@book{rasmussen2006gaussian,
  title={Gaussian processes for machine learning},
  author={Rasmussen, Carl Edward and Williams, Christopher KI},
  volume={1},
  year={2006},
  publisher={Springer}
}

@inproceedings{duan2020ngboost,
  title={Ngboost: Natural gradient boosting for probabilistic prediction},
  author={Duan, Tony and Anand, Avati and Ding, Daisy Yi and Thai, Khanh K and Basu, Sanjay and Ng, Andrew and Schuler, Alejandro},
  booktitle={International conference on machine learning},
  pages={2690--2700},
  year={2020},
  organization={PMLR}
}

@article{avati2018improving,
  title={Improving palliative care with deep learning},
  author={Avati, Anand and Jung, Kenneth and Harman, Stephanie and Downing, Lance and Ng, Andrew and Shah, Nigam H},
  journal={BMC medical informatics and decision making},
  volume={18},
  number={4},
  pages={55--64},
  year={2018},
  publisher={BioMed Central}
}


@InProceedings{pmlr-v238-abedsoltan24a,
  title = 	 { On the {N}yström Approximation for Preconditioning in Kernel Machines },
  author =       {Abedsoltan, Amirhesam and Pandit, Parthe and Rademacher, Luis and Belkin, Mikhail},
  booktitle = 	 {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {3718--3726},
  year = 	 {2024},
  editor = 	 {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
  volume = 	 {238},
  series = 	 {Proceedings of Machine Learning Research},
  publisher =    {PMLR},
}



@InProceedings{pmlr-v202-abedsoltan23a,
  title = 	 {Toward Large Kernel Models},
  author =       {Abedsoltan, Amirhesam and Belkin, Mikhail and Pandit, Parthe},
  booktitle = 	 {Proceedings of the 40th International Conference on Machine Learning},
  pages = 	 {61--78},
  year = 	 {2023},
  volume = 	 {202},
  series = 	 {Proceedings of Machine Learning Research},
}

@article{meanti2020kernel,
  title={Kernel methods through the roof: handling billions of points efficiently},
  author={Meanti, Giacomo and Carratino, Luigi and Rosasco, Lorenzo and Rudi, Alessandro},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={14410--14422},
  year={2020}
}
@article{rudi2017falkon,
  title={Falkon: An optimal large scale kernel method},
  author={Rudi, Alessandro and Carratino, Luigi and Rosasco, Lorenzo},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}
@article{ma2017diving,
  title={Diving into the shallows: a computational perspective on large-scale shallow learning},
  author={Ma, Siyuan and Belkin, Mikhail},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}
@article{ma2019kernel,
  title={Kernel machines that adapt to GPUs for effective large batch training},
  author={Ma, Siyuan and Belkin, Mikhail},
  journal={Proceedings of Machine Learning and Systems},
  volume={1},
  pages={360--373},
  year={2019}
}

@article{abedsoltan2023toward,
  title={Toward large kernel models},
  author={Abedsoltan, Amirhesam and Belkin, Mikhail and Pandit, Parthe},
  journal={arXiv preprint arXiv:2302.02605},
  year={2023}
}
@article{li2019enhanced,
  title={Enhanced convolutional neural tangent kernels},
  author={Li, Zhiyuan and Wang, Ruosong and Yu, Dingli and Du, Simon S and Hu, Wei and Salakhutdinov, Ruslan and Arora, Sanjeev},
  journal={arXiv preprint arXiv:1911.00809},
  year={2019}
}

@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}
}
@article{barragan2022towards,
  title={Towards a safe and efficient clinical implementation of machine learning in radiation oncology by exploring model interpretability, explainability and data-model dependency},
  author={Barrag{\'a}n-Montero, Ana and Bibal, Adrien and Dastarac, Margerie Huet and Draguet, Camille and Valdes, Gilmer and Nguyen, Dan and Willems, Siri and Vandewinckele, Liesbeth and Holmstr{\"o}m, Mats and L{\"o}fman, Fredrik and others},
  journal={Physics in Medicine \& Biology},
  volume={67},
  number={11},
  pages={11TR01},
  year={2022},
  publisher={IOP Publishing}
}
@article{dolezal2022uncertainty,
  title={Uncertainty-informed deep learning models enable high-confidence predictions for digital histopathology},
  author={Dolezal, James M and Srisuwananukorn, Andrew and Karpeyev, Dmitry and Ramesh, Siddhi and Kochanny, Sara and Cody, Brittany and Mansfield, Aaron S and Rakshit, Sagar and Bansal, Radhika and Bois, Melanie C and others},
  journal={Nature communications},
  volume={13},
  number={1},
  pages={6572},
  year={2022},
  publisher={Nature Publishing Group UK London}
}

