Related papers: Inequalities Among Symmetric Divergence Measures a…

The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the…

In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is…

Comparing probability distributions is an indispensable and ubiquitous task in machine learning and statistics. The most common way to compare a pair of Borel probability measures is to compute a metric between them, and by far the most…

Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…

Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the…

We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root of these divergences is a distance metric. As a corollary we obtain a proof of the metric property for…

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…

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 characterize Martin-L\"of randomness and Schnorr randomness in terms of the merging of opinions, along the lines of the Blackwell-Dubins Theorem. After setting up a general framework for defining notions of merging randomness, we focus…

Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…

Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…

In this paper we introduce the intuitive notion of trivergence of probability distributions (TPD). This notion allow us to calculate the similarity among triplets of objects. For this computation, we can use the well known measures of…

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…

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…

From geometrical point of view, Eve (2003) studied seven means. These means are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal mean. We have considered for the first time a new measure calling…

Parametric adversarial divergences, which are a generalization of the losses used to train generative adversarial networks (GANs), have often been described as being approximations of their nonparametric counterparts, such as the…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…

Many evaluation measures are used to evaluate social biases in masked language models (MLMs). However, we find that these previously proposed evaluation measures are lacking robustness in scenarios with limited datasets. This is because…