Rényi divergence variational inference

Abstract

This paper introduces the $\textit{variational Rényi bound}$ (VR) that extends traditional variational inference to Rényi’s $\alpha$-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 $\alpha$ that parametrises the divergence. The reparameterization trick, Monte Carlo approximation and stochastic optimisation methods are deployed to obtain a tractable and unified framework for optimisation. We further consider negative $\alpha$ values and propose a novel variational inference method as a new special case in the proposed framework. Experiments on Bayesian neural networks and variational auto-encoders demonstrate the wide applicability of the VR bound.YL thanks the Schlumberger Foundation FFTF fellowship. RET thanks EPSRC grants # EP/M026957/1 and EP/L000776/1