Combinatorics

Kullback–Leibler divergence

Mathematics

Statistics

Regular polygon

Convex analysis

Convex optimization

Mathematical analysis

Philosophy

Jensen's inequality

Divergence (linguistics)

Geometry

Linguistics

Applied mathematics

Bounded function

Upper and lower bounds

Results in Applied Mathematics

Based on the skewed Kullback-Leibler divergence introduced in the natural language processing, we derive the upper and lower bounds on the skewed version of the Jensen-Shannon divergence and investigate properties of them. In the process, we generalize the Bretagnolle-Huber inequality that offers an upper bound on the skewed Kullback-Leibler divergence. We further present how the skewed Jensen-Shannon divergence is bounded from below in terms of accuracy mismatch.

Some bounds for skewed α-Jensen-Shannon divergence