Related papers: Approximating the Total Variation Distance between…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…
In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
In this paper, we derive some upper and lower bounds and inequalities for the total variation distance (TVD) and the Kullback-Leibler divergence (KLD), also known as the relative entropy, between two probability measures $\mu$ and $\nu$…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…
This paper investigates the soft covering lemma under both the relative entropy and the total variation distance as the measures of deviation. The exact order of the expected deviation of the random i.i.d. code for the soft covering problem…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…
The Tully-Fisher relation is a vital distance indicator, but its precise inference is challenged by selection bias, statistical bias, and uncertain inclination corrections. This study presents a Bayesian framework that simultaneously…
Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
We study the Wasserstein distance $W_2$ for Gaussian samples. We establish the exact rate of convergence $\sqrt{\log\log n/n}$ of the expected value of the $W_2$ distance between the empirical and true $c.d.f.$'s for the normal…
The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and to Koopman Mode Decomposition (KMD)…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
The multivariate Gaussian rate-distortion (RD) function is crucial in various applications, such as digital communications, data storage, or neural networks. However, the complex form of the multivariate Gaussian RD function prevents its…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…