@inproceedings{calandra2016manifold,
  title={Manifold {G}aussian processes for regression},
  author={Calandra, Roberto and Peters, Jan and Rasmussen, Carl Edward and Deisenroth, Marc Peter},
  booktitle={2016 International Joint Conference on Neural Networks (IJCNN)},
  pages={3338--3345},
  year={2016},
  organization={IEEE}
}

@InProceedings{gordon16_DKL,
title = {Deep Kernel Learning}, 
author = {Andrew Gordon Wilson and Zhiting Hu and Ruslan Salakhutdinov and Eric P. Xing}, 
booktitle = {International Conference on Artificial Intelligence and Statistics (AISTATS)},
year = {2016},
 }

@inproceedings{wilson2016stochastic,
  title={Stochastic variational deep kernel learning},
  author={Wilson, Andrew Gordon and Hu, Zhiting and Salakhutdinov, Ruslan and Xing, Eric P},
  booktitle={Proceedings of the 30th International Conference on Neural Information Processing Systems},
  pages={2594--2602},
  year={2016}
}

@book{gp_book,
author = {Rasmussen, Carl Edward and Williams, Christopher K. I.},
title = {{G}aussian Processes for Machine Learning},
year = {2006},
publisher = {The MIT Press}
}

@article{achituve2021personalized,
  title={Personalized federated learning with {G}aussian processes},
  author={Achituve, Idan and Shamsian, Aviv and Navon, Aviv and Chechik, Gal and Fetaya, Ethan},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={8392--8406},
  year={2021}
}

@inproceedings{snell2020bayesian,
  title={{B}ayesian Few-Shot Classification with One-vs-Each {P\'o}lya-{G}amma Augmented {G}aussian Processes},
  author={Snell, Jake and Zemel, Richard},
  booktitle={International Conference on Learning Representations},
  year={2021}
}

@inproceedings{ober2021promises,
  title={The promises and pitfalls of deep kernel learning},
  author={Ober, Sebastian W and Rasmussen, Carl E and van der Wilk, Mark},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={1206--1216},
  year={2021},
  organization={PMLR}
}

@article{van2021feature,
  title={On feature collapse and deep kernel learning for single forward pass uncertainty},
  author={van Amersfoort, Joost and Smith, Lewis and Jesson, Andrew and Key, Oscar and Gal, Yarin},
  journal={arXiv preprint arXiv:2102.11409},
  year={2021}
}

@article{silverman1985some,
  title={Some aspects of the spline smoothing approach to non-parametric regression curve fitting},
  author={Silverman, Bernhard W},
  journal={Journal of the Royal Statistical Society: Series B (Methodological)},
  volume={47},
  number={1},
  pages={1--21},
  year={1985},
  publisher={Wiley Online Library}
}

@article{quinonero2005unifying,
  title={A unifying view of sparse approximate {G}aussian process regression},
  author={Quinonero-Candela, Joaquin and Rasmussen, Carl Edward},
  journal={The Journal of Machine Learning Research},
  volume={6},
  pages={1939--1959},
  year={2005},
  publisher={JMLR. org}
}

@inproceedings{sneldon_Gharamani_IP,
 author = {Snelson, Edward and Ghahramani, Zoubin},
 booktitle = {Advances in Neural Information Processing Systems},
 pages = {1257--1264},
 publisher = {MIT Press},
 title = {Sparse {G}aussian Processes using Pseudo-inputs},
 year = {2006}
}

@book{neal2012bayesian,
  title={Bayesian learning for neural networks},
  author={Neal, Radford M},
  volume={118},
  year={1996},
  publisher={Springer Science \& Business Media}
}

@inproceedings{LeeBNSPS18,
  author    = {Jaehoon Lee and
               Yasaman Bahri and
               Roman Novak and
               Samuel S. Schoenholz and
               Jeffrey Pennington and
               Jascha Sohl{-}Dickstein},
  title     = {Deep Neural Networks as {G}aussian Processes},
  booktitle = {6th International Conference on Learning Representations, {ICLR}},
  year      = {2018},
}

