Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference
This work addresses a key bottleneck in variational inference for machine learning practitioners, offering an incremental improvement to gradient estimation methods.
The authors tackled the problem of high variance in gradient estimators for variational inference by proposing a simpler, lower-variance estimator that removes the score function term, resulting in unbiased gradients with variance approaching zero as the approximation improves.
We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient estimator whose variance approaches zero as the approximate posterior approaches the exact posterior. We analyze the behavior of this gradient estimator theoretically and empirically, and generalize it to more complex variational distributions such as mixtures and importance-weighted posteriors.