$\alpha$-Geodesical Skew Divergence

TL;DR

This paper introduces the $oldsymbol{ extalpha}$-geodesical skew divergence, a new information geometric generalization of the skew divergence that approximates KL divergence without requiring absolute continuity, with theoretical property analysis.

Contribution

It proposes the $oldsymbol{ extalpha}$-geodesical skew divergence and studies its properties as a novel generalization within information geometry.

Findings

Defines the $oldsymbol{ extalpha}$-geodesical skew divergence

Analyzes its mathematical properties

Shows its relation to KL divergence approximation

Abstract

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.