%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/

%% Created for Matthias Bitzer at 2023-06-01 10:05:09 +0200 


%% Saved with string encoding Unicode (UTF-8) 



@article{algpsshapecontrol,
	author = {Yue, Xiaowei and Wen, Yuchen and Hunt, Jeffrey H. and Shi, Jianjun},
	date-added = {2023-06-01 10:02:58 +0200},
	date-modified = {2023-06-01 10:04:55 +0200},
	journal = {IEEE Transactions on Automation Science and Engineering},
	number = {1},
	pages = {36-46},
	title = {Active Learning for Gaussian Process Considering Uncertainties With Application to Shape Control of Composite Fuselage},
	volume = {18},
	year = {2021}}

@inproceedings{pmlr-v206-bitzer23a,
	abstract = {Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior. Machine learning methods that are used to produce the surrogate model should therefore address these problems by providing a scheme to keep the number of queries small, e.g. by using active learning and be able to capture the nonlinear and nonstationary properties of the system. One way of modeling the nonstationarity is to induce input-partitioning, a principle that has proven to be advantageous in active learning for Gaussian processes. However, these methods either assume a known partitioning, need to introduce complex sampling schemes or rely on very simple geometries. In this work, we present a simple, yet powerful kernel family that incorporates a partitioning that: i) is learnable via gradient-based methods, ii) uses a geometry that is more flexible than previous ones, while still being applicable in the low data regime. Thus, it provides a good prior for active learning procedures. We empirically demonstrate excellent performance on various active learning tasks.},
	author = {Bitzer, Matthias and Meister, Mona and Zimmer, Christoph},
	booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
	date-added = {2023-05-15 09:49:25 +0200},
	date-modified = {2023-05-15 09:49:25 +0200},
	editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
	month = {25--27 Apr},
	pages = {7897--7912},
	pdf = {https://proceedings.mlr.press/v206/bitzer23a/bitzer23a.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Hierarchical-Hyperplane Kernels for Actively Learning Gaussian Process Models of Nonstationary Systems},
	url = {https://proceedings.mlr.press/v206/bitzer23a.html},
	volume = {206},
	year = {2023},
	bdsk-url-1 = {https://proceedings.mlr.press/v206/bitzer23a.html}}

@inproceedings{CKS,
	address = {Atlanta, Georgia, USA},
	author = {Duvenaud, David and Lloyd, James and Grosse, Roger and Tenenbaum, Joshua and Zoubin, Ghahramani},
	booktitle = {Proceedings of the 30th International Conference on Machine Learning},
	editor = {Dasgupta, Sanjoy and McAllester, David},
	month = {17--19 Jun},
	number = {3},
	pages = {1166--1174},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Structure Discovery in Nonparametric Regression through Compositional Kernel Search},
	volume = {28},
	year = {2013}}

@inproceedings{AutomaticStatistician,
	author = {Lloyd, James Robert and Duvenaud, David and Grosse, Roger and Tenenbaum, Joshua B. and Ghahramani, Zoubin},
	booktitle = {Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence},
	location = {Qu\'{e}bec City, Qu\'{e}bec, Canada},
	numpages = {9},
	pages = {1242--1250},
	publisher = {AAAI Press},
	series = {AAAI'14},
	title = {Automatic Construction and Natural-Language Description of Nonparametric Regression Models},
	year = {2014}}

@inproceedings{BOMS,
	author = {Malkomes, Gustavo and Schaff, Charles and Garnett, Roman},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {D. Lee and M. Sugiyama and U. Luxburg and I. Guyon and R. Garnett},
	publisher = {Curran Associates, Inc.},
	title = {Bayesian optimization for automated model selection},
	volume = {29},
	year = {2016}}

@inproceedings{NASviaOT,
	address = {Red Hook, NY, USA},
	author = {Kandasamy, Kirthevasan and Neiswanger, Willie and Schneider, Jeff and P\'{o}czos, Barnab\'{a}s and Xing, Eric P.},
	booktitle = {Proceedings of the 32nd International Conference on Neural Information Processing Systems},
	location = {Montr\'{e}al, Canada},
	numpages = {10},
	pages = {2020--2029},
	publisher = {Curran Associates Inc.},
	series = {NIPS'18},
	title = {Neural Architecture Search with Bayesian Optimisation and Optimal Transport},
	year = {2018}}

