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Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…

Machine Learning · Computer Science 2024-12-18 Hongyu Shen , Zhizhen Zhao

The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…

Optimization and Control · Mathematics 2024-01-30 Muideen Adegoke , Lateef O. Jolaoso , Mardiyyah Oduwole

We consider statistical learning problems, when the distribution $P'$ of the training observations $Z'_1,\; \ldots,\; Z'_n$ differs from the distribution $P$ involved in the risk one seeks to minimize (referred to as the test distribution)…

Machine Learning · Statistics 2020-02-20 Robin Vogel , Mastane Achab , Stéphan Clémençon , Charles Tillier

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve…

Machine Learning · Computer Science 2018-02-15 Di Wang , Minwei Ye , Jinhui Xu

We consider the classical problem of learning rates for classes with finite VC dimension. It is well known that fast learning rates up to $O\left(\frac{d}{n}\right)$ are achievable by the empirical risk minimization algorithm (ERM) if low…

Machine Learning · Computer Science 2020-10-27 Olivier Bousquet , Nikita Zhivotovskiy

We present an extension of Vapnik's classical empirical risk minimizer (ERM) where the empirical risk is replaced by a median-of-means (MOM) estimator, the new estimators are called MOM minimizers. While ERM is sensitive to corruption of…

Statistics Theory · Mathematics 2018-08-10 Guillaume Lecué , Matthieu Lerasle , Timothée Mathieu

The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…

Statistics Theory · Mathematics 2015-05-13 Sébastien Loustau , Clément Marteau

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

Computational Finance · Quantitative Finance 2025-05-27 Liexin Cheng , Xue Cheng , Shuaiqiang Liu

In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each…

Machine Learning · Computer Science 2016-12-28 Vitaly Feldman

The universal learning framework has been developed to obtain guarantees on the learning rates that hold for any fixed distribution, which can be much faster than the ones uniformly hold over all the distributions. Given that the Empirical…

Machine Learning · Statistics 2025-07-16 Steve Hanneke , Mingyue Xu

We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…

Statistics Theory · Mathematics 2021-11-17 Raaz Dwivedi , Nhat Ho , Koulik Khamaru , Martin J. Wainwright , Michael I. Jordan , Bin Yu

We investigate the learning dynamics of classifiers in scenarios where classes are separable or classifiers are over-parameterized. In both cases, Empirical Risk Minimization (ERM) results in zero training error. However, there are many…

Machine Learning · Computer Science 2024-10-23 Julius Martinetz , Christoph Linse , Thomas Martinetz

This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance…

Machine Learning · Computer Science 2021-03-26 Yaqi Duan , Chi Jin , Zhiyuan Li

Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address…

Machine Learning · Computer Science 2021-03-18 Tian Li , Ahmad Beirami , Maziar Sanjabi , Virginia Smith

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 the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…

Machine Learning · Computer Science 2016-04-19 Amit Daniely , Sivan Sabato , Shai Ben-David , Shai Shalev-Shwartz

We obtain risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex. Results for the ERM are derived without assumptions on the outputs and under…

Statistics Theory · Mathematics 2019-07-01 Geoffrey Chinot , Lecué Guillaume , Lerasle Matthieu

Focusing on stochastic programming (SP) with covariate information, this paper proposes an empirical risk minimization (ERM) method embedded within a nonconvex piecewise affine decision rule (PADR), which aims to learn the direct mapping…

Optimization and Control · Mathematics 2025-09-29 Yiyang Zhang , Junyi Liu , Xiaobo Zhao

Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…

An interesting phenomenon arises: Empirical Risk Minimization (ERM) sometimes outperforms methods specifically designed for out-of-distribution tasks. This motivates an investigation into the reasons behind such behavior beyond algorithmic…

Machine Learning · Computer Science 2026-01-21 Hong Zheng , Fei Teng