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When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…

Methodology · Statistics 2026-02-16 Liujun Chen , Chen Zhou

We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…

Statistics Theory · Mathematics 2022-02-25 Jaouad Mourtada , Tomas Vaškevičius , Nikita Zhivotovskiy

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

We study scalable alternatives to robust gradient descent (RGD) techniques that can be used when the losses and/or gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to…

Machine Learning · Statistics 2020-12-15 Matthew J. Holland

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…

Machine Learning · Statistics 2025-11-20 The Tien Mai

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

Methodology · Statistics 2026-05-11 Zihao Song , Jicai Liu , Heng Lian , Weihua Zhao

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…

Methodology · Statistics 2016-01-20 John H. J. Einmahl , Anna Kiriliouk , Johan Segers

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed…

Statistics Theory · Mathematics 2026-05-26 Kejun Chen , Yuchang Lin , Qianqian Zhu

Restricting the variance of a policy's return is a popular choice in risk-averse Reinforcement Learning (RL) due to its clear mathematical definition and easy interpretability. Traditional methods directly restrict the total return…

Machine Learning · Computer Science 2023-11-06 Yudong Luo , Guiliang Liu , Pascal Poupart , Yangchen Pan

The modelling of multivariate extreme events is important in a wide variety of applications, including flood risk analysis, metocean engineering and financial modelling. A wide variety of statistical techniques have been proposed in the…

Methodology · Statistics 2025-09-16 Callum John Rowlandson Murphy-Barltrop , Ed Mackay , Philip Jonathan

High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…

Machine Learning · Statistics 2026-01-06 Even He

We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…

Methodology · Statistics 2023-05-23 Bikramjit Das

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…

Statistics Theory · Mathematics 2019-03-19 Xi Chen , Wen-Xin Zhou

A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…

Machine Learning · Statistics 2021-11-17 Nilesh Tripuraneni , Ben Adlam , Jeffrey Pennington

An important challenge in statistical analysis lies in controlling the estimation bias when handling the ever-increasing data size and model complexity of modern data settings. In this paper, we propose a reliable estimation and inference…

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

Machine Learning · Computer Science 2018-10-26 Lijun Zhang , Zhi-Hua Zhou

In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…

Methodology · Statistics 2022-04-05 Lingyu He , Yanrong Yang , Bo Zhang

We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…

Machine Learning · Statistics 2023-05-30 Ibrahim Merad , Stéphane Gaïffas

We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…

Statistics Theory · Mathematics 2026-01-01 Stéphane Girard , Cambyse Pakzad

Real-world data is often unbalanced and long-tailed, but deep models struggle to recognize rare classes in the presence of frequent classes. To address unbalanced data, most studies try balancing the data, the loss, or the classifier to…

Machine Learning · Computer Science 2021-11-02 Dvir Samuel , Gal Chechik