@inproceedings{ChemBO,
	author = {Korovina, Ksenia and Xu, Sailun and Kandasamy, Kirthevasan and Neiswanger, Willie and Poczos, Barnabas and Schneider, Jeff and Xing, Eric},
	booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
	editor = {Chiappa, Silvia and Calandra, Roberto},
	month = {26--28 Aug},
	pages = {3393--3403},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations},
	volume = {108},
	year = {2020}}

@inproceedings{NASviaWassersteinOT,
	author = {Nguyen, Vu and Le, Tam and Yamada, Makoto and Osborne, Michael A.},
	booktitle = {Proceedings of the 38th International Conference on Machine Learning},
	editor = {Meila, Marina and Zhang, Tong},
	month = {18--24 Jul},
	pages = {8084--8095},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search},
	volume = {139},
	year = {2021}}

@inproceedings{NKN,
	author = {Sun, Shengyang and Zhang, Guodong and Wang, Chaoqi and Zeng, Wenyuan and Li, Jiaman and Grosse, Roger},
	booktitle = {Proceedings of the 35th International Conference on Machine Learning},
	editor = {Dy, Jennifer and Krause, Andreas},
	month = {10--15 Jul},
	pages = {4828--4837},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Differentiable Compositional Kernel Learning for {G}aussian Processes},
	volume = {80},
	year = {2018}}

@inproceedings{KernelTransformer,
	author = {Simpson, Fergus and Davies, Ian and Lalchand, Vidhi and Vullo, Alessandro and Durrande, Nicolas and Rasmussen, Carl Edward},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
	pages = {10483--10495},
	publisher = {Curran Associates, Inc.},
	title = {Kernel Identification Through Transformers},
	url = {https://proceedings.neurips.cc/paper/2021/file/56c3b2c6ea3a83aaeeff35eeb45d700d-Paper.pdf},
	volume = {34},
	year = {2021},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2021/file/56c3b2c6ea3a83aaeeff35eeb45d700d-Paper.pdf}}

@inproceedings{MultipleKernelLearning,
	author = {Bach, Francis},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou},
	publisher = {Curran Associates, Inc.},
	title = {Exploring Large Feature Spaces with Hierarchical Multiple Kernel Learning},
	url = {https://proceedings.neurips.cc/paper/2008/file/a4a042cf4fd6bfb47701cbc8a1653ada-Paper.pdf},
	volume = {21},
	year = {2008},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2008/file/a4a042cf4fd6bfb47701cbc8a1653ada-Paper.pdf}}

@article{MKLAlgorithms,
	author = {G\"{o}nen, Mehmet and Alpayd\i{}n, Ethem},
	issn = {1532-4435},
	issue_date = {2/1/2011},
	month = {jul},
	number = {null},
	numpages = {58},
	pages = {2211--2268},
	publisher = {JMLR.org},
	title = {Multiple Kernel Learning Algorithms},
	volume = {12},
	year = {2011}}

@inproceedings{FastKernelLearningWilson,
	author = {Wilson, Andrew G and Gilboa, Elad and Nehorai, Arye and Cunningham, John P},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {Z. Ghahramani and M. Welling and C. Cortes and N. Lawrence and K.Q. Weinberger},
	publisher = {Curran Associates, Inc.},
	title = {Fast Kernel Learning for Multidimensional Pattern Extrapolation},
	url = {https://proceedings.neurips.cc/paper/2014/file/77369e37b2aa1404f416275183ab055f-Paper.pdf},
	volume = {27},
	year = {2014},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2014/file/77369e37b2aa1404f416275183ab055f-Paper.pdf}}

@inproceedings{WilsonExtrapolate,
	address = {Atlanta, Georgia, USA},
	author = {Wilson, Andrew and Adams, Ryan},
	booktitle = {Proceedings of the 30th International Conference on Machine Learning},
	editor = {Dasgupta, Sanjoy and McAllester, David},
	month = {17--19 Jun},
	number = {3},
	pages = {1067--1075},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Gaussian Process Kernels for Pattern Discovery and Extrapolation},
	volume = {28},
	year = {2013}}

