相关论文: On the Kullback-Leibler divergence between locatio…
Let $X,U,Y$ be spherically symmetric distributed having density $$\eta^{d +k/2} \, f\left(\eta(\|x-\theta|^2+ \|u\|^2 + \|y-c\theta\|^2 ) \right)\,,$$ with unknown parameters $\theta \in \mathbb{R}^d$ and $\eta>0$, and with known density…
Smooth Csisz\'ar $f$-divergences can be expressed as integrals over so-called hockey stick divergences. This motivates a natural quantum generalization in terms of quantum Hockey stick divergences, which we explore here. Using this recipe,…
In the multi-fractal analysis of large scale matter distribution, the scale of transition to homogeneity is defined as the scale above which the fractal dimension of underlying point distribution is equal to the ambient dimension of the…
This paper introduces link functions for transforming one probability distribution to another such that the Kullback-Leibler and R\'enyi divergences between the two distributions are symmetric. Two general classes of link models are…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the H\"older ordinary and reverse…
When sampling multi-modal probability distributions, correctly estimating the relative probability of each mode, even when the modes have been discovered and locally sampled, remains challenging. We test a simple reweighting scheme designed…
This paper describes a generalization of the Hellinger distance which we call the S -Hellinger distance; this general family connects the Hellinger distance smoothly with the $L_2$-divergence by a tuning parameter $\alpha$ and is indeed a…
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…
We derive a closed form solution for the Kullback-Leibler divergence between two generalized gamma distributions. These notes are meant as a reference and provide a guided tour towards a result of practical interest that is rarely…
We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in…
Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma…
The purpose of this paper is to examine the sampling problem through Euler discretization, where the potential function is assumed to be a mixture of locally smooth distributions and weakly dissipative. We introduce $\alpha_{G}$-mixture…
We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space ${\Bbb R}^n$.…
The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a…
The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive…
Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by…
The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the…