and Wei, Yichen and Wen, Fang and Sun, Jian},
 title = {Face Alignment by Explicit Shape Regression},
 journal = {Int. J. Comput. Vision},
 issue_date = {April     2014},
 volume = {107},
 number = {2},
 month = apr,
 year = {2014},
 issn = {0920-5691},
 pages = {177--190},
 numpages = {14},
 url = {http://dx.doi.org/10.1007/s11263-013-0667-3},
 doi = {10.1007/s11263-013-0667-3},
 acmid = {2597529},
 publisher = {Kluwer Academic Publishers},
 address = {Hingham, MA, USA},
 keywords = {Correlation based feature selection, Face alignment, Non-parametric shape constraint, Shape indexed feature, Tow-level boosted regression},
} 


@INPROCEEDINGS{Zhu_FPLL_2012, 
author={X. {Zhu} and D. {Ramanan}}, 
booktitle={2012 IEEE Conference on Computer Vision and Pattern Recognition}, 
title={Face detection, pose estimation, and landmark localization in the wild}, 
year={2012}, 
volume={}, 
number={}, 
pages={2879-2886}, 
keywords={computer vision;face recognition;object detection;pose estimation;trees (mathematics);face detection;pose estimation;landmark localization;landmark estimation;topological changes;tree-structured models;global elastic deformation;in-the-wild annotated dataset;Google Picasa;face.com;computer vision;Face;Computational modeling;Estimation;Shape;Detectors;Face detection;Google}, 
doi={10.1109/CVPR.2012.6248014}, 
ISSN={}, 
month={June},}

@inproceedings{Xiong_SDM_2013,
 author = {Xiong, Xuehan and De la Torre, Fernando},
 title = {Supervised Descent Method and Its Applications to Face Alignment},
 booktitle = {Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition},
 series = {CVPR '13},
 year = {2013},
 isbn = {978-0-7695-4989-7},
 pages = {532--539},
 numpages = {8},
 url = {https://doi.org/10.1109/CVPR.2013.75},
 doi = {10.1109/CVPR.2013.75},
 acmid = {2515959},
 publisher = {IEEE Computer Society},
 address = {Washington, DC, USA},
 keywords = {face alignment, facial feature tracking, non-linear least squares, supervised descent method},
} 

@INPROCEEDINGS{Kazemi_ERT_2014, 
author={V. {Kazemi} and J. {Sullivan}}, 
booktitle={2014 IEEE Conference on Computer Vision and Pattern Recognition}, 
title={One millisecond face alignment with an ensemble of regression trees}, 
year={2014}, 
volume={}, 
number={}, 
pages={1867-1874}, 
keywords={face recognition;feature selection;gradient methods;learning (artificial intelligence);optimisation;pose estimation;regression analysis;trees (mathematics);face alignment;regression tree ensemble;face landmark position estimation;pixel intensities;gradient boosting;square error loss sum optimization;feature selection;regularization strategies;overfitting;data augmentation;time 1 ms;Shape;Regression tree analysis;Face;Training;Boosting;Training data;Vectors;Face Alignment;Real-Time;Gradient Boosting;Decision Trees}, 
doi={10.1109/CVPR.2014.241}, 
ISSN={}, 
month={June},}


@inproceedings{Ren_LBF_2014,
 author = {Ren, Shaoqing and Cao, Xudong and Wei, Yichen and Sun, Jian},
 title = {Face Alignment at 3000 FPS via Regressing Local Binary Features},
 booktitle = {Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition},
 series = {CVPR '14},
 year = {2014},
 isbn = {978-1-4799-5118-5},
 pages = {1685--1692},
 numpages = {8},
 url = {https://doi.org/10.1109/CVPR.2014.218},
 doi = {10.1109/CVPR.2014.218},
 acmid = {2680179},
 publisher = {IEEE Computer Society},
 address = {Washington, DC, USA},
 keywords = {Face Alignment, Random Forest, Regression},
} 

@inproceedings{Zhu_CCL_2016,
author = {Zhu, Shizhan and Li, Cheng and Loy, Chen Change and Tang, Xiaoou},
year = {2016},
month = {06},
pages = {3409-3417},
title = {Unconstrained Face Alignment via Cascaded Compositional Learning},
doi = {10.1109/CVPR.2016.371}
}

@ARTICLE{Cui_recurrent_shape_regression, 
author={Z. {Cui} and S. {Xiao} and Z. {Niu} and S. {Yan} and W. {Zheng}}, 
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
title={Recurrent Shape Regression}, 
year={2019}, 
volume={41}, 
number={5}, 
pages={1271-1278}, 
keywords={computer vision;face recognition;feature extraction;hidden feature removal;learning (artificial intelligence);object detection;pose estimation;regression analysis;shape recognition;RSR;facial shape detection;computer vision problems;recurrent dynamic network;invariant regression transformation;shape-dependent dynamic regressors;high-order regression network;complex shape regression;global shape constraint;end-to-end network architecture;common latent models;recurrent shape regression;mimic virtual occlusion strategy;Shape;Feature extraction;Face;Training;Task analysis;Recurrent neural networks;Tools;Shape regression;cascaded regression;recurrent neural network;shape detection;face alignment}, 
doi={10.1109/TPAMI.2018.2828424}, 
ISSN={1939-3539}, 
month={May},}







@inproceedings{
nalisnick2018_do_generative,
title={Do Deep Generative Models Know What They Don't Know? },
author={Eric Nalisnick and Akihiro Matsukawa and Yee Whye Teh and Dilan Gorur and Balaji Lakshminarayanan},
booktitle={International Conference on Learning Representations},
year={2019},
url={https://openreview.net/forum?id=H1xwNhCcYm},
}

@INPROCEEDINGS{striking2019CVPR, author={S. {Khan} and M. {Hayat} and S. W. {Zamir} and J. {Shen} and L. {Shao}}, booktitle={2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, title={Striking the Right Balance With Uncertainty}, year={2019}, volume={}, number={}, pages={103-112},}



@InProceedings{Decompose2018ICML,
  title =    {Decomposition of Uncertainty in {B}ayesian Deep Learning for Efficient and Risk-sensitive Learning},
  author =   {Depeweg, Stefan and Hernandez-Lobato, Jose-Miguel and Doshi-Velez, Finale and Udluft, Steffen},
  booktitle =    {Proceedings of the 35th International Conference on Machine Learning},
  pages =    {1184--1193},
  year =   {2018},
  editor =   {Dy, Jennifer and Krause, Andreas},
  volume =   {80},
  series =   {Proceedings of Machine Learning Research},
  address =    {Stockholmsmässan, Stockholm Sweden},
  month =    {10--15 Jul},
  publisher =    {PMLR},
  pdf =    {http://proceedings.mlr.press/v80/depeweg18a/depeweg18a.pdf},
  url =    {http://proceedings.mlr.press/v80/depeweg18a.html},
  abstract =   {Bayesian neural networks with latent variables are scalable and flexible probabilistic models: they account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. Using these models we show how to perform and utilize a decomposition of uncertainty in aleatoric and epistemic components for decision making purposes. This allows us to successfully identify informative points for active learning of functions with heteroscedastic and bimodal noise. Using the decomposition we further define a novel risk-sensitive criterion for reinforcement learningto identify policies that balance expected cost, model-bias and noise aversion.}
}