@inproceedings{NLPKernel,
	author = {Collins, Michael and Duffy, Nigel},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {T. Dietterich and S. Becker and Z. Ghahramani},
	publisher = {MIT Press},
	title = {Convolution Kernels for Natural Language},
	url = {https://proceedings.neurips.cc/paper/2001/file/bf424cb7b0dea050a42b9739eb261a3a-Paper.pdf},
	volume = {14},
	year = {2001},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2001/file/bf424cb7b0dea050a42b9739eb261a3a-Paper.pdf}}

@inproceedings{PromisesAndPitfallsofDKL,
	author = {Ober, Sebastian W. and Rasmussen, Carl E. and van der Wilk, Mark},
	booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence},
	editor = {de Campos, Cassio and Maathuis, Marloes H.},
	month = {27--30 Jul},
	pages = {1206--1216},
	pdf = {https://proceedings.mlr.press/v161/ober21a/ober21a.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {The promises and pitfalls of deep kernel learning},
	volume = {161},
	year = {2021}}

@inproceedings{DKL,
	address = {Cadiz, Spain},
	author = {Wilson, Andrew Gordon and Hu, Zhiting and Salakhutdinov, Ruslan and Xing, Eric P.},
	booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
	pages = {370--378},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Deep Kernel Learning},
	volume = {51},
	year = {2016}}

@article{probInHD,
	added-at = {2019-06-09T20:31:32.000+0200},
	author = {van Handel, Ramon},
	biburl = {https://www.bibsonomy.org/bibtex/2a29d65d7d2e770511b492d5b617be0c0/kirk86},
	description = {APC550.pdf},
	interhash = {28060bf77784608166771ffb67c37d49},
	intrahash = {a29d65d7d2e770511b492d5b617be0c0},
	keywords = {book probability stats theory},
	timestamp = {2019-06-09T20:31:44.000+0200},
	title = {Probability in High Dimensions},
	url = {https://web.math.princeton.edu/~rvan/APC550.pdf},
	year = 2016,
	bdsk-url-1 = {https://web.math.princeton.edu/~rvan/APC550.pdf}}

@inproceedings{PracticalBO,
	author = {Snoek, Jasper and Larochelle, Hugo and Adams, Ryan P},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {F. Pereira and C.J. Burges and L. Bottou and K.Q. Weinberger},
	publisher = {Curran Associates, Inc.},
	title = {Practical Bayesian Optimization of Machine Learning Algorithms},
	url = {https://proceedings.neurips.cc/paper/2012/file/05311655a15b75fab86956663e1819cd-Paper.pdf},
	volume = {25},
	year = {2012},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2012/file/05311655a15b75fab86956663e1819cd-Paper.pdf}}

@inproceedings{SafeALTimeSeries,
	author = {Zimmer, Christoph and Meister, Mona and Nguyen-Tuong, Duy},
	booktitle = {Advances in Neural Information Processing Systems},
	publisher = {Curran Associates, Inc.},
	title = {Safe Active Learning for Time-Series Modeling with Gaussian Processes},
	volume = {31},
	year = {2018}}

@inproceedings{SchreiterSafeAL,
	address = {Gewerbestrasse 11 CH-6330, Cham (ZG), CHE},
	author = {Schreiter, Jens and Nguyen-Tuong, Duy and Eberts, Mona and Bischoff, Bastian and Markert, Heiner and Toussaint, Marc},
	booktitle = {Proceedings of the 2015th European Conference on Machine Learning and Knowledge Discovery in Databases - Volume Part III},
	isbn = {9783319234601},
	location = {Porto, Portugal},
	numpages = {17},
	pages = {133--149},
	publisher = {Springer},
	series = {ECMLPKDD'15},
	title = {Safe Exploration for Active Learning with Gaussian Processes},
	year = {2015}}

