Geometric Rényi divergence: A comparative measure with applications to atomic densities

Asymptotic Distribution of Divergence Measure with Applications

Variational Inference with Rényi Divergence

This paper introduces the variational Rényi bound (VR) that extends traditional variational inference to Rényi’s α-divergences. This new family of variational methods unifies a number of existing approaches, and enables a smooth interpolation from the evidence lower-bound to the log (marginal) likelihood that is controlled by the value of α that parametrises the divergence. The reparameterizati...

Rényi Divergence Variational Inference

This paper introduces the variational Rényi bound (VR) that extends traditional variational inference to Rényi’s α-divergences. This new family of variational methods unifies a number of existing approaches, and enables a smooth interpolation from the evidence lower-bound to the log (marginal) likelihood that is controlled by the value of α that parametrises the divergence. The reparameterizati...

Rényi divergence and majorization

Rényi divergence is related to Rényi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties of Rényi divergence, including it...

Rényi Divergence and Kullback-Leibler Divergence

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibl...