Pathwise Derivatives for Multivariate Distributions
This work addresses a technical bottleneck in variational inference for machine learning practitioners, offering incremental improvements to gradient estimation methods.
The paper tackles the problem of efficiently computing pathwise gradient estimators for multivariate distributions by exploiting the link between the transport equation and derivatives of expectations, focusing on adaptive control variates and multivariate Normal mixtures. The result demonstrates that their gradient estimators outperform other methods in variational inference experiments, particularly in high dimensions.
We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct gradient estimators with reduced variance. Second, we consider the case of multivariate mixture distributions. In particular we show how to compute pathwise derivatives for mixtures of multivariate Normal distributions with arbitrary means and diagonal covariances. We demonstrate in a variety of experiments in the context of variational inference that our gradient estimators can outperform other methods, especially in high dimensions.