Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# $alpha$-Geodesical Skew Divergence

Version 1 : Received: 1 April 2021 / Approved: 2 April 2021 / Online: 2 April 2021 (11:36:19 CEST)

How to cite: Kimura, M.; Hino, H. $alpha$-Geodesical Skew Divergence. Preprints 2021, 2021040055 (doi: 10.20944/preprints202104.0055.v1). Kimura, M.; Hino, H. $alpha$-Geodesical Skew Divergence. Preprints 2021, 2021040055 (doi: 10.20944/preprints202104.0055.v1).

## 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.

## Subject Areas

KL-divergence; JS-divergence; skew divergence; information geometry

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