Related papers: Sum decomposition of divergence into three diverge…
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…
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…
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.
The family of f-divergences is ubiquitously applied to generative modeling in order to adapt the distribution of the model to that of the data. Well-definedness of f-divergences, however, requires the distributions of the data and model to…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…
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.
The Bregman divergence have been the subject of several studies. We do not go to do an exhaustive study of its subclasses, but propose a proof that shows that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in this…
Metrization of statistical divergences is valuable in both theoretical and practical aspects. One approach to obtaining metrics associated with divergences is to consider their fractional powers. Motivated by this idea, Os\'an, Bussandri,…
We provide a general method for evaluation of the joint range of f-divergences for two different functions f. Via topological arguments we prove that the joint range for general distributions equals the convex hull of the joint range…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…
Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to…
f-divergence estimation is an important problem in the fields of information theory, machine learning, and statistics. While several divergence estimators exist, relatively few of their convergence rates are known. We derive the MSE…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram…
There are three classical divergence measures known in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber \cite{jef} \cite{kul} \textit{J-divergence}. Sibson-Burbea-Rao \cite{sib} \cite{bur1,…
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value…