@article{TreeGEP,
	address = {Berlin, Heidelberg},
	author = {Jin, Seung-Seop},
	doi = {10.1007/s00158-020-02559-7},
	issn = {1615-147X},
	issue_date = {Sep 2020},
	journal = {Struct. Multidiscip. Optim.},
	keywords = {Surrogate modeling, Tree-based genetic programming, Compositional kernel learning, Gaussian processes regression, Reliability analysis},
	month = {sep},
	number = {3},
	numpages = {39},
	pages = {1313--1351},
	publisher = {Springer-Verlag},
	title = {Compositional Kernel Learning Using Tree-Based Genetic Programming for Gaussian Process Regression},
	url = {https://doi.org/10.1007/s00158-020-02559-7},
	volume = {62},
	year = {2020},
	bdsk-url-1 = {https://doi.org/10.1007/s00158-020-02559-7}}

@book{3569,
	address = {Cambridge, MA, USA},
	author = {Rasmussen and Williams},
	month = jan,
	month_numeric = {1},
	organization = {Max-Planck-Gesellschaft},
	pages = {248},
	publisher = {MIT Press},
	school = {Biologische Kybernetik},
	series = {Adaptive Computation and Machine Learning},
	title = {Gaussian Processes for Machine Learning},
	year = {2006}}

@inproceedings{SnoekInputWarping,
	address = {Bejing, China},
	author = {Snoek, Jasper and Swersky, Kevin and Zemel, Rich and Adams, Ryan},
	booktitle = {Proceedings of the 31st International Conference on Machine Learning},
	editor = {Xing, Eric P. and Jebara, Tony},
	month = {22--24 Jun},
	number = {2},
	pages = {1674--1682},
	pdf = {http://proceedings.mlr.press/v32/snoek14.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Input Warping for Bayesian Optimization of Non-Stationary Functions},
	volume = {32},
	year = {2014}}

@article{GPflow2017,
	author = {Matthews, Alexander G. de G. and {van der Wilk}, Mark and Nickson, Tom and Fujii, Keisuke. and {Boukouvalas}, Alexis and {Le{\'o}n-Villagr{\'a}}, Pablo and Ghahramani, Zoubin and Hensman, James},
	journal = {Journal of Machine Learning Research},
	month = {apr},
	number = {40},
	pages = {1-6},
	title = {{{GP}flow: A {G}aussian process library using {T}ensor{F}low}},
	url = {http://jmlr.org/papers/v18/16-537.html},
	volume = {18},
	year = {2017},
	bdsk-url-1 = {http://jmlr.org/papers/v18/16-537.html}}

@inproceedings{occamsrazor,
	author = {Rasmussen, Carl and Ghahramani, Zoubin},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {T. Leen and T. Dietterich and V. Tresp},
	publisher = {MIT Press},
	title = {Occam's Razor},
	url = {https://proceedings.neurips.cc/paper/2000/file/0950ca92a4dcf426067cfd2246bb5ff3-Paper.pdf},
	volume = {13},
	year = {2000},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2000/file/0950ca92a4dcf426067cfd2246bb5ff3-Paper.pdf}}

@article{mackay92,
	author = {MacKay, David J. C.},
	doi = {10.1162/neco.1992.4.3.415},
	eprint = {https://direct.mit.edu/neco/article-pdf/4/3/415/812340/neco.1992.4.3.415.pdf},
	issn = {0899-7667},
	journal = {Neural Computation},
	month = {05},
	number = {3},
	pages = {415-447},
	title = {Bayesian Interpolation},
	url = {https://doi.org/10.1162/neco.1992.4.3.415},
	volume = {4},
	year = {1992},
	bdsk-url-1 = {https://doi.org/10.1162/neco.1992.4.3.415}}

@book{villani2008optimal,
	author = {Villani, C.},
	isbn = {9783540710509},
	lccn = {2008932183},
	publisher = {Springer Berlin Heidelberg},
	series = {Grundlehren der mathematischen Wissenschaften},
	title = {Optimal Transport: Old and New},
	url = {https://books.google.de/books?id=hV8o5R7\_5tkC},
	year = {2008},
	bdsk-url-1 = {https://books.google.de/books?id=hV8o5R7%5C_5tkC}}

@inbook{FKL,
	address = {Red Hook, NY, USA},
	articleno = {1340},
	author = {Benton, Gregory W. and Maddox, Wesley J. and Salkey, Jayson P. and Albinati, Julio and Wilson, Andrew Gordon},
	booktitle = {Proceedings of the 33rd International Conference on Neural Information Processing Systems},
	numpages = {12},
	publisher = {Curran Associates Inc.},
	title = {Function-Space Distributions over Kernels},
	year = {2019}}

