Notes on Kullback-Leibler Divergence and Likelihood

TL;DR

How KL divergence arises from likelihood theory in an attempt to provide some intuition is discussed and a rigorous (but rather simple) derivation for the appendix is reserved.

Abstract

The Kullback-Leibler (KL) divergence is a fundamental equation of information theory that quantifies the proximity of two probability distributions. Although difficult to understand by examining the equation, an intuition and understanding of the KL divergence arises from its intimate relationship with likelihood theory. We discuss how KL divergence arises from likelihood theory in an attempt to provide some intuition and reserve a rigorous (but rather simple) derivation for the appendix. Finally, we comment on recent applications of KL divergence in the neural coding literature and highlight its natural application.