Related papers: Minimax optimal submatrix detection: Sharp non-asy…
We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…
We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…
In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise sparsity and element-wise sparsity in each group. By combining the Gilbert-Varshamov bound and its…
Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…
We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…
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 consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived…
This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The…
Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be…
This paper tackles a fundamental inference problem: given $n$ observations from a distribution $P$ over $\mathbb{R}^d$ with unknown mean $\boldsymbol{\mu}$, we must form a confidence set for the index (or indices) corresponding to the…
We consider the problem of detecting an anomaly in the form of a path of correlations hidden in white noise. We provide a minimax lower bound and a test that, under mild assumptions, is able to achieve the lower bound up to a multiplicative…
We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…