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Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the…

Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…

In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…

Probabilistic classifiers are central for making informed decisions under uncertainty. Based on the maximum expected utility principle, optimal decision rules can be derived using the posterior class probabilities and misclassification…

We consider the problem of multi-class classification and a stochastic opti- mization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm…

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…

Let $\mathcal{F}$ be a class of measurable functions $f:S\mapsto [0,1]$ defined on a probability space $(S,\mathcal{A},P)$. Given a sample (X_1,...,X_n) of i.i.d. random variables taking values in S with common distribution P, let P_n…

We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous…

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 study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix…

Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…

Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error…

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…

The quantification problem consists of determining the prevalence of a given label in a target population. However, one often has access to the labels in a sample from the training population but not in the target population. A common…

In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…

This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…

In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…