//sampling-free epistemic uncertainty

@InProceedings{Gast_2018_CVPR_lightweight,
author = {Gast, Jochen and Roth, Stefan},
title = {Lightweight Probabilistic Deep Networks},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2018}
}

@InProceedings{Postels_2019_ICCV_varianceprop,
author = {Postels, Janis and Ferroni, Francesco and Coskun, Huseyin and Navab, Nassir and Tombari, Federico},
title = {Sampling-Free Epistemic Uncertainty Estimation Using Approximated Variance Propagation},
booktitle = {The IEEE International Conference on Computer Vision (ICCV)},
month = {October},
year = {2019}
}

@incollection{Tagasovska_2019_NIPS_8870_certificate,
title = {Single-Model Uncertainties for Deep Learning},
author = {Tagasovska, Natasa and Lopez-Paz, David},
booktitle = {Advances in Neural Information Processing Systems 32},
pages = {6417--6428},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/8870-single-model-uncertainties-for-deep-learning.pdf}
}
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},


@incollection{epi_define_2004,
title = "Chapter I - Reality, Mathematics, and Computation",
editor = "Ivan Hlaváěek and Jan Chleboun and Ivo Babuška",
series = "North-Holland Series in Applied Mathematics and Mechanics",
publisher = "North-Holland",
volume = "46",
pages = "1 - 49",
year = "2004",
booktitle = "Uncertain Input Data Problems and the Worst Scenario Method",
issn = "0167-5931",
doi = "https://doi.org/10.1016/S0167-5931(04)80005-6",
url = "http://www.sciencedirect.com/science/article/pii/S0167593104800056",
author = "Ivan Hlaváěek and Jan Chleboun and Ivo Babuška"
}


@article{BALD_2017,
  author    = {Yarin Gal and
               Riashat Islam and
               Zoubin Ghahramani},
  title     = {Deep Bayesian Active Learning with Image Data},
  journal   = {CoRR},
  volume    = {abs/1703.02910},
  year      = {2017},
  url       = {http://arxiv.org/abs/1703.02910},
  archivePrefix = {arXiv},
  eprint    = {1703.02910},
  timestamp = {Mon, 13 Aug 2018 16:48:21 +0200},
  biburl    = {https://dblp.org/rec/journals/corr/GalIG17.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}


@incollection{eval_datasetshift_NIPS2019,
title = {Can you trust your model's uncertainty?  Evaluating predictive uncertainty under dataset shift},
author = {Snoek, Jasper and Ovadia, Yaniv and Fertig, Emily and Lakshminarayanan, Balaji and Nowozin, Sebastian and Sculley, D. and Dillon, Joshua and Ren, Jie and Nado, Zachary},
booktitle = {Advances in Neural Information Processing Systems 32},
pages = {13991--14002},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/9547-can-you-trust-your-models-uncertainty-evaluating-predictive-uncertainty-under-dataset-shift.pdf}
}


@article{baseline_BDL_2018,
  author    = {Jishnu Mukhoti and
               Pontus Stenetorp and
               Yarin Gal},
  title     = {On the Importance of Strong Baselines in Bayesian Deep Learning},
  journal   = {CoRR},
  volume    = {abs/1811.09385},
  year      = {2018},
  url       = {http://arxiv.org/abs/1811.09385},
  archivePrefix = {arXiv},
  eprint    = {1811.09385},
  timestamp = {Fri, 30 Nov 2018 12:44:28 +0100},
  biburl    = {https://dblp.org/rec/journals/corr/abs-1811-09385.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

@article{zhao2018empirical,
  title={An Empirical Evaluation of Bayesian Inference Methods for Bayesian Neural Networks},
  author={Zhao, Rui and Ji, Qiang},
  booktitle={NIPS Bayesian Deep Learning Workshop},
  year={2018}
}


@article{yao2019quality,
  title={Quality of uncertainty quantification for Bayesian neural network inference},
  author={Yao, Jiayu and Pan, Weiwei and Ghosh, Soumya and Doshi-Velez, Finale},
  journal={arXiv preprint arXiv:1906.09686},
  year={2019}
}

// datasets

@article{OMNIGLOT_lake2015,
  title={Human-level concept learning through probabilistic program induction},
  author={Lake, Brenden M and Salakhutdinov, Ruslan and Tenenbaum, Joshua B},
  journal={Science},
  volume={350},
  number={6266},
  pages={1332--1338},
  year={2015},
  publisher={American Association for the Advancement of Science}
}


// dataset

  @article{lecun-mnisthandwrittendigit-2010,
  added-at = {2010-06-28T21:16:30.000+0200},
  author = {LeCun, Yann and Cortes, Corinna},
  biburl = {https://www.bibsonomy.org/bibtex/2935bad99fa1f65e03c25b315aa3c1032/mhwombat},
  groups = {public},
  howpublished = {http://yann.lecun.com/exdb/mnist/},
  interhash = {21b9d0558bd66279df9452562df6e6f3},
  intrahash = {935bad99fa1f65e03c25b315aa3c1032},
  keywords = {MSc _checked character_recognition mnist network neural},
  lastchecked = {2016-01-14 14:24:11},
  timestamp = {2016-07-12T19:25:30.000+0200},
  title = {{MNIST} handwritten digit database},
  url = {http://yann.lecun.com/exdb/mnist/},
  username = {mhwombat},
  year = 2010
}


@article{cifar10,
title= {CIFAR-10 (Canadian Institute for Advanced Research)},
journal= {},
author= {Alex Krizhevsky and Vinod Nair and Geoffrey Hinton},
year= {},
url= {http://www.cs.toronto.edu/~kriz/cifar.html},
abstract= {The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. 

The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly-selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. },
keywords= {Dataset},
terms= {}
}



@article{action-jingen-wild,
  author = {Jingen Liu, and Jiebo Luo and Mubarak Shah},
  title = {Recognizing Realistic Actions from Videos "in the Wild"},
  journal = {IEEE International Conference on Computer Vision and Pattern Recognition},
  year = {2009},
  url = {http://server.cs.ucf.edu/~vision/projects/liujg/realistic_action_recognition.html}
}


// accidents

  @MISC{uber-accident,
  author = {Mark Rosenker and Amitai Bin-Nun},
  title = {After tragic self-driving Uber accident, the government needs to set safety standards},
  editor = {USA Today},
  month = {April},
  year = {2018},
  url = {https://www.usatoday.com/story/opinion/2018/03/30/after-tragic-self-driving-uber-accident-government-needs-set-safety-standards-column/460114002/},
  }

  @MISC{Tesla-accident,
  author = {Marco della Cava},
  title = {Tesla Model S was on Autopilot, Utah driver tells police},
  editor = {USA Today},
  month = {May},
  year = {2018},
  url = {https://www.usatoday.com/story/tech/2018/05/14/tesla-model-s-crash-utah-involved-autopilot-distracted-driver/609596002/},
  }
  