@article{tran2021deep,
  title={Deep learning in cancer diagnosis, prognosis and treatment selection},
  author={Tran, Khoa A and Kondrashova, Olga and Bradley, Andrew and Williams, Elizabeth D and Pearson, John V and Waddell, Nicola},
  journal={Genome Medicine},
  volume={13},
  number={1},
  pages={1--17},
  year={2021},
  publisher={BioMed Central}
}
@article{nicora2022evaluating,
  title={Evaluating pointwise reliability of machine learning prediction},
  author={Nicora, Giovanna and Rios, Miguel and Abu-Hanna, Ameen and Bellazzi, Riccardo},
  journal={Journal of Biomedical Informatics},
  volume={127},
  pages={103996},
  year={2022},
  publisher={Elsevier}
}

@article{linmans2023predictive,
  title={Predictive uncertainty estimation for out-of-distribution detection in digital pathology},
  author={Linmans, Jasper and Elfwing, Stefan and van der Laak, Jeroen and Litjens, Geert},
  journal={Medical Image Analysis},
  volume={83},
  pages={102655},
  year={2023},
  publisher={Elsevier}
}
@article{forecast,
author = {Gneiting, Tilmann and Katzfuss, Matthias},
title = {Probabilistic Forecasting},
journal = {Annual Review of Statistics and Its Application},
volume = {1},
number = {1},
pages = {125-151},
year = {2014},
}
@article{chua2023tackling,
  title={Tackling prediction uncertainty in machine learning for healthcare},
  author={Chua, Michelle and Kim, Doyun and Choi, Jongmun and Lee, Nahyoung G and Deshpande, Vikram and Schwab, Joseph and Lev, Michael H and Gonzalez, Ramon G and Gee, Michael S and Do, Synho},
  journal={Nature Biomedical Engineering},
  volume={7},
  number={6},
  pages={711--718},
  year={2023},
  publisher={Nature Publishing Group UK London}
}

@article{kompa2021second,
  title={Second opinion needed: communicating uncertainty in medical machine learning},
  author={Kompa, Benjamin and Snoek, Jasper and Beam, Andrew L},
  journal={NPJ Digital Medicine},
  volume={4},
  number={1},
  pages={4},
  year={2021},
  publisher={Nature Publishing Group UK London}
}

@article{radhakrishnan2022feature_old,
  title={Feature learning in neural networks and kernel machines that recursively learn features},
  author={Radhakrishnan, Adityanarayanan and Beaglehole, Daniel and Pandit, Parthe and Belkin, Mikhail},
  journal={arXiv preprint arXiv:2212.13881},
  year={2022}
}

@article{radhakrishnan2022feature,
    author = {Adityanarayanan Radhakrishnan  and Daniel Beaglehole  and Parthe Pandit  and Mikhail Belkin },
    title = {Mechanism for feature learning in neural networks and backpropagation-free machine learning models},
    journal = {Science},
    volume = {383},
    number = {6690},
    pages = {1461-1467},
    year = {2024},
}


@article{mackay1998introduction,
  title={Introduction to Gaussian processes},
  author={MacKay, David JC and others},
  journal={NATO ASI series F computer and systems sciences},
  volume={168},
  pages={133--166},
  year={1998},
  publisher={Citeseer}
}

@inproceedings{wilson2016deep,
  title={Deep kernel learning},
  author={Wilson, Andrew G and Hu, Zhiting and Salakhutdinov, Ruslan and Xing, Eric P},
  booktitle={Artificial intelligence and statistics},
  pages={370--378},
  year={2016},
  organization={PMLR}
}

@inproceedings{calandra2016manifold,
  title={Manifold Gaussian 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}
}

@article{mackay1992bayesian,
  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~…}
}

@misc{neal1996bayesian,
  title={Bayesian Learning for Neural Networks},
  author={Neal, Radford M},
  year={1996},
  publisher={Springer-Verlag}
}

