Markovian Score Climbing: Variational Inference with KL(p

Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of that family that is closest to the exact posterior p. Traditionally, VI algorithms minimize the "exclusive Kullback-Leibler (KL)" KL(q p), often for computational convenience. Recent research, however, has also focused on the "inclusive KL" KL(p q), which has good statistical properties that makes it more appropriate for certain inference problems. This paper develops a simple algorithm for reliably minimizing the inclusive KL using stochastic gradients with vanishing bias. This method, which we call Markovian score climbing (MSC), converges to a local optimum of the inclusive KL.