Related papers: Sharp Inequalities between Total Variation and Hel…
In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of solutions $u$ to total variation denoising. We demonstrated that the technique…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are…
In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…
Mixture distributions arise in many application areas, for example as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a…
The Kullback-Leibler (KL) divergence is not a proper distance metric and does not satisfy the triangle inequality, posing theoretical challenges in certain practical applications. Existing work has demonstrated that KL divergence between…
We study the influence of the assumption behind the use of the inverse Tully-Fisher relation: that there should be no observational cutoffs in the TF parameter log(V_M). It is noted how lower and upper cutoffs would be seen in a log(H_0)…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
We investigate the convergence properties of popular data-augmentation samplers for Bayesian probit regression. Leveraging recent results on Gibbs samplers for log-concave targets, we provide simple and explicit non-asymptotic bounds on the…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…
Motivated in part by models arising from mathematical descriptions of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain…
We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
The Gromov-Wasserstein (GW) distance is frequently used in machine learning to compare distributions across distinct metric spaces. Despite its utility, it remains computationally intensive, especially for large-scale problems. Recently, a…
Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…
This paper investigates covert communication over an additive white Gaussian noise (AWGN) channel in finite block length regime on the assumption of Gaussian codebooks. We first review some achievability and converse bounds on the…