Generalized Symmetric Divergence Measures and the Probability of Error

TL;DR

This paper introduces generalized symmetric divergence measures encompassing classical divergences, deriving bounds on the probability of error and extending these bounds to differences of divergence measures.

Contribution

It proposes a unified framework for symmetric divergence measures and derives new bounds on error probability based on these generalized measures.

Findings

Bounds on probability of error in terms of generalized divergence measures

Extension of bounds to differences of divergence measures

Unification of classical divergence measures within a generalized framework

Abstract

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja Arithmetic-Geometric divergence. These three measures bear an interesting relationship among each other. The divergence measures like Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination are also known in the literature. In this paper, we have considered generalized symmetric divergence measures having the measures given above as particular cases. Bounds on the probability of error are obtained in terms of generalized symmetric divergence measures. Study of bounds on probability of error is extended for the difference of divergence measures.