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Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…

Optimization and Control · Mathematics 2021-02-23 Hongjian Wang , Mert Gürbüzbalaban , Lingjiong Zhu , Umut Şimşekli , Murat A. Erdogdu

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

Machine Learning · Computer Science 2016-08-11 Chang Liu , Bo Li , Yevgeniy Vorobeychik , Alina Oprea

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

Statistics Theory · Mathematics 2018-10-11 Qiang Sun , Wenxin Zhou , Jianqing Fan

Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…

Statistics Theory · Mathematics 2019-08-20 Jun Zhao , Guan'ao Yan , Yi Zhang

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

Methodology · Statistics 2021-10-01 Bingyuan Liu , Qi Zhang , Lingzhou Xue , Peter X. K. Song , Jian Kang

We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…

Machine Learning · Computer Science 2019-05-31 Liu Liu , Tianyang Li , Constantine Caramanis

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

Methodology · Statistics 2023-01-12 Meadhbh O'Neill , Kevin Burke

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Machine Learning · Computer Science 2019-05-31 Liu Liu , Yanyao Shen , Tianyang Li , Constantine Caramanis

We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+\epsilon)$-th moments for some $\epsilon \in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise…

Machine Learning · Computer Science 2026-03-17 Naoto Tani , Futoshi Futami

Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse…

Machine Learning · Statistics 2026-02-10 Yingjie Wang , Mokhtar Z. Alaya , Salim Bouzebda , Xinsheng Liu

Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…

Machine Learning · Computer Science 2022-04-13 Jacob Deasy , Nikola Simidjievski , Pietro Liò

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Machine Learning · Statistics 2018-03-21 Ziping Zhao , Daniel P. Palomar

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

Methodology · Statistics 2026-02-25 Xiaoning Kang , Lulu Kang

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

Machine Learning · Computer Science 2026-05-26 Xinwen Zhang , Yihan Zhang , Heng Liang , Hongchang Gao

We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise…

Optimization and Control · Mathematics 2025-09-23 Zhan Yu , Lan Liao , Deming Yuan , Daniel W. C. Ho , Ding-Xuan Zhou

Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…

Methodology · Statistics 2026-05-25 Jiyuan Tu , Suqi Wu , Yichen Zhang , Wen-Xin Zhou

We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than $\mathcal{O}(K^{-2(\alpha - 1)/\alpha})$, when the…

Optimization and Control · Mathematics 2024-04-18 Nikita Puchkin , Eduard Gorbunov , Nikolay Kutuzov , Alexander Gasnikov

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…

Methodology · Statistics 2022-04-15 Jian-Feng Cai , Jingyang Li , Dong Xia

Empirical research in economics increasingly relies on restricted-access data held by multiple firms or agencies, making it impossible to construct the estimator of interest on the pooled sample. At the same time, heavy-tailed distributions…

Methodology · Statistics 2026-05-06 Wen Zhang , Songshan Yang , Liping Zhu

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…

Methodology · Statistics 2025-10-30 Dominik Sturm , Ivo F. Sbalzarini