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In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…

Machine Learning · Computer Science 2020-07-22 Alexander Mey , Marco Loog

Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…

Machine Learning · Computer Science 2021-02-17 Jessie Finocchiaro , Rafael Frongillo , Bo Waggoner

Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…

Machine Learning · Statistics 2021-11-30 Vincent Plassier , François Portier , Johan Segers

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

Machine Learning · Statistics 2009-07-23 Andreas Maurer , Massimiliano Pontil

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

Methodology · Statistics 2018-11-26 Le-Yu Chen , Sokbae Lee

We study binary classification in the setting where the learner is presented with multiple corrupted training samples, with possibly different sample sizes and degrees of corruption, and introduce an approach based on minimizing a weighted…

Machine Learning · Statistics 2019-10-11 Clayton Scott , Jianxin Zhang

We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative…

Machine Learning · Computer Science 2024-05-24 Yuyang Deng , Mingda Qiao

We study over-parameterized classifiers where Empirical Risk Minimization (ERM) for learning leads to zero training error. In these over-parameterized settings there are many global minima with zero training error, some of which generalize…

Machine Learning · Computer Science 2023-12-05 Julius Martinetz , Thomas Martinetz

The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…

Machine Learning · Computer Science 2022-10-11 Hai Victor Habi , Hagit Messer , Yoram Bresler

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

Numerical Analysis · Mathematics 2021-02-09 Michael Gnewuch

Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be…

Machine Learning · Statistics 2015-06-26 Kazuto Fukuchi , Jun Sakuma

Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…

Machine Learning · Computer Science 2022-05-31 Yu Bai , Song Mei , Huan Wang , Yingbo Zhou , Caiming Xiong

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

Probability · Mathematics 2019-05-01 Miles E. Lopes

Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…

Machine Learning · Statistics 2026-05-19 Tobias Brock , Thomas Nagler

In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…

Machine Learning · Computer Science 2021-05-04 Guohao Shen , Yuling Jiao , Yuanyuan Lin , Jian Huang

We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational…

Machine Learning · Statistics 2009-01-06 Mark D. Reid , Robert C. Williamson

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of…

Machine Learning · Computer Science 2013-11-26 Hsiang-Fu Yu , Prateek Jain , Purushottam Kar , Inderjit S. Dhillon

The $\ell_0$-constrained empirical risk minimization ($\ell_0$-ERM) is a promising tool for high-dimensional statistical estimation. The existing analysis of $\ell_0$-ERM estimator is mostly on parameter estimation and support recovery…

Statistics Theory · Mathematics 2020-01-22 Xiao-Tong Yuan , Ping Li

Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…

Optimization and Control · Mathematics 2022-10-14 Yibo Zeng , Henry Lam