@inproceedings{MatthewsHRTG18,
  author    = {Alexander G. de G. Matthews and
               Jiri Hron and
               Mark Rowland and
               Richard E. Turner and
               Zoubin Ghahramani},
  title     = {Gaussian Process Behaviour in Wide Deep Neural Networks},
  booktitle = {6th International Conference on Learning Representations, {ICLR}},
  year      = {2018},
}

@inproceedings{Garriga-AlonsoR19,
  author    = {Adri{\`{a}} Garriga{-}Alonso and
               Carl Edward Rasmussen and
               Laurence Aitchison},
  title     = {Deep Convolutional Networks as shallow {G}aussian Processes},
  booktitle = {7th International Conference on Learning Representations, {ICLR}},
  year      = {2019},
}

@inproceedings{NovakXBLYHAPS19,
  author    = {Roman Novak and
               Lechao Xiao and
               Yasaman Bahri and
               Jaehoon Lee and
               Greg Yang and
               Jiri Hron and
               Daniel A. Abolafia and
               Jeffrey Pennington and
               Jascha Sohl{-}Dickstein},
  title     = {Bayesian Deep Convolutional Networks with Many Channels are {G}aussian
               Processes},
  booktitle = {7th International Conference on Learning Representations, {ICLR}},
  year      = {2019},
}

@article{yang2019scaling,
  title={Scaling limits of wide neural networks with weight sharing: {G}aussian process behavior, gradient independence, and neural tangent kernel derivation},
  author={Yang, Greg},
  journal={arXiv preprint arXiv:1902.04760},
  year={2019}
}

@inproceedings{titsias2009variational,
  title={Variational learning of inducing variables in sparse {G}aussian processes},
  author={Titsias, Michalis},
  booktitle={Artificial intelligence and statistics},
  pages={567--574},
  year={2009},
  organization={PMLR}
}

@inproceedings{matthews2016sparse,
  title={On sparse variational methods and the {K}ullback-{L}eibler divergence between stochastic processes},
  author={Matthews, Alexander G de G and Hensman, James and Turner, Richard and Ghahramani, Zoubin},
  booktitle={Artificial Intelligence and Statistics},
  pages={231--239},
  year={2016},
  organization={PMLR}
}

@inproceedings{sunfunctional,
  title={Functional variational {B}ayesian neural networks},
  author={Sun, Shengyang and Zhang, Guodong and Shi, Jiaxin and Grosse, Roger},
  booktitle = {7th International Conference on Learning Representations, {ICLR}},
  year      = {2019},
}

@article{ma2021functional,
  title={Functional variational inference based on stochastic process generators},
  author={Ma, Chao and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={21795--21807},
  year={2021}
}

@inproceedings{mallick2021deep,
  title={Deep kernels with probabilistic embeddings for small-data learning},
  author={Mallick, Ankur and Dwivedi, Chaitanya and Kailkhura, Bhavya and Joshi, Gauri and Han, T Yong-Jin},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={918--928},
  year={2021},
  organization={PMLR}
}

@article{liu2021deep,
  title={Deep latent-variable kernel learning},
  author={Liu, Haitao and Ong, Yew-Soon and Jiang, Xiaomo and Wang, Xiaofang},
  journal={IEEE Transactions on Cybernetics},
  volume={52},
  number={10},
  pages={10276--10289},
  year={2021},
  publisher={IEEE}
}

@inproceedings{burtunderstanding,
  title={Understanding Variational Inference in Function-Space},
  author={Burt, David R and Ober, Sebastian W and Garriga-Alonso, Adri{\`a} and van der Wilk, Mark},
  booktitle={Third Symposium on Advances in Approximate Bayesian Inference},
  year={2020},
}

@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}
}

@inproceedings{lotfi2022bayesian,
  title={Bayesian model selection, the marginal likelihood, and generalization},
  author={Lotfi, Sanae and Izmailov, Pavel and Benton, Gregory and Goldblum, Micah and Wilson, Andrew Gordon},
  booktitle={International Conference on Machine Learning},
  pages={14223--14247},
  year={2022},
  organization={PMLR}
}

@inproceedings{hensman2013gaussian,
  title={Gaussian Processes for Big Data},
  author={Hensman, James and Fusi, Nicolo and Lawrence, Neil D},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={282},
  year={2013},
  organization={Citeseer}
}