@inproceedings{AHGP,
	author = {Liu, Sulin and Sun, Xingyuan and Ramadge, Peter J and Adams, Ryan P},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
	pages = {21440--21452},
	publisher = {Curran Associates, Inc.},
	title = {Task-Agnostic Amortized Inference of Gaussian Process Hyperparameters},
	url = {https://proceedings.neurips.cc/paper/2020/file/f52db9f7c0ae7017ee41f63c2a7353bc-Paper.pdf},
	volume = {33},
	year = {2020},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2020/file/f52db9f7c0ae7017ee41f63c2a7353bc-Paper.pdf}}

@article{rehn2022amortized,
	author = {Rehn, Aki},
	journal = {Master Thesis},
	publisher = {Helsingin yliopisto},
	title = {Amortized Bayesian inference of Gaussian process hyperparameters},
	year = {2022}}

@inproceedings{AttentionIsAllYouNeed,
	author = {Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser, \L ukasz and Polosukhin, Illia},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {I. Guyon and U. Von Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
	publisher = {Curran Associates, Inc.},
	title = {Attention is All you Need},
	url = {https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf},
	volume = {30},
	year = {2017},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf}}

@inproceedings{bitzer2022structural,
	author = {Matthias Bitzer and Mona Meister and Christoph Zimmer},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
	title = {Structural Kernel Search via Bayesian Optimization and Symbolical Optimal Transport},
	url = {https://openreview.net/forum?id=-bLLVk-WRPy},
	year = {2022},
	bdsk-url-1 = {https://openreview.net/forum?id=-bLLVk-WRPy}}

@inproceedings{RADAM,
	author = {Liyuan Liu and Haoming Jiang and Pengcheng He and Weizhu Chen and Xiaodong Liu and Jianfeng Gao and Jiawei Han},
	bibsource = {dblp computer science bibliography, https://dblp.org},
	biburl = {https://dblp.org/rec/conf/iclr/LiuJHCLG020.bib},
	booktitle = {8th International Conference on Learning Representations, {ICLR} 2020, Addis Ababa, Ethiopia, April 26-30, 2020},
	publisher = {OpenReview.net},
	timestamp = {Mon, 30 May 2022 13:48:58 +0200},
	title = {On the Variance of the Adaptive Learning Rate and Beyond},
	url = {https://openreview.net/forum?id=rkgz2aEKDr},
	year = {2020},
	bdsk-url-1 = {https://openreview.net/forum?id=rkgz2aEKDr}}

@inproceedings{KernelIdentWithTrafo,
	author = {Simpson, Fergus and Davies, Ian and Lalchand, Vidhi and Vullo, Alessandro and Durrande, Nicolas and Rasmussen, Carl Edward},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
	pages = {10483--10495},
	publisher = {Curran Associates, Inc.},
	title = {Kernel Identification Through Transformers},
	url = {https://proceedings.neurips.cc/paper/2021/file/56c3b2c6ea3a83aaeeff35eeb45d700d-Paper.pdf},
	volume = {34},
	year = {2021},
	bdsk-url-1 = {https://proceedings.neurips.cc/paper/2021/file/56c3b2c6ea3a83aaeeff35eeb45d700d-Paper.pdf}}

@inproceedings{hypernetworkUnknownArch,
	author = {Boris Knyazev and Michal Drozdzal and Graham W. Taylor and Adriana Romero},
	booktitle = {Advances in Neural Information Processing Systems},
	editor = {A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
	title = {Parameter Prediction for Unseen Deep Architectures},
	url = {https://openreview.net/forum?id=vqHak8NLk25},
	year = {2021},
	bdsk-url-1 = {https://openreview.net/forum?id=vqHak8NLk25}}

@inproceedings{PFN,
	author = {Samuel M{\"u}ller and Noah Hollmann and Sebastian Pineda Arango and Josif Grabocka and Frank Hutter},
	booktitle = {International Conference on Learning Representations},
	title = {Transformers Can Do Bayesian Inference},
	url = {https://openreview.net/forum?id=KSugKcbNf9},
	year = {2022},
	bdsk-url-1 = {https://openreview.net/forum?id=KSugKcbNf9}}