// aleatoric uncertainty


  @article{Le2005,
  abstract = {This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate vari- ance local ly unlike standard Gaussian Pro- cess regression or SVMs. This means that our estimator adapts to the local noise. The problem is cast in the setting of maximum a posteriori estimation in exponential families. Unlike previous work, we obtain a convex op- timization problem which can be solved via Newtons method.},
  author = {Le, Quoc and Smola, Alex and Canu, St{\'{e}}phane},
  doi = {10.1145/1102351.1102413},
  isbn = {1-59593-180-5},
  issn = {01697439},
  journal = {Proceedings of the 22nd international conference on Machine learning ICML 05},
  keywords = {learning,statistics {\&} optimisation},
  pages = {489--496},
  title = {{Heteroscedastic Gaussian Process Regression}},
  url = {http://eprints.pascal-network.org/archive/00002009/},
  volume = {227},
  year = {2005}
  }

  @book{Goodfellow-et-al-2016,
    title={Deep Learning},
    author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher={MIT Press},
    note={\url{http://www.deeplearningbook.org}},
    year={2016}
  }

// Epistemic uncertainty



@book{Abu-Mostafa2012,
 author = {Abu-Mostafa, Yaser S. and Magdon-Ismail, Malik and Lin, Hsuan-Tien},
 title = {Learning From Data},
 year = {2012},
 isbn = {1600490069, 9781600490064},
 publisher = {AMLBook},
} 

@book{weiss2006,
  title={A Course in Probability},
  author={Weiss, N.A. and Holmes, P.T. and Hardy, M.},
  isbn={9780201774719},
  lccn={2004051068},
  url={https://books.google.com/books?id=Be9fJwAACAAJ},
  year={2006},
  publisher={Pearson Addison Wesley}
}

@book{Mahler2001,
title={Foundations of Casualty Actuarial Science},
edition={4th},
publisher={Casualty Actuarial Society},
author={Mahler, Howard C. and Dean, Curtis Gary},
year={2001},
isbn={9780962476228},
chapter={8},
pages={525–526}
}


//BNN literature review

@article{Lakshminarayanan2016,
abstract = {Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which learn a distribution over weights, are currently the state-of-the-art for estimating predictive uncertainty; however these require significant modifications to the training procedure and are computationally expensive compared to standard (non-Bayesian) NNs. We propose an alternative to Bayesian NNs that is simple to implement, readily parallelizable, requires very little hyperparameter tuning, and yields high quality predictive uncertainty estimates. Through a series of experiments on classification and regression benchmarks, we demonstrate that our method produces well-calibrated uncertainty estimates which are as good or better than approximate Bayesian NNs. To assess robustness to dataset shift, we evaluate the predictive uncertainty on test examples from known and unknown distributions, and show that our method is able to express higher uncertainty on out-of-distribution examples. We demonstrate the scalability of our method by evaluating predictive uncertainty estimates on ImageNet.},
archivePrefix = {arXiv},
arxivId = {1612.01474},
author = {Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
eprint = {1612.01474},
file = {:G$\backslash$:/Ji/reference/confidence/ensemble.pdf:pdf},
mendeley-groups = {Ji/confidence},
title = {{Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles}},
url = {http://arxiv.org/abs/1612.01474},
year = {2016}
}





@article{Zhu2017,
abstract = {Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection across millions of metrics. Classical time series models are often used in conjunction with a probabilistic formulation for uncertainty estimation. However, such models are hard to tune, scale, and add exogenous variables to. Motivated by the recent resurgence of Long Short Term Memory networks, we propose a novel end-to-end Bayesian deep model that provides time series prediction along with uncertainty estimation. We provide detailed experiments of the proposed solution on completed trips data, and successfully apply it to large-scale time series anomaly detection at Uber.},
archivePrefix = {arXiv},
arxivId = {1709.01907},
author = {Zhu, Lingxue and Laptev, Nikolay},
doi = {10.1109/ICDMW.2017.19},
eprint = {1709.01907},
file = {:C$\backslash$:/Users/lenovo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhu, Laptev - 2017 - Deep and Confident Prediction for Time Series at Uber.pdf:pdf},
keywords = {anomaly detection,bayesian neural networks,predictive uncertainty,time series},
mendeley-groups = {Ji/confidence},
title = {{Deep and Confident Prediction for Time Series at Uber}},
url = {http://arxiv.org/abs/1709.01907},
year = {2017}
}

@article{Denker1991,
abstract = {(1) The outputs of a typical multi-output classification network do not satisfy the axioms of probability; probabilities should be positive and sum to one. This problem can be solved by treating the trained network as a preprocessor that produces a feature vector that can be further processed, for instance by classical statistical estimation techniques. (2) We present a method for computing the first two moments ofthe probability distribution indicating the range of outputs that are consistent with the input and the training data. It is particularly useful to combine these two ideas: we implement the ideas of section 1 using Parzen windows, where the shape and relative size of each window is computed using the ideas of section 2. This allows us to make contact between important theoretical ideas (e.g. the ensemble formalism) and practical techniques (e.g. back-prop). Our results also shed new light on and generalize the well-known "soft max" scheme.},
archivePrefix = {arXiv},
arxivId = {11359-901120-05},
author = {Denker, John S and LeCun, Yann},
doi = {10.1.1.32.7096},
eprint = {11359-901120-05},
journal = {Advances in Neural Information Processing Systems 3},
pages = {853--859},
title = {{Transforming Neural-Net Output Levels to Probability Distributions}},
url = {http://papers.nips.cc/paper/419-transforming-neural-net-output-levels-to-probability-distributions.pdf{\%}5Cnfiles/4250/Denker ? LeCun - 1991 - Transforming Neural-Net Output Levels to Probabili.pdf{\%}5Cnfiles/4251/419-transforming-neural-net-output-levels-to-},
year = {1991}
}

@article{Warner1997,
abstract = {Two features distinguish the Bayesian approach to learning models from data. First, beliefs derived from background knowledge are used to select a prior probability distribution for the model parameters. Second, predictions of future observations are made by integrating the model's predictions with respect to the posterior parameter distribution obtained by updating this prior to take account of the data. For neural network models, both these aspects present diiculties | the prior over network parameters has no obvious relation to our prior knowledge, and integration over the posterior is computationally very demanding. I address the problem by deening classes of prior distributions for network param-eters that reach sensible limits as the size of the network goes to innnity. In this limit, the properties of these priors can be elucidated. Some priors converge to Gaussian processes, in which functions computed by the network may be smooth, Brownian, or fractionally Brownian. Other priors converge to non-Gaussian stable processes. Interesting eeects are obtained by combining priors of both sorts in networks with more than one hidden layer.},
author = {Warner, Bradley a. and Neal, Radford M.},
doi = {10.2307/2965731},
isbn = {0387947248},
issn = {01621459},
journal = {Journal of the American Statistical Association},
keywords = {Automatic Relevance Detarmination,Gaussian Process,Neal},
pages = {791},
pmid = {3473},
title = {{Bayesian Learning for Neural Networks}},
url = {http://www.jstor.org/stable/2965731?origin=crossref},
volume = {92},
year = {1997}
}

