Related papers: Generalized Symmetric Divergence Measures and Ineq…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…
We propose a new concept of codivergence, which quantifies the similarity between two probability measures $P_1, P_2$ relative to a reference probability measure $P_0$. In the neighborhood of the reference measure $P_0$, a codivergence…
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities…
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…
This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, by measuring distances between structural breaks within such a…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
In general, classical measurement statistics of a quantum measurement is disturbed by performing an additional incompatible quantum measurement beforehand. Using this observation, we introduce a state-independent definition of disturbance…
Jensen-Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic…
We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as…
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…
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…
Mutual information $I(X;Y)$ is a useful definition in information theory to estimate how much information the random variable $Y$ holds about the random variable $X$. One way to define the mutual information is by comparing the joint…
Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy…
The theory of digital sequences is a fundamental topic in QMC theory. Digital sequences are prototypes of sequences with low discrepancy. First examples were given by Il'ya Meerovich Sobol' and by Henri Faure with their famous…
The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems:…
Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and {\Gamma} be an arithmetic lattice. One can associate a probability measure {\mu}(H) on {\Gamma}\G for each…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
In this work, we present formulations for regularized Kullback-Leibler and R\'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two different settings,…
We consider a general class of metric measure spaces equipped with a regular Dirichlet form and then provide a lower bound on the hitting time probabilities of the associated Hunt process. Using these estimates we establish (i) a…