相关论文: Locally minimax optimal confidence sets for the be…

In this work, we study local minimax convergence estimation rates subject to $\epsilon$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of…

The aim of this paper is to establish non-asymptotic minimax rates of testing for goodness-of-fit hypotheses in a heteroscedastic setting. More precisely, we deal with sequences $(Y_j)_{j\in J}$ of independent Gaussian random variables,…

The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

Given an observation $\mathbf Y \in \mathbb{R}^{d_1\times d_2}$ from the model $\mathbf Y = \mathbf X + \mathbf E$ where $\mathbf X$ is constant and $\mathbf E$ has i.i.d. $N(0,1)$ entries, we consider the problem of detecting a planted…

Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s^*$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(s^{*}d / nm\varepsilon^2)$. This can be…

We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…

For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In…

We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…

We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation…

We study minimax testing in a statistical inverse problem when the associated operator is unknown. In particular, we consider observations from an inverse Gaussian regression model where the associated operator is unknown but contained in a…

Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…

We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

State estimation is a fundamental problem for multi-sensor information fusion, essential in applications such as target tracking, power systems, and control automation. Previous research mostly ignores the correlation between sensors and…

In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced…

This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on…

We consider a Gaussian sequence model that contains ill-posed inverse problems as special cases. We assume that the associated operator is partially unknown in the sense that its singular functions are known and the corresponding singular…

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

A rich line of recent work has studied distributionally robust learning approaches that seek to learn a hypothesis that performs well, in the worst-case, on many different distributions over a population. We argue that although the most…