@article{Graves2011,
abstract = {Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.},
author = {Graves, Alex},
isbn = {9781618395993},
journal = {Nips},
pages = {1--9},
title = {{Practical Variational Inference for Neural Networks.}},
url = {https://papers.nips.cc/paper/4329-practical-variational-inference-for-neural-networks.pdf},
year = {2011}
}


@article{Blundell2015,
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.},
archivePrefix = {arXiv},
arxivId = {1505.05424},
author = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
eprint = {1505.05424},
file = {:C$\backslash$:/Users/lenovo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Blundell et al. - 2015 - Weight Uncertainty in Neural Networks.pdf:pdf},
isbn = {9781510810587},
mendeley-groups = {Ji/confidence},
title = {{Weight Uncertainty in Neural Networks}},
url = {http://arxiv.org/abs/1505.05424},
volume = {37},
year = {2015}
}




@article{Hernandez-Lobato2015,
abstract = {Black-box alpha (BB-$\alpha$) is a new approximate inference method based on the minimization of $\alpha$-divergences. BB-$\alpha$ scales to large datasets because it can be implemented using stochastic gradient descent. BB-$\alpha$ can be applied to com- plex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be eas- ily obtained using automatic differentiation. By changing the divergence parameter$\alpha$, the method is able to interpolate between variational Bayes (VB) ($\alpha$→0) and an algorithm similar to expec- tation propagation (EP) ($\alpha$ = 1). Experiments on probit regression and neural network regression and classification problems show that BB-$\alpha$ with non-standard settings of $\alpha$, such as $\alpha$ = 0.5, usu- ally produces better predictions than with $\alpha$→0 (VB) or $\alpha$ = 1 (EP).},
archivePrefix = {arXiv},
arxivId = {arXiv:1511.03243v1},
author = {Hern{\'{a}}ndez-Lobato, Jos{\'{e}} Miguel and Li, Yingzhen and Hern{\'{a}}ndez-Lobato, Daniel and Bui, Thang and Turner, Richard},
eprint = {arXiv:1511.03243v1},
isbn = {9781510829008},
issn = {1938-7228},
journal = {Black box learning {\&} inference workshop (NIPS)},
pages = {1--5},
title = {{Black-box $\alpha$ divergence Minimization}},
year = {2015}
}



@article{Gal2015,
abstract = {Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10.},
archivePrefix = {arXiv},
arxivId = {1506.02158},
author = {Gal, Yarin and Ghahramani, Zoubin},
doi = {10.1029/2003JD002581},
eprint = {1506.02158},
file = {:G$\backslash$:/Ji/reference/confidence/1506.02158.pdf:pdf},
isbn = {9781611970685},
issn = {0004-6361},
mendeley-groups = {Ji/confidence},
pages = {1--12},
pmid = {23459267},
title = {{Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference}},
url = {http://arxiv.org/abs/1506.02158},
year = {2015}
}



@article{Srivastava2014,
abstract = {Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different " thinned " networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.},
archivePrefix = {arXiv},
arxivId = {1102.4807},
author = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
doi = {10.1214/12-AOS1000},
eprint = {1102.4807},
isbn = {1532-4435},
issn = {15337928},
journal = {Journal of Machine Learning Research},
keywords = {deep learning,model combination,neural networks,regularization},
pages = {1929--1958},
pmid = {23285570},
title = {{Dropout: A Simple Way to Prevent Neural Networks from Overfitting}},
volume = {15},
year = {2014}
}


@article{Miyato2016,
abstract = {Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations to numerous entries of the input vector, which is inappropriate for sparse high-dimensional inputs such as one-hot word representations. We extend adversarial and virtual adversarial training to the text domain by applying perturbations to the word embeddings in a recurrent neural network rather than to the original input itself. The proposed method achieves state of the art results on multiple benchmark semi-supervised and purely supervised tasks. We provide visualizations and analysis showing that the learned word embeddings have improved in quality and that while training, the model is less prone to overfitting.},
archivePrefix = {arXiv},
arxivId = {1605.07725},
author = {Miyato, Takeru and Dai, Andrew M. and Goodfellow, Ian},
doi = {10.2507/daaam.scibook.2010.27},
eprint = {1605.07725},
isbn = {2840601737},
issn = {17269687},
journal = {arXiv},
number = {2015},
pages = {1--9},
pmid = {19963286},
title = {{Virtual Adversarial Training for Semi-Supervised Text Classification}},
url = {http://arxiv.org/abs/1605.07725},
year = {2016}
}

// dropout

@article{Hinton2012,
abstract = {When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.},
archivePrefix = {arXiv},
arxivId = {1207.0580},
author = {Hinton, Geoffrey E. and Srivastava, Nitish and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan R.},
doi = {arXiv:1207.0580},
eprint = {1207.0580},
file = {:D$\backslash$:/Lisha/document/reference/confidence/BNN/dropout/1207.0580.pdf:pdf},
isbn = {9781467394673},
issn = {9781467394673},
mendeley-groups = {Ji/confidence/BNN/dropout},
pages = {1--18},
pmid = {1000104337},
title = {{Improving neural networks by preventing co-adaptation of feature detectors}},
url = {http://arxiv.org/abs/1207.0580},
year = {2012}
}



// library

@article{Shi2017zhusuan,
abstract = {In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.},
archivePrefix = {arXiv},
arxivId = {1709.05870},
author = {Shi, Jiaxin and Chen, Jianfei and Zhu, Jun and Sun, Shengyang and Luo, Yucen and Gu, Yihong and Zhou, Yuhao},
eprint = {1709.05870},
file = {:C$\backslash$:/Users/ziheng/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Shi et al. - 2017 - ZhuSuan A Library for Bayesian Deep Learning.pdf:pdf},
keywords = {bayesian inference,deep gen-,deep learning,probabilistic programming},
mendeley-groups = {Ji/confidence/BDL,Ji/confidence/BNN},
pages = {1--29},
title = {{ZhuSuan: A Library for Bayesian Deep Learning}},
url = {http://arxiv.org/abs/1709.05870},
year = {2017}
}

@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}
}

@inproceedings{tran2017edward,
  author = {Dustin Tran and Matthew D. Hoffman and Rif A. Saurous and Eugene Brevdo and Kevin Murphy and David M. Blei},
  title = {Deep probabilistic programming},
  booktitle = {International Conference on Learning Representations},
  year = {2017}
}


@misc{UberPyro,
  author = {Noah Goodman},
  title = {Uber AI Labs Open Sources Pyro, a Deep Probabilistic Programming Language},
  note = {Available at \url{https://eng.uber.com/pyro/}, last access 2018-01-12}
}




