Related papers: Optimal sub-Gaussian variance proxy for 3-mass dis…
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima.…
This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…
We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…
We present a new method for proving the norm concentration inequality of sub-Gaussian variables. Our proof is based on an averaged version of the moment generating function, termed the averaged moment generating function. Our method applies…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three…