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We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…

Statistics Theory · Mathematics 2010-01-14 Jussi Klemelä , Enno Mammen

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

Methodology · Statistics 2023-12-18 Liujun Chen , Deyuan Li , Chen Zhou

In the first part of this paper, we show that the small-ball condition, recently introduced by Mendelson (2015), may behave poorly for important classes of localized functions such as wavelets, piecewise polynomials or trigonometric…

Statistics Theory · Mathematics 2016-10-19 Adrien Saumard

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class…

Machine Learning · Computer Science 2014-11-25 Nishant A. Mehta , Robert C. Williamson

We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…

Machine Learning · Statistics 2014-10-28 Chang Xu , Tongliang Liu , Dacheng Tao , Chao Xu

Conditional Value-at-Risk (CVaR) is a widely used risk-sensitive objective for learning under rare but high-impact losses, yet its statistical behavior under heavy-tailed data remains poorly understood. Unlike expectation-based risk, CVaR…

Machine Learning · Statistics 2026-02-23 Dinesh Karthik Mulumudi , Piyushi Manupriya , Gholamali Aminian , Anant Raj

We study the problem of excess risk evaluation for empirical risk minimization (ERM) under convex losses. We show that by leveraging the idea of wild refitting, one can upper bound the excess risk through the so-called "wild optimism,"…

Machine Learning · Computer Science 2026-03-26 Haichen Hu , David Simchi-Levi

We study the excess risk evaluation of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the idea of wild refitting, one can efficiently upper bound the excess risk through the so-called…

Machine Learning · Statistics 2025-11-25 Haichen Hu , David Simchi-Levi

The successful application of machine learning (ML) methods becomes increasingly dependent on their interpretability or explainability. Designing explainable ML systems is instrumental to ensuring transparency of automated decision-making…

Machine Learning · Computer Science 2022-07-04 L. Zhang , G. Karakasidis , A. Odnoblyudova , L. Dogruel , A. Jung

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…

Methodology · Statistics 2023-04-17 Julien Hambuckers , Marie Kratz , Antoine Usseglio-Carleve

This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework…

Econometrics · Economics 2026-02-23 Chiara Amorino , Christian Brownlees , Ankita Ghosh

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…

Statistics Theory · Mathematics 2021-01-01 Xiaoou Pan , Qiang Sun , Wen-Xin Zhou

Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with…

Statistics Theory · Mathematics 2008-12-18 Charles Mitchell , Sara van de Geer

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…

Machine Learning · Computer Science 2022-11-15 Samir M. Perlaza , Gaetan Bisson , Iñaki Esnaola , Alain Jean-Marie , Stefano Rini

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of…

Machine Learning · Computer Science 2013-11-26 Hsiang-Fu Yu , Prateek Jain , Purushottam Kar , Inderjit S. Dhillon

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…

Machine Learning · Computer Science 2017-11-23 Yuanhong Wang , Yuyi Wang , Xingwu Liu , Juhua Pu

In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover,…

Optimization and Control · Mathematics 2015-06-09 Dominik Csiba , Peter Richtárik

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…

Machine Learning · Statistics 2016-09-08 Gábor Balázs , András György , Csaba Szepesvári

We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the $\ell_0$-norm of the mean change vector, we separately consider dense and sparse…

Statistics Theory · Mathematics 2025-10-14 Mengchu Li , Yudong Chen , Tengyao Wang , Yi Yu