@inproceedings{huang2015scalable,
  title={Scalable Gaussian process regression using deep neural networks},
  author={Huang, Wenbing and Zhao, Deli and Sun, Fuchun and Liu, Huaping and Chang, Edward},
  booktitle={Twenty-fourth international joint conference on artificial intelligence},
  year={2015},
  organization={Citeseer}
}

@inproceedings{chen2016xgboost,
  title={Xgboost: A scalable tree boosting system},
  author={Chen, Tianqi and Guestrin, Carlos},
  booktitle={Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining},
  pages={785--794},
  year={2016}
}

@article{ke2017lightgbm,
  title={Lightgbm: A highly efficient gradient boosting decision tree},
  author={Ke, Guolin and Meng, Qi and Finley, Thomas and Wang, Taifeng and Chen, Wei and Ma, Weidong and Ye, Qiwei and Liu, Tie-Yan},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}

@article{prokhorenkova2018catboost,
  title={CatBoost: unbiased boosting with categorical features},
  author={Prokhorenkova, Liudmila and Gusev, Gleb and Vorobev, Aleksandr and Dorogush, Anna Veronika and Gulin, Andrey},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}

@inproceedings{freund1995desicion,
  title={A desicion-theoretic generalization of on-line learning and an application to boosting},
  author={Freund, Yoav and Schapire, Robert E},
  booktitle={European conference on computational learning theory},
  pages={23--37},
  year={1995},
  organization={Springer}
}

@article{grinsztajn2022tree,
  title={Why do tree-based models still outperform deep learning on typical tabular data?},
  author={Grinsztajn, L{\'e}o and Oyallon, Edouard and Varoquaux, Ga{\"e}l},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={507--520},
  year={2022}
}

@article{mcelfresh2023neural,
  title={When Do Neural Nets Outperform Boosted Trees on Tabular Data?},
  author={McElfresh, Duncan and Khandagale, Sujay and Valverde, Jonathan and Ramakrishnan, Ganesh and Goldblum, Micah and White, Colin and others},
  journal={arXiv preprint arXiv:2305.02997},
  year={2023}
}

@inproceedings{malinin2021uncertainty,
    title={Uncertainty in Gradient Boosting via Ensembles},
    author={Andrey Malinin and Liudmila Prokhorenkova and Aleksei Ustimenko},
    booktitle={International Conference on Learning Representations},
    year={2021},
}

@inproceedings{shaker2020aleatoric,
  title={Aleatoric and epistemic uncertainty with random forests},
  author={Shaker, Mohammad Hossein and H{\"u}llermeier, Eyke},
  booktitle={Advances in Intelligent Data Analysis XVIII: 18th International Symposium on Intelligent Data Analysis, IDA 2020, Konstanz, Germany, April 27--29, 2020, Proceedings 18},
  pages={444--456},
  year={2020},
  organization={Springer}
}

@article{schlosser2019distributional,
    author = {Lisa Schlosser and Torsten Hothorn and Reto Stauffer and Achim Zeileis},
    title = {{Distributional regression forests for probabilistic precipitation forecasting in complex terrain}},
    volume = {13},
    journal = {The Annals of Applied Statistics},
    number = {3},
    publisher = {Institute of Mathematical Statistics},
    pages = {1564 -- 1589},
    keywords = {GAMLSS, Parametric models, probabilistic forecasting, random forests, recursive partitioning, regression trees},
    year = {2019},
}

@article{friedman2001greedy,
  title={Greedy function approximation: a gradient boosting machine},
  author={Friedman, Jerome H},
  journal={Annals of statistics},
  pages={1189--1232},
  year={2001},
  publisher={JSTOR}
}

@article{shwartz2022tabular,
  title={Tabular data: Deep learning is not all you need},
  author={Shwartz-Ziv, Ravid and Armon, Amitai},
  journal={Information Fusion},
  volume={81},
  pages={84--90},
  year={2022},
  publisher={Elsevier}
}

@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{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{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}
}

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

@inproceedings{gal2016dropout,
  title={Dropout as a bayesian approximation: Representing model uncertainty in deep learning},
  author={Gal, Yarin and Ghahramani, Zoubin},
  booktitle={international conference on machine learning},
  pages={1050--1059},
  year={2016},
  organization={PMLR}
}

