Pathwise Derivatives for Multivariate Distributions

Martin Jankowiak, Theofanis Karaletsos
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:333-342, 2019.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Pathwise Derivatives for Multivariate Distributions %A Martin Jankowiak %A Theofanis Karaletsos %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-jankowiak19a %I PMLR %P 333--342 %U https://proceedings.mlr.press/v89/jankowiak19a.html %V 89 %X 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.
APA
Jankowiak, M. & Karaletsos, T.. (2019). Pathwise Derivatives for Multivariate Distributions. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:333-342 Available from https://proceedings.mlr.press/v89/jankowiak19a.html.

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