Refined α-Divergence Variational Inference via Rejection Sampling
We present an approximate inference method, based on a synergistic combination of Rényi αdivergence variational inference (RDVI) and rejection sampling (RS). RDVI is based on minimization of Rényi α-divergence Dα(p||q) between the true distribution p(x) and a variational approximation q(x); RS draws samples from a distribution p(x) = p̃(x)/Zp using a proposal q(x), s.t. Mq(x) ≥ p̃(x),∀x. Our inference method is based on a crucial observation that D∞(p||q) equals logM(θ) where M(θ) is the optimal value of the RS constant for a given proposal qθ(x). This enables us to develop a two-stage hybrid inference algorithm.