// other confidence model literature review

@article{HORA1996_intro,
title = "Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management",
journal = "Reliability Engineering and System Safety",
volume = "54",
number = "2",
pages = "217 - 223",
year = "1996",
note = "Treatment of Aleatory and Epistemic Uncertainty",
issn = "0951-8320",
doi = "https://doi.org/10.1016/S0951-8320(96)00077-4",
url = "http://www.sciencedirect.com/science/article/pii/S0951832096000774",
author = "Stephen C. Hora",
}




@article{uncertainty_keith,
author = {Keith Beven},
title = {Facets of uncertainty: epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication},
journal = {Hydrological Sciences Journal},
volume = {61},
number = {9},
pages = {1652-1665},
year  = {2016},
publisher = {Taylor & Francis},
doi = {10.1080/02626667.2015.1031761},
URL = {https://doi.org/10.1080/02626667.2015.1031761},
eprint = {https://doi.org/10.1080/02626667.2015.1031761}
}


//outlier detection
@article{Pimentel_2014_review_novelty, 
author = {Pimentel, Marco A. F. and Clifton, David A. and Clifton, Lei and Tarassenko, Lionel}, 
title = {Review: A Review of Novelty Detection}, 
year = {2014}, 
issue_date = {June, 2014}, 
publisher = {Elsevier North-Holland, Inc.}, 
address = {USA}, 
volume = {99}, 
issn = {0165-1684}, 
url = {https://doi.org/10.1016/j.sigpro.2013.12.026}, 
doi = {10.1016/j.sigpro.2013.12.026}, 
journal = {Signal Process.}, 
month = jun, 
pages = {215–249}, 
numpages = {35}, 
keywords = {Novelty detection, Machine learning, One-class classification} }


@inproceedings{Khan_2009_oneclass, 
author = {Khan, Shehroz S. and Madden, Michael G.},
title = {A Survey of Recent Trends in One Class Classification}, 
year = {2009}, 
isbn = {364217079X}, 
publisher = {Springer-Verlag}, 
address = {Berlin, Heidelberg}, 
booktitle = {Proceedings of the 20th Irish Conference on Artificial Intelligence and Cognitive Science}, 
pages = {188–197}, 
numpages = {10}, 
keywords = {outlier detection, support vector machines, one class classification, positive and unlabeled data}, 
location = {Dublin, Ireland}, 
series = {AICS’09} }

@article{malinin2019ensemble,
  title={Ensemble distribution distillation},
  author={Malinin, Andrey and Mlodozeniec, Bruno and Gales, Mark},
  journal={arXiv preprint arXiv:1905.00076},
  year={2019}
}

@article{charpentier2020posterior,
  title={Posterior network: Uncertainty estimation without ood samples via density-based pseudo-counts},
  author={Charpentier, Bertrand and Z{\"u}gner, Daniel and G{\"u}nnemann, Stephan},
  journal={arXiv preprint arXiv:2006.09239},
  year={2020}
}

@article{mackay1998choice,
  title={Choice of basis for Laplace approximation},
  author={MacKay, David JC},
  journal={Machine learning},
  volume={33},
  number={1},
  pages={77--86},
  year={1998},
  publisher={Springer}
}

@article{geman1984stochastic,
  title={Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images},
  author={Geman, Stuart and Geman, Donald},
  journal={IEEE Transactions on pattern analysis and machine intelligence},
  number={6},
  pages={721--741},
  year={1984},
  publisher={IEEE}
}

@article{hastings1970monte,
  title={Monte Carlo sampling methods using Markov chains and their applications},
  author={Hastings, W Keith},
  year={1970},
  publisher={Oxford University Press}
}

@inproceedings{daxberger2021bayesian,
  title={Bayesian deep learning via subnetwork inference},
  author={Daxberger, Erik and Nalisnick, Eric and Allingham, James U and Antor{\'a}n, Javier and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel},
  booktitle={International Conference on Machine Learning},
  pages={2510--2521},
  year={2021},
  organization={PMLR}
}

@inproceedings{kristiadi2020being,
  title={Being bayesian, even just a bit, fixes overconfidence in relu networks},
  author={Kristiadi, Agustinus and Hein, Matthias and Hennig, Philipp},
  booktitle={International Conference on Machine Learning},
  pages={5436--5446},
  year={2020},
  organization={PMLR}
}

@inproceedings{ritter2018scalable,
  title={A scalable laplace approximation for neural networks},
  author={Ritter, Hippolyt and Botev, Aleksandar and Barber, David},
  booktitle={6th International Conference on Learning Representations, ICLR 2018-Conference Track Proceedings},
  volume={6},
  year={2018},
  organization={International Conference on Representation Learning}
}

@inproceedings{lee2020estimating,
  title={Estimating model uncertainty of neural networks in sparse information form},
  author={Lee, Jongseok and Humt, Matthias and Feng, Jianxiang and Triebel, Rudolph},
  booktitle={International Conference on Machine Learning},
  pages={5702--5713},
  year={2020},
  organization={PMLR}
}

@article{sensoy2018evidential,
  title={Evidential deep learning to quantify classification uncertainty},
  author={Sensoy, Murat and Kaplan, Lance and Kandemir, Melih},
  journal={arXiv preprint arXiv:1806.01768},
  year={2018}
}

@article{wu2019quantifying,
  title={Quantifying intrinsic uncertainty in classification via deep dirichlet mixture networks},
  author={Wu, Qingyang and Li, He and Li, Lexin and Yu, Zhou},
  journal={arXiv preprint arXiv:1906.04450},
  year={2019}
}

@article{liu2020energy,
  title={Energy-based out-of-distribution detection},
  author={Liu, Weitang and Wang, Xiaoyun and Owens, John D and Li, Yixuan},
  journal={arXiv preprint arXiv:2010.03759},
  year={2020}
}

@article{sethi2021face,
  title={Face mask detection using deep learning: An approach to reduce risk of Coronavirus spread},
  author={Sethi, Shilpa and Kathuria, Mamta and Kaushik, Trilok},
  journal={Journal of Biomedical Informatics},
  volume={120},
  pages={103848},
  year={2021},
  publisher={Elsevier}
}

@misc{Chiang2020,
  author = {D. Chiang.},
  title = {“Detect faces and determine whether people are wearing mask,},
  year = {2020},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/AIZOOTech/FaceMaskDetection}}
}

@article{jiang2020retinamask,
  title={Retinamask: A face mask detector},
  author={Jiang, Mingjie and Fan, Xinqi and Yan, Hong},
  journal={arXiv preprint arXiv:2005.03950},
  year={2020}
}

@article{chen2019deep,
  title={Deep structured prediction for facial landmark detection},
  author={Chen, Lisha and Su, Hui and Ji, Qiang},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  pages={2450--2460},
  year={2019}
}

@article{deng2012mnist,
  title={The mnist database of handwritten digit images for machine learning research},
  author={Deng, Li},
  journal={IEEE Signal Processing Magazine},
  volume={29},
  number={6},
  pages={141--142},
  year={2012},
  publisher={IEEE}
}

