# Generalized Bregman and Jensen divergences which include some f-divergences

arXiv: https://arxiv.org/abs/1808.06148 · HTML: https://mlsanity.com/paper/1808.06148/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Bias-variance decompositions: the exclusive privilege of Bregman divergences](https://mlsanity.com/paper/2501.18581/) (2025)

## Abstract (arXiv)

In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-divergences include divergences which belong to a class of f-divergence (the Hellinger distance, the chi-square divergence and the alpha-divergence in addition to the Kullback-Leibler divergence). Moreover, we derive an inequality between the g-Bregman divergence and the skew g-Jensen divergence and show this inequality is a generalization of Lin's inequality.