@article{bradshaw2017adversarial,
  title={Adversarial examples, uncertainty, and transfer testing robustness in {G}aussian process hybrid deep networks},
  author={Bradshaw, John and Matthews, Alexander G de G and Ghahramani, Zoubin},
  journal={arXiv preprint arXiv:1707.02476},
  year={2017}
}

@inproceedings{achituve2021gp,
  title={{GP}-{T}ree: A {G}aussian process classifier for few-shot incremental learning},
  author={Achituve, Idan and Navon, Aviv and Yemini, Yochai and Chechik, Gal and Fetaya, Ethan},
  booktitle={International Conference on Machine Learning},
  pages={54--65},
  year={2021},
  organization={PMLR}
}

@article{williams1996computing,
  title={Computing with infinite networks},
  author={Williams, Christopher},
  journal={Advances in neural information processing systems},
  volume={9},
  year={1996}
}

@article{cho2009kernel,
  title={Kernel methods for deep learning},
  author={Cho, Youngmin and Saul, Lawrence},
  journal={Advances in neural information processing systems},
  volume={22},
  year={2009}
}

@inproceedings{NovakXHLASS20,
  author    = {Roman Novak and
               Lechao Xiao and
               Jiri Hron and
               Jaehoon Lee and
               Alexander A. Alemi and
               Jascha Sohl{-}Dickstein and
               Samuel S. Schoenholz},
  title     = {Neural Tangents: Fast and Easy Infinite Neural Networks in Python},
  booktitle = {8th International Conference on Learning Representations, {ICLR}},
  year      = {2020},
}

@article{jacot2018neural,
  title={Neural tangent kernel: Convergence and generalization in neural networks},
  author={Jacot, Arthur and Gabriel, Franck and Hongler, Cl{\'e}ment},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}

@inproceedings{VardiS21,
  author    = {Gal Vardi and
               Ohad Shamir},
title     = {Implicit Regularization in ReLU Networks with the Square Loss},
  booktitle = {Conference on Learning Theory ({COLT})},
  year      = {2021}
}

@inproceedings{KingmaW13,
  author    = {Diederik P. Kingma and
               Max Welling},
  title     = {Auto-Encoding Variational Bayes},
  booktitle = {2nd International Conference on Learning Representations, {ICLR}},
  year      = {2014},
}

@misc{asuncion2007uci ,
author = "Dua, Dheeru and Graff, Casey",
year = "2017",
title = "{UCI} Machine Learning Repository",
url = "http://archive.ics.uci.edu/ml",
institution = "University of California, Irvine, School of Information and Computer Sciences" }

@article{salimbeni2017doubly,
  title={Doubly stochastic variational inference for deep {G}aussian processes},
  author={Salimbeni, Hugh and Deisenroth, Marc},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

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

@article{milios2018dirichlet,
  title={Dirichlet-based {G}aussian processes for large-scale calibrated classification},
  author={Milios, Dimitrios and Camoriano, Raffaello and Michiardi, Pietro and Rosasco, Lorenzo and Filippone, Maurizio},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  year={2018}
}

@inproceedings{ZagoruykoK16,
  author    = {Sergey Zagoruyko and
               Nikos Komodakis},
  title     = {Wide Residual Networks},
  booktitle = {Proceedings of the British Machine Vision Conference {BMVC}},
  year      = {2016},
}

@article{brier1950verification,
  title={Verification of forecasts expressed in terms of probability},
  author={Brier, Glenn W},
  journal={Monthly weather review},
  volume={78},
  number={1},
  pages={1--3},
  year={1950}
}

@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}
}

@article{leclercq2018bayesian,
  title={Bayesian optimization for likelihood-free cosmological inference},
  author={Leclercq, Florent},
  journal={Physical Review D},
  volume={98},
  number={6},
  pages={063511},
  year={2018},
  publisher={APS}
}

@inproceedings{KingmaB14,
  author    = {Diederik P. Kingma and
               Jimmy Ba},
  title     = {{ADAM}: {A} Method for Stochastic Optimization},
  booktitle = {3rd International Conference on Learning Representations, {ICLR}},
  year      = {2015},
}

