Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger. On calibration of modern neural networks. In International conference on machine learning, pages 1321-1330. PMLR, 2017.
László Győrfi, Michael Köhler, Adam Krzyżak, and Harro Walk. A distribution-free theory of nonparametric regression, volume 1. Springer, 2002.
Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Multilayer feedforward networks are universal approximators. Neural networks, 2(5):359-366, 1989.
Steven R Howard and Aaditya Ramdas. Sequential estimation of quantiles with applications to a/b testing and best-arm identification. Bernoulli, 28(3):1704-1728, 2022.
Alex Kendall and Yarin Gal. What uncertainties do we need in bayesian deep learning for computer vision? Advances in neural information processing systems, 30, 2017.
Ravi Kumar Kolla, LA Prashanth, Sanjay P Bhat, and Krishna Jagannathan. Concentration bounds for empirical conditional value-at-risk: The unbounded case. *Operations Research Letters*, 47(1): 16-20, 2019.
Vladimir Koltchinskii. Local rademacher complexities and oracle inequalities in risk minimization. The Annals of Statistics, pages 2593-2656, 2006.
Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon. Accurate uncertainties for deep learning using calibrated regression. In International conference on machine learning, pages 2796-2804. PMLR, 2018.
Ananya Kumar, Percy S Liang, and Tengyu Ma. Verified uncertainty calibration. Advances in Neural Information Processing Systems, 32, 2019.
Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30, 2017.
Jing Lei and Larry Wasserman. Distribution-free prediction bands for non-parametric regression. Journal of the Royal Statistical Society: Series B: Statistical Methodology, pages 71-96, 2014.
Jing Lei, Max G'Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman. Distribution-free predictive inference for regression. Journal of the American Statistical Association, 113(523): 1094-1111, 2018.
Rachel Luo, Aadyot Bhatnagar, Yu Bai, Shengjia Zhao, Huan Wang, Caiming Xiong, Silvio Savarese, Stefano Ermon, Edward Schmerling, and Marco Pavone. Local calibration: metrics and recalibration. In Uncertainty in Artificial Intelligence, pages 1286-1295. PMLR, 2022.
David JC MacKay. A practical bayesian framework for backpropagation networks. Neural computation, 4(3):448-472, 1992.
Pascal Massart. The tight constant in the dvoretzky-kiefer-wolfowitz inequality. The annals of Probability, pages 1269-1283, 1990.
Andreas Maurer and Massimiliano Pontil. Empirical bernstein bounds and sample variance penalization. arXiv preprint arXiv:0907.3740, 2009.
Medical expenditure panel survey panel 19, 2017. URL https://meps.ahrq.gov/mepsweb/data.stats/download_data_files_detail.jsp?cboPufNumber=HC-181.
Medical expenditure panel survey panel 20, 2017. URL https://meps.ahrq.gov/mepsweb/data.stats/download_data_files_detail.jsp?cboPufNumber=HC-181.
Medical expenditure panel survey panel 21, 2017. URL https://meps.ahrq.gov/mepsweb/data.stats/download_data_files_detail.jsp?cboPufNumber=HC-192.
Harris Papadopoulos, Kostas Proedrou, Volodya Vovk, and Alex Gammerman. Inductive confidence machines for regression. In Machine Learning: ECML 2002: 13th European Conference on Machine Learning Helsinki, Finland, August 19-23, 2002 Proceedings 13, pages 345-356. Springer, 2002.