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From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

Machine Learning · Computer Science 2021-02-09 Taejong Joo , Uijung Chung

We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a…

Machine Learning · Statistics 2019-10-31 Chenri Ni , Nontawat Charoenphakdee , Junya Honda , Masashi Sugiyama

Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…

Machine Learning · Computer Science 2021-12-30 Kartik Gupta , Amir Rahimi , Thalaiyasingam Ajanthan , Thomas Mensink , Cristian Sminchisescu , Richard Hartley

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

Machine Learning · Computer Science 2023-12-13 Samuel Stanton , Wesley Maddox , Andrew Gordon Wilson

Accurately knowing uncertainties in appearance-based gaze tracking is critical for ensuring reliable downstream applications. Due to the lack of individual uncertainty labels, current uncertainty-aware approaches adopt probabilistic models…

Computer Vision and Pattern Recognition · Computer Science 2026-03-13 Qiaojie Zheng , Jiucai Zhang , Xiaoli Zhang

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We…

Machine Learning · Statistics 2025-08-28 Xianli Zeng , Kevin Jiang , Guang Cheng , Edgar Dobriban

Machine learning applications often require calibrated predictions, e.g. a 90\% credible interval should contain the true outcome 90\% of the times. However, typical definitions of calibration only require this to hold on average, and offer…

Machine Learning · Statistics 2020-09-10 Shengjia Zhao , Tengyu Ma , Stefano Ermon

We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…

Machine Learning · Computer Science 2021-10-26 Pradeep Kr. Banerjee , Guido Montúfar

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…

Statistics Theory · Mathematics 2007-06-13 Yoav Freund , Yishay Mansour , Robert E. Schapire

In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model…

Machine Learning · Computer Science 2024-06-24 Lunjia Hu , Arun Jambulapati , Kevin Tian , Chutong Yang

Estimated uncertainty by approximate posteriors in Bayesian neural networks are prone to miscalibration, which leads to overconfident predictions in critical tasks that have a clear asymmetric cost or significant losses. Here, we extend the…

Machine Learning · Computer Science 2022-06-17 Biraja Ghoshal , Allan Tucker

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Machine Learning · Statistics 2024-06-18 Tomoya Wakayama

Application of deep neural networks to medical imaging tasks has in some sense become commonplace. Still, a "thorn in the side" of the deep learning movement is the argument that deep networks are prone to overfitting and are thus unable to…

Machine Learning · Computer Science 2021-07-12 Anthony Sicilia , Xingchen Zhao , Anastasia Sosnovskikh , Seong Jae Hwang

We establish disintegrated PAC-Bayesian generalisation bounds for models trained with gradient descent methods or continuous gradient flows. Contrary to standard practice in the PAC-Bayesian setting, our result applies to optimisation…

Machine Learning · Statistics 2025-02-12 Eugenio Clerico , Tyler Farghly , George Deligiannidis , Benjamin Guedj , Arnaud Doucet

Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…

Statistics Theory · Mathematics 2023-01-11 Timo Dimitriadis , Lutz Duembgen , Alexander Henzi , Marius Puke , Johanna Ziegel

We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…

High Energy Physics - Phenomenology · Physics 2020-12-23 Gregor Kasieczka , Michel Luchmann , Florian Otterpohl , Tilman Plehn

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Statistics Theory · Mathematics 2023-03-17 Anna Scampicchio , Elena Arcari , Melanie N. Zeilinger

We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…

Methodology · Statistics 2026-03-11 David T. Frazier , Christopher Drovandi , Robert Kohn

Modern deterministic retrieval pipelines prioritize achieving state-of-the-art performance but often lack interpretability in decision-making. These models face challenges in assessing uncertainty, leading to overconfident predictions. To…

Information Retrieval · Computer Science 2024-02-06 EuiYul Song , Philhoon Oh , Sangryul Kim , James Thorne

Process capability indices such as $C_{pk}$ are widely used for manufacturing decisions, yet are typically applied via deterministic thresholding of finite-sample estimates, ignoring uncertainty and leading to unstable outcomes near the…

Applications · Statistics 2026-04-16 Fei Jiang , Lei Yang