@inproceedings{SafeALMOGP,
	abstract = { Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the inherent correlations and provide reliable uncertainty estimates. In many applications, however, acquiring the data is expensive and safety concerns might arise (e.g. robotics, engineering). We propose a safe active learning approach for multi-output Gaussian process regression. This approach queries the most informative data or output taking the relatedness between the regressors and safety constraints into account. We prove the effectiveness of our approach by providing theoretical analysis and by demonstrating empirical results on simulated datasets and on a real-world engineering dataset. On all datasets, our approach shows improved convergence compared to its competitors. },
	author = {Li, Cen-You and Rakitsch, Barbara and Zimmer, Christoph},
	booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
	editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
	month = {28--30 Mar},
	pages = {4512--4551},
	pdf = {https://proceedings.mlr.press/v151/li22d/li22d.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Safe Active Learning for Multi-Output Gaussian Processes},
	url = {https://proceedings.mlr.press/v151/li22d.html},
	volume = {151},
	year = {2022},
	bdsk-url-1 = {https://proceedings.mlr.press/v151/li22d.html}}

@inproceedings{svgp,
	abstract = {Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, out-performing the state of the art on benchmark datasets. Importantly, the variational formulation an be exploited to allow classification in problems with millions of data points, as we demonstrate in experiments.},
	address = {San Diego, California, USA},
	author = {Hensman, James and Matthews, Alexander and Ghahramani, Zoubin},
	booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
	editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
	month = {09--12 May},
	pages = {351--360},
	pdf = {http://proceedings.mlr.press/v38/hensman15.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {{Scalable Variational Gaussian Process Classification}},
	url = {https://proceedings.mlr.press/v38/hensman15.html},
	volume = {38},
	year = {2015},
	bdsk-url-1 = {https://proceedings.mlr.press/v38/hensman15.html}}

@inproceedings{amortized_infer2,
	abstract = {We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning.   Our algorithm introduces a recognition model to represent an approximate posterior distribution and uses this for optimisation of a variational lower bound.  We develop stochastic backpropagation -- rules for gradient backpropagation through stochastic variables -- and   derive an algorithm that allows for joint optimisation of the parameters of both the generative and recognition models.  We demonstrate on several real-world data sets that by using stochastic backpropagation and variational inference, we obtain models that are able to  generate realistic samples of data, allow for accurate imputations of missing data, and provide a useful tool for high-dimensional data visualisation.},
	address = {Bejing, China},
	author = {Rezende, Danilo Jimenez and Mohamed, Shakir and Wierstra, Daan},
	booktitle = {Proceedings of the 31st International Conference on Machine Learning},
	editor = {Xing, Eric P. and Jebara, Tony},
	month = {22--24 Jun},
	number = {2},
	pages = {1278--1286},
	pdf = {http://proceedings.mlr.press/v32/rezende14.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Stochastic Backpropagation and Approximate Inference in Deep Generative Models},
	url = {https://proceedings.mlr.press/v32/rezende14.html},
	volume = {32},
	year = {2014},
	bdsk-url-1 = {https://proceedings.mlr.press/v32/rezende14.html}}

@inproceedings{SetTransformer,
	abstract = {Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.},
	author = {Lee, Juho and Lee, Yoonho and Kim, Jungtaek and Kosiorek, Adam and Choi, Seungjin and Teh, Yee Whye},
	booktitle = {Proceedings of the 36th International Conference on Machine Learning},
	editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
	month = {09--15 Jun},
	pages = {3744--3753},
	pdf = {http://proceedings.mlr.press/v97/lee19d/lee19d.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks},
	url = {https://proceedings.mlr.press/v97/lee19d.html},
	volume = {97},
	year = {2019},
	bdsk-url-1 = {https://proceedings.mlr.press/v97/lee19d.html}}