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

@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}
}

@article{ovadia2019can,
  title={Can you trust your model's uncertainty? Evaluating predictive uncertainty under dataset shift},
  author={Ovadia, Yaniv and Fertig, Emily and Ren, Jie and Nado, Zachary and Sculley, David and Nowozin, Sebastian and Dillon, Joshua and Lakshminarayanan, Balaji and Snoek, Jasper},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@book{scholkopf2002learning,
  title={Learning with kernels: support vector machines, regularization, optimization, and beyond},
  author={Sch{\"o}lkopf, Bernhard and Smola, Alexander J},
  year={2002},
  publisher={MIT press}
}

@article{aronszajn1950theory,
  title={Theory of reproducing kernels},
  author={Aronszajn, Nachman},
  journal={Transactions of the American mathematical society},
  volume={68},
  number={3},
  pages={337--404},
  year={1950}
}

@article{kimeldorf1970correspondence,
  title={A correspondence between Bayesian estimation on stochastic processes and smoothing by splines},
  author={Kimeldorf, George S and Wahba, Grace},
  journal={The Annals of Mathematical Statistics},
  volume={41},
  number={2},
  pages={495--502},
  year={1970},
  publisher={JSTOR}
}

@article{paszke2019pytorch,
  title={Pytorch: An imperative style, high-performance deep learning library},
  author={Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and others},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@article{gardner2018gpytorch,
  title={Gpytorch: Blackbox matrix-matrix gaussian 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}
}

@article{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik P and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@article{loshchilov2016sgdr,
  title={Sgdr: Stochastic gradient descent with warm restarts},
  author={Loshchilov, Ilya and Hutter, Frank},
  journal={arXiv preprint arXiv:1608.03983},
  year={2016}
}

@inproceedings{hernandez2015probabilistic,
  title={Probabilistic backpropagation for scalable learning of bayesian neural networks},
  author={Hern{\'a}ndez-Lobato, Jos{\'e} Miguel and Adams, Ryan},
  booktitle={International conference on machine learning},
  pages={1861--1869},
  year={2015},
  organization={PMLR}
}

@misc{asuncion2007uci,
  title={{UCI} machine learning repository},
  author={Asuncion, Arthur and Newman, David},
  year={2007},
  publisher={Irvine, CA, USA}
}

@article{vanschoren2014openml,
  title={OpenML: networked science in machine learning},
  author={Vanschoren, Joaquin and Van Rijn, Jan N and Bischl, Bernd and Torgo, Luis},
  journal={ACM SIGKDD Explorations Newsletter},
  volume={15},
  number={2},
  pages={49--60},
  year={2014},
  publisher={ACM New York, NY, USA}
}

@inproceedings{eriksson2021high,
  title={High-dimensional Bayesian optimization with sparse axis-aligned subspaces},
  author={Eriksson, David and Jankowiak, Martin},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={493--503},
  year={2021},
  organization={PMLR}
}

@inproceedings{garnett2014active,
    author = {Garnett, Roman and Osborne, Michael A. and Hennig, Philipp},
    title = {Active Learning of Linear Embeddings for Gaussian Processes},
    year = {2014},
    publisher = {AUAI Press},
    address = {Arlington, Virginia, USA},
    booktitle = {Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence},
    pages = {230–239},
    numpages = {10},
}

@article{vivarelli1998discovering,
  title={Discovering hidden features with Gaussian processes regression},
  author={Vivarelli, Francesco and Williams, Christopher},
  journal={Advances in Neural Information Processing Systems},
  volume={11},
  year={1998}
}

@article{letham2020re,
  title={Re-examining linear embeddings for high-dimensional Bayesian optimization},
  author={Letham, Ben and Calandra, Roberto and Rai, Akshara and Bakshy, Eytan},
  journal={Advances in neural information processing systems},
  volume={33},
  pages={1546--1558},
  year={2020}
}

@article{radhakrishnan2024linear,
  title={Linear Recursive Feature Machines provably recover low-rank matrices},
  author={Radhakrishnan, Adityanarayanan and Belkin, Mikhail and Drusvyatskiy, Dmitriy},
  journal={arXiv preprint arXiv:2401.04553},
  year={2024}
}

@inproceedings{wilson2015kernel,
  title={Kernel interpolation for scalable structured Gaussian processes (KISS-GP)},
  author={Wilson, Andrew G and Nickisch, Hannes},
  booktitle={International conference on machine learning},
  pages={1775--1784},
  year={2015},
  organization={PMLR}
}