Related papers: $f$-Divergence Inequalities via Functional Dominat…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…
$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
We propose new bounds on the domination number and on the independence number of a graph and show that our bounds compare favorably to recent ones. Our bounds are obtained by using the Bhatia-Davis inequality linking the variance, the…
Identifying and mitigating the spread of fake information is a challenging issue that has become dominant with the rise of social media. We consider a generalization of the Domination problem that can be used to detect a set of individuals…
This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…
The similarity of feature representations plays a pivotal role in the success of problems related to domain adaptation. Feature similarity includes both the invariance of marginal distributions and the closeness of conditional distributions…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
In this paper, we investigate the relation between the (fractional) domination number of a digraph $G$ and the independence number of its underlying graph, denoted by $\alpha(G)$. More precisely, we prove that every digraph $G$ has…
We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…
For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to…
This paper initiates the study of fractional eternal domination in graphs, a natural relaxation of the well-studied eternal domination problem. We study the connections to flows and linear programming in order to obtain results on the…
We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
The paper describes several applications of information inequalities to problems in database theory. The problems discussed include: upper bounds of a query's output, worst-case optimal join algorithms, the query domination problem, and the…