Related papers: Minimax fast rates for discriminant analysis with …

The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a…

Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the…

Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing…

This paper reviews recent developments in fundamental limits and optimal algorithms for change point analysis. We focus on minimax optimal rates in change point detection and localisation, in both parametric and nonparametric models. We…

We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…

It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested…

We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded…

We establish optimal convergence rates up to a log-factor for a class of deep neural networks in a classification setting under a restraint sometimes referred to as the Tsybakov noise condition. We construct classifiers in a general setting…

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the…

This paper introduces an approach to multi-stream quickest change detection and fault isolation for unnormalized and score-based statistical models. Traditional optimal algorithms in the quickest change detection literature require explicit…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

We obtain the optimal Bayesian minimax rate for the unconstrained large covariance matrix of multivariate normal sample with mean zero, when both the sample size, n, and the dimension, p, of the covariance matrix tend to infinity.…

Let $(X,Y)\in\mathcal{X}\times \mathcal{Y}$ be a random couple with unknown distribution $P$. Let $\GG$ be a class of measurable functions and $\ell$ a loss function. The problem of statistical learning deals with the estimation of the…

Machine learning models are routinely used to support decisions that affect individuals -- be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from…

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

Multiple fairness constraints have been proposed in the literature, motivated by a range of concerns about how demographic groups might be treated unfairly by machine learning classifiers. In this work we consider a different motivation;…

Adversarial robustness has become a fundamental requirement in modern machine learning applications. Yet, there has been surprisingly little statistical understanding so far. In this paper, we provide the first result of the optimal minimax…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the…

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…