@article{krizhevsky2014cifar,
  title={The cifar-10 dataset},
  author={Krizhevsky, Alex and Nair, Vinod and Hinton, Geoffrey},
  journal={online: http://www. cs. toronto. edu/kriz/cifar. html},
  volume={55},
  number={5},
  year={2014}
}

@article{lake2015human,
  title={Human-level concept learning through probabilistic program induction},
  author={Lake, Brenden M and Salakhutdinov, Ruslan and Tenenbaum, Joshua B},
  journal={Science},
  volume={350},
  number={6266},
  pages={1332--1338},
  year={2015},
  publisher={American Association for the Advancement of Science}
}

@article{xiao2017fashion,
  title={Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms},
  author={Xiao, Han and Rasul, Kashif and Vollgraf, Roland},
  journal={arXiv preprint arXiv:1708.07747},
  year={2017}
}

@article{netzer2011reading,
  title={Reading digits in natural images with unsupervised feature learning},
  author={Netzer, Yuval and Wang, Tao and Coates, Adam and Bissacco, Alessandro and Wu, Bo and Ng, Andrew Y},
  year={2011}
}

@article{journals/corr/YuZSSX15,
  added-at = {2018-08-13T00:00:00.000+0200},
  author = {Yu, Fisher and Zhang, Yinda and Song, Shuran and Seff, Ari and Xiao, Jianxiong},
  biburl = {https://www.bibsonomy.org/bibtex/2446d4ffb99a5d7d2ab6e5417a12e195f/dblp},
  ee = {http://arxiv.org/abs/1506.03365},
  interhash = {3e9306c4ce2ead125f3b2ab0e25adc85},
  intrahash = {446d4ffb99a5d7d2ab6e5417a12e195f},
  journal = {CoRR},
  keywords = {dblp},
  timestamp = {2018-08-14T15:08:59.000+0200},
  title = {LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop.},
  url = {http://dblp.uni-trier.de/db/journals/corr/corr1506.html#YuZSSX15},
  volume = {abs/1506.03365},
  year = 2015
}

@inproceedings{carreira2017quo,
  title={Quo vadis, action recognition? a new model and the kinetics dataset},
  author={Carreira, Joao and Zisserman, Andrew},
  booktitle={proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},
  pages={6299--6308},
  year={2017}
}

@inproceedings{tran2015learning,
  title={Learning spatiotemporal features with 3d convolutional networks},
  author={Tran, Du and Bourdev, Lubomir and Fergus, Rob and Torresani, Lorenzo and Paluri, Manohar},
  booktitle={Proceedings of the IEEE international conference on computer vision},
  pages={4489--4497},
  year={2015}
}

@article{soomro2012ucf101,
  title={UCF101: A dataset of 101 human actions classes from videos in the wild},
  author={Soomro, Khurram and Zamir, Amir Roshan and Shah, Mubarak},
  journal={arXiv preprint arXiv:1212.0402},
  year={2012}
}

@inproceedings{gal2017deep,
  title={Deep bayesian active learning with image data},
  author={Gal, Yarin and Islam, Riashat and Ghahramani, Zoubin},
  booktitle={International Conference on Machine Learning},
  pages={1183--1192},
  year={2017},
  organization={PMLR}
}

@article{daxberger2021laplace,
  title={Laplace Redux-Effortless Bayesian Deep Learning},
  author={Daxberger, Erik and Kristiadi, Agustinus and Immer, Alexander and Eschenhagen, Runa and Bauer, Matthias and Hennig, Philipp},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  year={2021}
}

@article{amari1998natural,
  title={Natural gradient works efficiently in learning},
  author={Amari, Shun-Ichi},
  journal={Neural computation},
  volume={10},
  number={2},
  pages={251--276},
  year={1998},
  publisher={MIT Press}
}

@article{schraudolph2002fast,
  title={Fast curvature matrix-vector products for second-order gradient descent},
  author={Schraudolph, Nicol N},
  journal={Neural computation},
  volume={14},
  number={7},
  pages={1723--1738},
  year={2002},
  publisher={MIT Press}
}

@article{valdenegro2019deep,
  title={Deep sub-ensembles for fast uncertainty estimation in image classification},
  author={Valdenegro-Toro, Matias},
  journal={arXiv preprint arXiv:1910.08168},
  year={2019}
}

@article{littwin2020collegial,
  title={Collegial ensembles},
  author={Littwin, Etai and Myara, Ben and Sabah, Sima and Susskind, Joshua and Zhai, Shuangfei and Golan, Oren},
  journal={arXiv preprint arXiv:2006.07678},
  year={2020}
}

@article{lee2015m,
  title={Why M heads are better than one: Training a diverse ensemble of deep networks},
  author={Lee, Stefan and Purushwalkam, Senthil and Cogswell, Michael and Crandall, David and Batra, Dhruv},
  journal={arXiv preprint arXiv:1511.06314},
  year={2015}
}

@article{wenzel2020hyperparameter,
  title={Hyperparameter ensembles for robustness and uncertainty quantification},
  author={Wenzel, Florian and Snoek, Jasper and Tran, Dustin and Jenatton, Rodolphe},
  journal={arXiv preprint arXiv:2006.13570},
  year={2020}
}

@inproceedings{ritter2018scalable,
  title={A scalable laplace approximation for neural networks},
  author={Ritter, Hippolyt and Botev, Aleksandar and Barber, David},
  booktitle={6th International Conference on Learning Representations, ICLR 2018-Conference Track Proceedings},
  volume={6},
  year={2018},
  organization={International Conference on Representation Learning}
}

@article{sensoy2018evidential,
  title={Evidential deep learning to quantify classification uncertainty},
  author={Sensoy, Murat and Kaplan, Lance and Kandemir, Melih},
  journal={arXiv preprint arXiv:1806.01768},
  year={2018}
}

@article{zaidi2020neural,
  title={Neural Ensemble Search for Uncertainty Estimation and Dataset Shift},
  author={Zaidi, Sheheryar and Zela, Arber and Elsken, Thomas and Holmes, Chris and Hutter, Frank and Teh, Yee Whye},
  year={2020}
}

@article{izmailov2021bayesian,
  title={What Are Bayesian Neural Network Posteriors Really Like?},
  author={Izmailov, Pavel and Vikram, Sharad and Hoffman, Matthew D and Wilson, Andrew Gordon},
  journal={arXiv preprint arXiv:2104.14421},
  year={2021}
}


@inproceedings{depeweg2018decomposition,
  title={Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning},
  author={Depeweg, Stefan and Hernandez-Lobato, Jose-Miguel and Doshi-Velez, Finale and Udluft, Steffen},
  booktitle={International Conference on Machine Learning},
  pages={1184--1193},
  year={2018},
  organization={PMLR}
}

@inproceedings{guo2017calibration,
  title={On calibration of modern neural networks},
  author={Guo, Chuan and Pleiss, Geoff and Sun, Yu and Weinberger, Kilian Q},
  booktitle={International Conference on Machine Learning},
  pages={1321--1330},
  year={2017},
  organization={PMLR}
}

