Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences
Year: 2022
Type: article
Abstract: By calculating the Kullback-Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel-Young divergence. Inspired by this formula, we define the duo Fenchel-Young divergence and report a majorization condition on its pair of strictly convex generators, which guarantees that this divergence is always non-negative. The duo Fenchel-Young divergence is also equivalent to a duo Bregman divergence. We show how to use these duo divergences by calculating the Kullback-Leibler divergence between densities of truncated exponential families with nested supports, and report a formula for the Kullback-Leibler divergence between truncated normal distributions. Finally, we prove that the skewed Bhattacharyya distances between truncated exponential families amount to equivalent skewed duo Jensen divergences.
Source: Entropy
DOI: 10.3390/e24030421
Author: Frank Nielsen
Institution: Sony Computer Science Laboratories
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,885
OpenAlex ID: W4220876393