Related papers: An efficiency upper bound for inverse covariance e…

Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…

In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…

The problem of optimal node density for ad hoc sensor networks deployed for making inferences about two dimensional correlated random fields is considered. Using a symmetric first order conditional autoregressive Gauss-Markov random field…

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…

This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…

Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained.…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…

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

We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…

We construct an estimator $\widehat{\Sigma}$ for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements $X_1,...,X_N$ of X and the wanted confidence level. We show under…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

We prove that the maximum of the sample importance weights in a high-dimensional Gaussian particle filter converges to unity unless the ensemble size grows exponentially in the system dimension. Our work is motivated by and parallels the…

We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…