f-Divergence Variational Inference

This paper introduces the $f$-divergence variational inference ($f$-VI) that generalizes variational inference to all $f$-divergences. Initiated from minimizing a crafty surrogate $f$-divergence that shares the statistical consistency with the $f$-divergence, the $f$-VI framework not only unifies a number of existing VI methods, e.g. Kullback-Leibler VI, R\'{e}nyi's $\alpha$-VI, and $\chi$-VI, but offers a standardized toolkit for VI subject to arbitrary divergences from $f$-divergence family. A general $f$-variational bound is derived and provides a sandwich estimate of marginal likelihood (or evidence). The development of the $f$-VI unfolds with a stochastic optimization scheme that utilizes the reparameterization trick, importance weighting and Monte Carlo approximation; a mean-field approximation scheme that generalizes the well-known coordinate ascent variational inference (CAVI) is also proposed for $f$-VI. Empirical examples, including variational autoencoders and Bayesian neural networks, are provided to demonstrate the effectiveness and the wide applicability of $f$-VI.
Comment: Dapeng Li and Neng Wan contributed equally to this paper. Supplementary material is attached. The links to code are provided in the paper, supplementary material and reference list. To appear in Advances in Neural Information Processing Systems 33 (NeurIPS 2020)