Generalized Bregman and Jensen divergences which include some f-divergences
This work provides a theoretical extension for divergence measures in machine learning and statistics, but it appears incremental as it builds on existing divergence frameworks without clear practical applications.
The paper introduces new classes of divergences, called g-Bregman and skew g-Jensen divergences, by extending Bregman and skew Jensen divergences, and shows that these include some f-divergences like the Hellinger distance and chi-square divergence, while also generalizing Lin's inequality.
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.