A non-negative expansion for small Jensen-Shannon Divergences

TL;DR

This paper introduces a non-negative series expansion for the Jensen-Shannon divergence, improving numerical calculations especially when the distributions are similar, by reducing errors in such cases.

Contribution

It presents a novel non-negative series expansion for the Jensen-Shannon divergence tailored for accurate numerical computation with similar distributions.

Findings

Series expansion is non-negative and numerically stable.

Effective for small differences between probability distributions.

Enhances precision in divergence calculations.

Abstract

In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical errors dominate evaluation.