Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference ( ) in this paper. The performance of crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo ( ) sampling. replaces N i.i.d. samples from a uniform probability distribution by a deterministic sequence of samples of length N . This sequence covers the underlying random variable space more evenly than i.i.d. draws, reducing the variance of the gradient estimator. With our novel approach, both the score function and the reparameterization gradient estimators lead to much faster convergence. We also propose a new algorithm for Monte Carlo objectives, where we operate with a constant learning rate and increase the number of samples per iteration. We prove that this way, our algorithm can converge asymptotically at a faster rate than . We furthermore provide theoretical guarantees on for Monte Carlo objectives that go beyond , and support our findings by several experiments on large-scale data sets from various domains.
QMC Variational Inference: Buchholz et al. REF propose using QMC to reduce the variance of the gradient estimators of Monte Carlo Variational Inference.
Quasi-Monte Carlo Variational Inference
Published in the proceedings of the 35th International Conference on Machine Learning (ICML 2018)
Mathematics Computer Science