Related papers: On Empirical Risk Minimization with Dependent and …

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

The $\ell_0$-constrained empirical risk minimization ($\ell_0$-ERM) is a promising tool for high-dimensional statistical estimation. The existing analysis of $\ell_0$-ERM estimator is mostly on parameter estimation and support recovery…

Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…

Meta learning is a promising paradigm in the era of large models and task distributional robustness has become an indispensable consideration in real-world scenarios. Recent advances have examined the effectiveness of tail task risk…

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

We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…

We consider statistical learning problems, when the distribution $P'$ of the training observations $Z'_1,\; \ldots,\; Z'_n$ differs from the distribution $P$ involved in the risk one seeks to minimize (referred to as the test distribution)…

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

We study risk-sensitive reinforcement learning in finite discounted MDPs with recursive entropic risk measures (ERM), where the risk parameter $\beta \neq 0$ controls the agent's risk attitude: $\beta>0$ for risk-averse and $\beta<0$ for…

The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has…

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…

A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed…

As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…

This paper introduces ergodic-risk criteria, which capture long-term cumulative risks associated with controlled Markov chains through probabilistic limit theorems--in contrast to existing methods that require assumptions of either finite…

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

Obtaining accurate class labels is often costly or unreliable, and may also be limited by privacy or other practical conditions. Compared with asking an annotator to provide the exact class, it is often easier to ask whether the true label…

This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

The generalization ability of minimizers of the empirical risk in the context of binary classification has been investigated under a wide variety of complexity assumptions for the collection of classifiers over which optimization is…