Variational Rejection Sampling
This addresses a bottleneck in variational inference for machine learning practitioners, offering a method to improve posterior approximations with computational trade-offs.
The paper tackles the challenge of high variance in gradient estimates when learning latent variable models with stochastic variational inference, by proposing a novel rejection sampling step that discards low-likelihood samples from the variational posterior. This approach achieves improvements of 3.71 nats and 0.21 nats over state-of-the-art alternatives for estimating marginal log-likelihoods on MNIST.
Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likelihoods by the model. Our approach provides an arbitrarily accurate approximation of the true posterior at the expense of extra computation. Using a new gradient estimator for the resulting unnormalized proposal distribution, we achieve average improvements of 3.71 nats and 0.21 nats over state-of-the-art single-sample and multi-sample alternatives respectively for estimating marginal log-likelihoods using sigmoid belief networks on the MNIST dataset.