Related papers: A note on distance variance for categorical variab…

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…

We consider linear error correcting codes associated to higher dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

In this paper we study bounds for the total variation distance between two second degree polynomials in normal random variables provided that they essentially depend on at least three variables.

In a previous article (Rahman, Guns, Rousseau, and Engels, 2015) we described several approaches to determine the cognitive distance between two units. One of these approaches was based on what we called barycenters in N dimensions. The…

There are many open questions pertaining to the statistical analysis of random objects, which are increasingly encountered. A major challenge is the absence of linear operations in such spaces. A basic statistical task is to quantify…

Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for…

We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…

The fractional order generalization of Shannon entropy proposed by Ubriaco has been studied for discrete distributions. In the current paper, we conduct a detailed study of the continuous analogue of this entropy termed as fractional…

The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…

We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savar\'e [DNS]. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined…

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can…

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic…

The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total…

We study three preferential attachment models where the parameters are such that the asymptotic degree distribution has infinite variance. Every edge is equipped with a non-negative i.i.d. weight. We study the weighted distance between two…

Standard statistical methods applied to matrix random variables often fail to describe the underlying structure in multiway data sets. In this paper we will discuss the concept of an array variate random variable and introduce a class of…

Diversity is an important criterion for many areas of machine learning (ML), including generative modeling and dataset curation. However, existing metrics for measuring diversity are often domain-specific and limited in flexibility. In this…

The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…

Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…