@inproceedings{pre_layer_norm_trans,
	abstract = {The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.},
	author = {Xiong, Ruibin and Yang, Yunchang and He, Di and Zheng, Kai and Zheng, Shuxin and Xing, Chen and Zhang, Huishuai and Lan, Yanyan and Wang, Liwei and Liu, Tieyan},
	booktitle = {Proceedings of the 37th International Conference on Machine Learning},
	editor = {III, Hal Daum{\'e} and Singh, Aarti},
	month = {13--18 Jul},
	pages = {10524--10533},
	pdf = {http://proceedings.mlr.press/v119/xiong20b/xiong20b.pdf},
	publisher = {PMLR},
	series = {Proceedings of Machine Learning Research},
	title = {On Layer Normalization in the Transformer Architecture},
	url = {https://proceedings.mlr.press/v119/xiong20b.html},
	volume = {119},
	year = {2020},
	bdsk-url-1 = {https://proceedings.mlr.press/v119/xiong20b.html}}

@inproceedings{amortized_infer1,
	abstract = {How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions is two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.},
	added-at = {2020-10-15T14:36:56.000+0200},
	author = {Kingma, Diederik P. and Welling, Max},
	biburl = {https://www.bibsonomy.org/bibtex/242e5be6faa01cba2587f4907ac99dce8/annakrause},
	booktitle = {2nd International Conference on Learning Representations, {ICLR} 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings},
	eprint = {http://arxiv.org/abs/1312.6114v10},
	eprintclass = {stat.ML},
	eprinttype = {arXiv},
	file = {:http\://arxiv.org/pdf/1312.6114v10:PDF;:KingmaWelling_Auto-EncodingVariationalBayes.pdf:PDF},
	interhash = {a626a9d77a123c52405a08da983203cb},
	intrahash = {42e5be6faa01cba2587f4907ac99dce8},
	keywords = {cs.LG stat.ML vae},
	timestamp = {2021-02-01T17:13:18.000+0100},
	title = {{Auto-Encoding Variational Bayes}},
	year = 2014}

@article{hypernetworkHyperparamInp,
	author = {Jonathan Lorraine and David Duvenaud},
	bibsource = {dblp computer science bibliography, https://dblp.org},
	biburl = {https://dblp.org/rec/journals/corr/abs-1802-09419.bib},
	eprint = {1802.09419},
	eprinttype = {arXiv},
	journal = {CoRR},
	timestamp = {Thu, 14 Oct 2021 09:14:35 +0200},
	title = {Stochastic Hyperparameter Optimization through Hypernetworks},
	url = {http://arxiv.org/abs/1802.09419},
	volume = {abs/1802.09419},
	year = {2018},
	bdsk-url-1 = {http://arxiv.org/abs/1802.09419}}

@inproceedings{hypernetworks,
	author = {David Ha and Andrew M. Dai and Quoc V. Le},
	booktitle = {International Conference on Learning Representations},
	title = {HyperNetworks},
	url = {https://openreview.net/forum?id=rkpACe1lx},
	year = {2017},
	bdsk-url-1 = {https://openreview.net/forum?id=rkpACe1lx}}

@book{kernel_methods_pattern,
	author = {Shawe-Taylor, John and Cristianini, Nello},
	place = {Cambridge},
	publisher = {Cambridge University Press},
	title = {Kernel Methods for Pattern Analysis},
	year = {2004}}

@article{sparseTransformer,
	author = {Rewon Child and Scott Gray and Alec Radford and Ilya Sutskever},
	bibsource = {dblp computer science bibliography, https://dblp.org},
	biburl = {https://dblp.org/rec/journals/corr/abs-1904-10509.bib},
	eprint = {1904.10509},
	eprinttype = {arXiv},
	journal = {CoRR},
	timestamp = {Thu, 02 May 2019 15:13:44 +0200},
	title = {Generating Long Sequences with Sparse Transformers},
	url = {http://arxiv.org/abs/1904.10509},
	volume = {abs/1904.10509},
	year = {2019},
	bdsk-url-1 = {http://arxiv.org/abs/1904.10509}}

@inproceedings{gardner2018gpytorch,
	author = {Gardner, Jacob R and Pleiss, Geoff and Bindel, David and Weinberger, Kilian Q and Wilson, Andrew Gordon},
	booktitle = {Advances in Neural Information Processing Systems},
	title = {GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration},
	year = {2018}}
