Related papers: Inequalities Among Symmetric Divergence Measures a…
We prove that the $f$-divergences between univariate Cauchy distributions are all symmetric, and can be expressed as strictly increasing scalar functions of the symmetric chi-squared divergence. We report the corresponding scalar functions…
Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and approximating a target measure $\pi$ as a perturbation of a…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
This article is the collection of the six research papers, recently written by the authors. In these papers authors refine the inequalities of trigonometric and hyperbolic functions such as Adamovic-Mitrinovic inequality, Cusa-Huygens…
We generalize the family of $\alpha$-divergences using a pair of strictly comparable weighted means. In particular, we obtain the $1$-divergence in the limit case $\alpha\rightarrow 1$ (a generalization of the Kullback-Leibler divergence)…
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…
A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…
Feature selection is a key step when dealing with high dimensional data. In particular, these techniques simplify the process of knowledge discovery from the data by selecting the most relevant features out of the noisy, redundant and…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
We examine the role of information geometry in the context of classical Cram\'er-Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying…
A physical magnetic field has a divergence of zero. Numerical error in constructing a model field and computing the divergence, however, introduces a finite divergence into these calculations. A popular metric for measuring divergence is…
The book is structured into four main chapters. Chapter 1 introduces the foundational concepts of divergence measures, including the well-known Kullback-Leibler divergence and its limitations. It then presents a detailed exploration of…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by…
Inequalities among symmetric polynomial functions are fundamental questions in mathematics and have various applications in science and engineering. This paper investigates a beautiful and inspiring conjecture, proposed by Cuttler, Greene…
The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case…