Pathwise Derivatives for Multivariate Distributions
Martin Jankowiak, Theofanis Karaletsos
Abstract
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.
BibTeX
@InProceedings{pmlr-v89-jankowiak19a,
title = {Pathwise Derivatives for Multivariate Distributions},
author = {Jankowiak, Martin and Karaletsos, Theofanis},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {333--342},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/jankowiak19a/jankowiak19a.pdf},
url = {https://proceedings.mlr.press/v89/jankowiak19a.html},
abstract = {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.}
}