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In this paper, we investigate the impact of compression on stochastic gradient algorithms for machine learning, a technique widely used in distributed and federated learning. We underline differences in terms of convergence rates between…

Machine Learning · Computer Science 2025-07-25 Constantin Philippenko , Aymeric Dieuleveut

Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a…

Optimization and Control · Mathematics 2025-07-10 Florian Hübler , Ilyas Fatkhullin , Niao He

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…

Numerical Analysis · Mathematics 2018-01-22 Marie Kubínová , James G. Nagy

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…

Machine Learning · Statistics 2020-03-26 Daniel LeJeune , Hamid Javadi , Richard G. Baraniuk

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…

Statistics Theory · Mathematics 2012-03-22 Lee Dicker

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

Machine Learning · Statistics 2021-09-02 Ansgar Steland

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Optimization and Control · Mathematics 2025-05-30 Jun Fan , Ailing Yan , Xianchao Xiu , Wanquan Liu

Standard risk metrics used in model validation, such as the Kolmogorov-Smirnov distance, fail to converge at practical rates when applied to high-frequency financial data characterized by heavy tails (infinite skewness). This creates a…

Probability · Mathematics 2026-01-09 Armen Petrosyan

We derive minimax adaptive rates for a new, broad class of Tikhonov-regularized learning problems in Hilbert scales under general source conditions. Our analysis does not require the regression function to be contained in the hypothesis…

Statistics Theory · Mathematics 2023-09-19 Prem Talwai , David Simchi-Levi

We study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified…

Machine Learning · Statistics 2026-04-09 Dimitri Meunier , Zhu Li , Tim Christensen , Arthur Gretton

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical…

Machine Learning · Computer Science 2023-03-28 Heyang Zhao , Dongruo Zhou , Jiafan He , Quanquan Gu

Inspired by the recent work [28] on the statistical robustness of empirical risks in reproducing kernel Hilbert space (RKHS) where the training data are potentially perturbed or even corrupted, we take a step further in this paper to…

Optimization and Control · Mathematics 2024-06-18 Sainan Zhang , Huifu Xu , Hailin Sun

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

Machine Learning · Computer Science 2022-10-20 Fanghui Liu , Lei Shi , Xiaolin Huang , Jie Yang , Johan A. K. Suykens

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying…

Machine Learning · Computer Science 2014-10-23 Shahar Mendelson

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

Optimization and Control · Mathematics 2023-05-23 Zijian Liu , Zhengyuan Zhou

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…

Systems and Control · Electrical Eng. & Systems 2021-08-03 Emilio T. Maddalena , Paul Scharnhorst , Colin N. Jones

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

Optimization and Control · Mathematics 2024-09-02 Eduard Gorbunov , Marina Danilova , Innokentiy Shibaev , Pavel Dvurechensky , Alexander Gasnikov

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the…

Statistics Theory · Mathematics 2023-06-07 Cong Ma , Reese Pathak , Martin J. Wainwright

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

Statistics Theory · Mathematics 2024-06-19 Ayoub El Hanchi , Chris J. Maddison , Murat A. Erdogdu

We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent $q>0$, as well as its limit case $q=\infty$, which we refer to as the \emph{hard…

Machine Learning · Computer Science 2026-05-06 Nathanael Tepakbong , Xiang Zhou , Ding-Xuan Zhou