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From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…

Machine Learning · Statistics 2022-10-03 Bruno Loureiro , Cédric Gerbelot , Maria Refinetti , Gabriele Sicuro , Florent Krzakala

We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…

Data Analysis, Statistics and Probability · Physics 2015-05-27 Eugene B. Postnikov , Igor M. Sokolov

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…

Statistics Theory · Mathematics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…

Machine Learning · Statistics 2022-05-13 Amanda Olmin , Fredrik Lindsten

This paper introduces the partial Gini covariance, a novel dependence measure that addresses the challenges of high-dimensional inference with heavy-tailed errors, often encountered in fields like finance, insurance, climate, and biology.…

Methodology · Statistics 2024-11-21 Yilin Zhang , Songshan Yang , Yunan Wu , Lan Wang

Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not…

Machine Learning · Computer Science 2024-03-18 Chinmaya Kausik , Kashvi Srivastava , Rishi Sonthalia

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 study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…

The consistency of doubly robust estimators relies on consistent estimation of at least one of two nuisance regression parameters. In moderate to large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving…

Machine Learning · Statistics 2019-01-30 Iván Díaz

Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…

Machine Learning · Computer Science 2026-04-08 Arash Jamshidi , Katsiaryna Haitsiukevich , Kai Puolamäki

Neural network compression has been an increasingly important subject, not only due to its practical relevance, but also due to its theoretical implications, as there is an explicit connection between compressibility and generalization…

Machine Learning · Statistics 2024-02-13 Yijun Wan , Melih Barsbey , Abdellatif Zaidi , Umut Simsekli

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

Statistics Theory · Mathematics 2013-03-13 Sahand N. Negahban , Pradeep Ravikumar , Martin J. Wainwright , Bin Yu

We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…

Probability · Mathematics 2023-01-30 Milad Bakhshizadeh

Continual learning is motivated by the need to adapt to real-world dynamics in tasks and data distribution while mitigating catastrophic forgetting. Despite significant advances in continual learning techniques, the theoretical…

Methodology · Statistics 2025-08-22 Yihan Zhao , Wenqing Su , Ying Yang

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

Statistics Theory · Mathematics 2019-09-04 Tino Werner

We study the algorithmic problem of robust mean estimation of an identity covariance Gaussian in the presence of mean-shift contamination. In this contamination model, we are given a set of points in $\mathbb{R}^d$ generated i.i.d. via the…

Data Structures and Algorithms · Computer Science 2025-02-21 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Thanasis Pittas

Distributional Reinforcement Learning (RL) estimates return distribution mainly by learning quantile values via minimizing the quantile Huber loss function, entailing a threshold parameter often selected heuristically or via hyperparameter…

Machine Learning · Computer Science 2024-01-09 Parvin Malekzadeh , Konstantinos N. Plataniotis , Zissis Poulos , Zeyu Wang

Heavy-tailed noise in nonconvex stochastic optimization has garnered increasing research interest, as empirical studies, including those on training attention models, suggest it is a more realistic gradient noise condition. This paper…

Optimization and Control · Mathematics 2026-04-17 Shuhua Yu , Dusan Jakovetic , Soummya Kar

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…

Machine Learning · Computer Science 2026-05-14 Hamza Cherkaoui , Hélène Halconruy , Antonio Ocello

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine…

Machine Learning · Statistics 2021-03-09 Mojtaba Sahraee-Ardakan , Tung Mai , Anup Rao , Ryan Rossi , Sundeep Rangan , Alyson K. Fletcher