@article{gardner2018gpytorch,
  title={{GP}y{T}orch: Blackbox matrix-matrix {G}aussian process inference with gpu acceleration},
  author={Gardner, Jacob and Pleiss, Geoff and Weinberger, Kilian Q and Bindel, David and Wilson, Andrew G},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}


@inproceedings{linderman2015dependent,
  title={Dependent multinomial models made easy: stick breaking with the {P\'o}lya-{G}amma augmentation},
  author={Linderman, Scott W and Johnson, Matthew J and Adams, Ryan P},
  booktitle={Proceedings of the 28th International Conference on Neural Information Processing Systems-Volume 2},
  pages={3456--3464},
  year={2015}
}

@inproceedings{galy2020multi,
  title={Multi-class {G}aussian process classification made conjugate: Efficient inference via data augmentation},
  author={Galy-Fajou, Th{\'e}o and Wenzel, Florian and Donner, Christian and Opper, Manfred},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={755--765},
  year={2020},
  organization={PMLR}
}

@article{minka2000bayesian,
  title={Bayesian model averaging is not model combination},
  author={Minka, Thomas P},
  journal={Available electronically at http://www. stat. cmu. edu/minka/papers/bma. html},
  pages={1--2},
  year={2000}
}

@book{mackay1992bayesian,
  title={Bayesian methods for adaptive models},
  author={Mackay, David John Cameron},
  year={1992},
  publisher={California Institute of Technology}
}

@article{mackay1995probable,
  title={Probable networks and plausible predictions-a review of practical Bayesian methods for supervised neural networks},
  author={MacKay, David JC},
  journal={Network: computation in neural systems},
  volume={6},
  number={3},
  pages={469},
  year={1995},
  publisher={IOP Publishing}
}

@article{mackay1992bayesianint,
  title={Bayesian interpolation},
  author={MacKay, David JC},
  journal={Neural computation},
  volume={4},
  number={3},
  pages={415--447},
  year={1992},
  publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…}
}

@article{daxberger2021laplace,
  title={Laplace redux-effortless {B}ayesian 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},
  pages={20089--20103},
  year={2021}
}

@article{khan2019approximate,
  title={Approximate inference turns deep networks into {G}aussian processes},
  author={Khan, Mohammad Emtiyaz E and Immer, Alexander and Abedi, Ehsan and Korzepa, Maciej},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@inproceedings{welling2011bayesian,
  title={Bayesian learning via stochastic gradient {L}angevin dynamics},
  author={Welling, Max and Teh, Yee W},
  booktitle={Proceedings of the 28th international conference on machine learning (ICML-11)},
  pages={681--688},
  year={2011}
}

@inproceedings{chen2014stochastic,
  title={Stochastic gradient {H}amiltonian {M}onte {C}arlo},
  author={Chen, Tianqi and Fox, Emily and Guestrin, Carlos},
  booktitle={International conference on machine learning},
  pages={1683--1691},
  year={2014},
  organization={PMLR}
}

@inproceedings{ZhangLZCW20,
  author    = {Ruqi Zhang and
               Chunyuan Li and
               Jianyi Zhang and
               Changyou Chen and
               Andrew Gordon Wilson},
  title     = {Cyclical Stochastic Gradient {MCMC} for {B}ayesian Deep Learning},
  booktitle = {8th International Conference on Learning Representations, {ICLR}},
  year      = {2020},
}

@article{graves2011practical,
  title={Practical variational inference for neural networks},
  author={Graves, Alex},
  journal={Advances in neural information processing systems},
  volume={24},
  year={2011}
}

@inproceedings{blundell2015weight,
  title={Weight uncertainty in neural network},
  author={Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
  booktitle={International conference on machine learning},
  pages={1613--1622},
  year={2015},
  organization={PMLR}
}

@article{kingma2015variational,
  title={Variational dropout and the local reparameterization trick},
  author={Kingma, Durk P and Salimans, Tim and Welling, Max},
  journal={Advances in neural information processing systems},
  volume={28},
  year={2015}
}