@inproceedings{gustafsson2020evaluating,
  title={Evaluating scalable bayesian deep learning methods for robust computer vision},
  author={Gustafsson, Fredrik K and Danelljan, Martin and Schon, Thomas B},
  booktitle={Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops},
  pages={318--319},
  year={2020}
}

@inproceedings{immer2021scalable,
  title={Scalable marginal likelihood estimation for model selection in deep learning},
  author={Immer, Alexander and Bauer, Matthias and Fortuin, Vincent and R{\"a}tsch, Gunnar and Emtiyaz, Khan Mohammad},
  booktitle={International Conference on Machine Learning},
  pages={4563--4573},
  year={2021},
  organization={PMLR}
}
@article{humt2020bayesian,
  title={Bayesian optimization meets laplace approximation for robotic introspection},
  author={Humt, Matthias and Lee, Jongseok and Triebel, Rudolph},
  journal={arXiv preprint arXiv:2010.16141},
  year={2020}
}
@article{franchi2020encoding,
  title={Encoding the latent posterior of Bayesian Neural Networks for uncertainty quantification},
  author={Franchi, Gianni and Bursuc, Andrei and Aldea, Emanuel and Dubuisson, S{\'e}verine and Bloch, Isabelle},
  journal={arXiv preprint arXiv:2012.02818},
  year={2020}
}
@article{huang2017snapshot,
  title={Snapshot ensembles: Train 1, get m for free},
  author={Huang, Gao and Li, Yixuan and Pleiss, Geoff and Liu, Zhuang and Hopcroft, John E and Weinberger, Kilian Q},
  journal={arXiv preprint arXiv:1704.00109},
  year={2017}
}

@article{wilson2020bayesian,
  title={Bayesian deep learning and a probabilistic perspective of generalization},
  author={Wilson, Andrew G and Izmailov, Pavel},
  journal={Advances in neural information processing systems},
  volume={33},
  pages={4697--4708},
  year={2020}
}
@article{fort2019deep,
  title={Deep ensembles: A loss landscape perspective},
  author={Fort, Stanislav and Hu, Huiyi and Lakshminarayanan, Balaji},
  journal={arXiv preprint arXiv:1912.02757},
  year={2019}
}
@article{bian2021does,
  title={When does diversity help generalization in classification ensembles?},
  author={Bian, Yijun and Chen, Huanhuan},
  journal={IEEE Transactions on Cybernetics},
  year={2021},
  publisher={IEEE}
}
@article{zhang2020diversified,
  title={The diversified ensemble neural network},
  author={Zhang, Shaofeng and Liu, Meng and Yan, Junchi},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={16001--16011},
  year={2020}
}

@inproceedings{li2012diversity,
  title={Diversity regularized ensemble pruning},
  author={Li, Nan and Yu, Yang and Zhou, Zhi-Hua},
  booktitle={Joint European conference on machine learning and knowledge discovery in databases},
  pages={330--345},
  year={2012},
  organization={Springer}
}

@article{zaid2021efficiency,
  title={Efficiency through Diversity in Ensemble Models applied to Side-Channel Attacks:--A Case Study on Public-Key Algorithms--Efficiency through Diversity in Ensemble Models applied to Side-Channel Attacks:--A Case Study on Public-Key Algorithms--},
  author={Zaid, Gabriel and Bossuet, Lilian and Habrard, Amaury and Venelli, Alexandre},
  journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
  pages={60--96},
  year={2021}
}
@inproceedings{jain2020maximizing,
  title={Maximizing overall diversity for improved uncertainty estimates in deep ensembles},
  author={Jain, Siddhartha and Liu, Ge and Mueller, Jonas and Gifford, David},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={34},
  number={04},
  pages={4264--4271},
  year={2020}
}

@article{tan2021diversity,
  title={Diversity Enhanced Active Learning with Strictly Proper Scoring Rules},
  author={Tan, Wei and Du, Lan and Buntine, Wray},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  year={2021}
}
@inproceedings{dvornik2019diversity,
  title={Diversity with cooperation: Ensemble methods for few-shot classification},
  author={Dvornik, Nikita and Schmid, Cordelia and Mairal, Julien},
  booktitle={Proceedings of the IEEE/CVF International Conference on Computer Vision},
  pages={3723--3731},
  year={2019}
}
@inproceedings{wu2021boosting,
  title={Boosting ensemble accuracy by revisiting ensemble diversity metrics},
  author={Wu, Yanzhao and Liu, Ling and Xie, Zhongwei and Chow, Ka-Ho and Wei, Wenqi},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={16469--16477},
  year={2021}
}

@inproceedings{wu2020promoting,
  title={Promoting high diversity ensemble learning with ensemblebench},
  author={Wu, Yanzhao and Liu, Ling and Xie, Zhongwei and Bae, Juhyun and Chow, Ka-Ho and Wei, Wenqi},
  booktitle={2020 IEEE Second International Conference on Cognitive Machine Intelligence (CogMI)},
  pages={208--217},
  year={2020},
  organization={IEEE}
}

@article{liu1999ensemble,
  title={Ensemble learning via negative correlation},
  author={Liu, Yong and Yao, Xin},
  journal={Neural networks},
  volume={12},
  number={10},
  pages={1399--1404},
  year={1999},
  publisher={Elsevier}
}

@inproceedings{pearce2020uncertainty,
  title={Uncertainty in neural networks: Approximately bayesian ensembling},
  author={Pearce, Tim and Leibfried, Felix and Brintrup, Alexandra},
  booktitle={International conference on artificial intelligence and statistics},
  pages={234--244},
  year={2020},
  organization={PMLR}
}

@article{zhou2018diverse,
  title={Diverse ensemble evolution: Curriculum data-model marriage},
  author={Zhou, Tianyi and Wang, Shengjie and Bilmes, Jeff A},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  year={2018}
}
@article{liao2018sharpening,
  title={Sharpening Jensen's inequality},
  author={Liao, JG and Berg, Arthur},
  journal={The American Statistician},
  year={2018},
  publisher={Taylor \& Francis}
}

@article{gelman2011induction,
  title={Induction and deduction in Bayesian data analysis},
  author={Gelman, Andrew},
  year={2011}
}

@article{kleijn2012bernstein,
  title={The Bernstein-von-Mises theorem under misspecification},
  author={Kleijn, Bas JK and van der Vaart, Aad W},
  journal={Electronic Journal of Statistics},
  volume={6},
  pages={354--381},
  year={2012},
  publisher={Institute of Mathematical Statistics and Bernoulli Society}
}
@inproceedings{yang2016active,
  title={Active learning using uncertainty information},
  author={Yang, Yazhou and Loog, Marco},
  booktitle={2016 23rd International Conference on Pattern Recognition (ICPR)},
  pages={2646--2651},
  year={2016},
  organization={IEEE}
}

@article{hellman1970probability,
  title={Probability of error, equivocation, and the Chernoff bound},
  author={Hellman, Martin and Raviv, Josef},
  journal={IEEE Transactions on Information Theory},
  volume={16},
  number={4},
  pages={368--372},
  year={1970},
  publisher={IEEE}
}

