Generalized Beta Divergence
This work provides a theoretical extension for researchers in statistical divergence and information theory, but it is incremental as it builds on existing Tweedie models.
The paper generalizes beta divergence beyond its classical form by representing it as a compact definite integral based on variance functions of exponential dispersion models, simplifying derivations of properties like scaling and translation, and shows equivalence between beta divergence and statistical deviance.
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many properties such as scaling, translation and expectation of the beta divergence. Further, we show that beta divergence and (half of) the statistical deviance are equivalent measures.