@inproceedings{WangRZZ19,
  author    = {Ziyu Wang and
               Tongzheng Ren and
               Jun Zhu and
               Bo Zhang},
  title     = {Function Space Particle Optimization for {B}ayesian Neural Networks},
  booktitle = {7th International Conference on Learning Representations, {ICLR}},
  year      = {2019},
}

@inproceedings{rudner2021tractable,
  title={Tractable function-space variational inference in Bayesian neural networks},
  author={Rudner, Tim GJ and Chen, Zonghao and Teh, Yee Whye and Gal, Yarin},
  booktitle={Advances in Neural Information Processing Systems},
  year={2021}
}

@inproceedings{kristiadi2020being,
  title={Being {B}ayesian, even just a bit, fixes overconfidence in {R}elu networks},
  author={Kristiadi, Agustinus and Hein, Matthias and Hennig, Philipp},
  booktitle={International conference on machine learning},
  pages={5436--5446},
  year={2020},
  organization={PMLR}
}

@inproceedings{damianou2013deep,
  title={Deep {G}aussian processes},
  author={Damianou, Andreas and Lawrence, Neil D},
  booktitle={Artificial intelligence and statistics},
  pages={207--215},
  year={2013},
  organization={PMLR}
}

@article{liu2020simple,
  title={Simple and principled uncertainty estimation with deterministic deep learning via distance awareness},
  author={Liu, Jeremiah and Lin, Zi and Padhy, Shreyas and Tran, Dustin and Bedrax Weiss, Tania and Lakshminarayanan, Balaji},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={7498--7512},
  year={2020}
}

@article{liu2016stein,
  title={Stein variational gradient descent: A general purpose {B}ayesian inference algorithm},
  author={Liu, Qiang and Wang, Dilin},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}

@article{lakshminarayanan2017simple,
  title={Simple and scalable predictive uncertainty estimation using deep ensembles},
  author={Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@inproceedings{jankowiak2020parametric,
  title={Parametric {G}aussian process regressors},
  author={Jankowiak, Martin and Pleiss, Geoff and Gardner, Jacob},
  booktitle={International Conference on Machine Learning},
  pages={4702--4712},
  year={2020},
  organization={PMLR}
}

@article{brosse2020last,
  title={On last-layer algorithms for classification: Decoupling representation from uncertainty estimation},
  author={Brosse, Nicolas and Riquelme, Carlos and Martin, Alice and Gelly, Sylvain and Moulines, {\'E}ric},
  journal={arXiv preprint arXiv:2001.08049},
  year={2020}
}

@article{polya_gamma,
author = { Nicholas G.   Polson  and  James G.   Scott  and  Jesse   Windle },
title = {{B}ayesian Inference for Logistic Models Using {P}ólya–{G}amma Latent Variables},
journal = {Journal of the American Statistical Association},
pages = {1339-1349},
year  = {2013}
}

@inproceedings{pensofunctional,
  title={Functional Ensemble Distillation},
  author={Penso, Coby and Achituve, Idan and Fetaya, Ethan},
  booktitle={Advances in Neural Information Processing Systems},
  year  = {2022}
}

@article{adlam2023kernel,
  title={Kernel Regression with Infinite-Width Neural Networks on Millions of Examples},
  author={Adlam, Ben and Lee, Jaehoon and Padhy, Shreyas and Nado, Zachary and Snoek, Jasper},
  journal={arXiv preprint arXiv:2303.05420},
  year={2023}
}

@inproceedings{aitchison2021deep,
  title={Deep kernel processes},
  author={Aitchison, Laurence and Yang, Adam and Ober, Sebastian W},
  booktitle={International Conference on Machine Learning},
  pages={130--140},
  year={2021},
  organization={PMLR}
}

@article{ober2021variational,
  title={A variational approximate posterior for the deep Wishart process},
  author={Ober, Sebastian and Aitchison, Laurence},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={6567--6579},
  year={2021}
}

@article{yang2021theory,
  title={A theory of representation learning in deep neural networks gives a deep generalisation of kernel methods},
  author={Yang, Adam X and Robeyns, Maxime and Milsom, Edward and Schoots, Nandi and Aitchison, Laurence},
  journal={arXiv preprint arXiv:2108.13097},
  year={2021}
}