@inproceedings{khan2019striking,
  title={Striking the right balance with uncertainty},
  author={Khan, Salman and Hayat, Munawar and Zamir, Syed Waqas and Shen, Jianbing and Shao, Ling},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={103--112},
  year={2019}
}

@inproceedings{cohen2017emnist,
  title={EMNIST: Extending MNIST to handwritten letters},
  author={Cohen, Gregory and Afshar, Saeed and Tapson, Jonathan and Van Schaik, Andre},
  booktitle={2017 international joint conference on neural networks (IJCNN)},
  pages={2921--2926},
  year={2017},
  organization={IEEE}
}

@article{krizhevsky2009learning,
  title={Learning multiple layers of features from tiny images},
  author={Krizhevsky, Alex and Hinton, Geoffrey and others},
  year={2009},
  publisher={Citeseer}
}

@article{wen2020batchensemble,
  title={Batchensemble: an alternative approach to efficient ensemble and lifelong learning},
  author={Wen, Yeming and Tran, Dustin and Ba, Jimmy},
  journal={arXiv preprint arXiv:2002.06715},
  year={2020}
}


@article{postels2021practicality,
  title={On the Practicality of Deterministic Epistemic Uncertainty},
  author={Postels, Janis and Segu, Mattia and Sun, Tao and Van Gool, Luc and Yu, Fisher and Tombari, Federico},
  journal={arXiv preprint arXiv:2107.00649},
  year={2021}
}

@article{van2008visualizing,
  title={Visualizing data using t-SNE.},
  author={Van der Maaten, Laurens and Hinton, Geoffrey},
  journal={Journal of machine learning research},
  volume={9},
  number={11},
  year={2008}
}

@article{clanuwat2018deep,
  title={Deep learning for classical japanese literature},
  author={Clanuwat, Tarin and Bober-Irizar, Mikel and Kitamoto, Asanobu and Lamb, Alex and Yamamoto, Kazuaki and Ha, David},
  journal={arXiv preprint arXiv:1812.01718},
  year={2018}
}

@inproceedings{hein2019relu,
  title={Why relu networks yield high-confidence predictions far away from the training data and how to mitigate the problem},
  author={Hein, Matthias and Andriushchenko, Maksym and Bitterwolf, Julian},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={41--50},
  year={2019}
}

@article{eschenhagen2021mixtures,
  title={Mixtures of Laplace Approximations for Improved Post-Hoc Uncertainty in Deep Learning},
  author={Eschenhagen, Runa and Daxberger, Erik and Hennig, Philipp and Kristiadi, Agustinus},
  journal={arXiv preprint arXiv:2111.03577},
  year={2021}
}

@inproceedings{wabartha2021handling,
  title={Handling black swan events in deep learning with diversely extrapolated neural networks},
  author={Wabartha, Maxime and Durand, Audrey and Francois-Lavet, Vincent and Pineau, Joelle},
  booktitle={Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence},
  pages={2140--2147},
  year={2021}
}

@article{tiulpin2021greedy,
  title={Greedy Bayesian posterior approximation with deep ensembles},
  author={Tiulpin, Aleksei and Blaschko, Matthew B},
  journal={arXiv preprint arXiv:2105.14275},
  year={2021}
}

@article{d2021repulsive,
  title={Repulsive deep ensembles are bayesian},
  author={D'Angelo, Francesco and Fortuin, Vincent},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={3451--3465},
  year={2021}
}

@article{yashima2022feature,
  title={Feature Space Particle Inference for Neural Network Ensembles},
  author={Yashima, Shingo and Suzuki, Teppei and Ishikawa, Kohta and Sato, Ikuro and Kawakami, Rei},
  journal={arXiv preprint arXiv:2206.00944},
  year={2022}
}

@article{wang2019function,
  title={Function space particle optimization for bayesian neural networks},
  author={Wang, Ziyu and Ren, Tongzheng and Zhu, Jun and Zhang, Bo},
  journal={arXiv preprint arXiv:1902.09754},
  year={2019}
}

@article{freund1997decision,
  title={A decision-theoretic generalization of on-line learning and an application to boosting},
  author={Freund, Yoav and Schapire, Robert E},
  journal={Journal of computer and system sciences},
  volume={55},
  number={1},
  pages={119--139},
  year={1997},
  publisher={Elsevier}
}

@article{hastie2009multi,
  title={Multi-class adaboost},
  author={Hastie, Trevor and Rosset, Saharon and Zhu, Ji and Zou, Hui},
  journal={Statistics and its Interface},
  volume={2},
  number={3},
  pages={349--360},
  year={2009},
  publisher={International Press of Boston}
}

@article{Tiny,
  author = {Stanford CS231N},
  title = {Tiny Imagenet},
  year = 2017,
  url = {https://tiny-imagenet.herokuapp.com/}
}

@inproceedings{dusenberry2020efficient,
  title={Efficient and scalable bayesian neural nets with rank-1 factors},
  author={Dusenberry, Michael and Jerfel, Ghassen and Wen, Yeming and Ma, Yian and Snoek, Jasper and Heller, Katherine and Lakshminarayanan, Balaji and Tran, Dustin},
  booktitle={International conference on machine learning},
  pages={2782--2792},
  year={2020},
  organization={PMLR}
}

@article{havasi2020training,
  title={Training independent subnetworks for robust prediction},
  author={Havasi, Marton and Jenatton, Rodolphe and Fort, Stanislav and Liu, Jeremiah Zhe and Snoek, Jasper and Lakshminarayanan, Balaji and Dai, Andrew M and Tran, Dustin},
  journal={arXiv preprint arXiv:2010.06610},
  year={2020}
}

@article{liu2021deep,
  title={Deep ensembling with no overhead for either training or testing: The all-round blessings of dynamic sparsity},
  author={Liu, Shiwei and Chen, Tianlong and Atashgahi, Zahra and Chen, Xiaohan and Sokar, Ghada and Mocanu, Elena and Pechenizkiy, Mykola and Wang, Zhangyang and Mocanu, Decebal Constantin},
  journal={arXiv preprint arXiv:2106.14568},
  year={2021}
}

@article{jantre2022sequential,
  title={Sequential Bayesian Neural Subnetwork Ensembles},
  author={Jantre, Sanket and Madireddy, Sandeep and Bhattacharya, Shrijita and Maiti, Tapabrata and Balaprakash, Prasanna},
  journal={arXiv preprint arXiv:2206.00794},
  year={2022}
}

@article{goodfellow2014explaining,
  title={Explaining and harnessing adversarial examples},
  author={Goodfellow, Ian J and Shlens, Jonathon and Szegedy, Christian},
  journal={arXiv preprint arXiv:1412.6572},
  year={2014}
}

@inproceedings{van2020uncertainty,
  title={Uncertainty estimation using a single deep deterministic neural network},
  author={Van Amersfoort, Joost and Smith, Lewis and Teh, Yee Whye and Gal, Yarin},
  booktitle={International conference on machine learning},
  pages={9690--9700},
  year={2020},
  organization={PMLR}
}