ICML 2020poster44 citations
Provable Smoothness Guarantees for Black-Box Variational Inference
Abstract
Black-box variational inference tries to approximate a complex target distribution through a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the target is M-Lipschitz smooth, then so is the “energy” part of the variational objective. The key proof idea is to describe gradients in a certain inner-product space, thus permitting the use of Bessel’s inequality. This result gives bounds on the location of the optimal parameters, and is a key ingredient for convergence guarantees.
BibTeX
@InProceedings{pmlr-v119-domke20a,
title = {Provable Smoothness Guarantees for Black-Box Variational Inference},
author = {Domke, Justin},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {2587--2596},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/domke20a/domke20a.pdf},
url = {https://proceedings.mlr.press/v119/domke20a.html},
abstract = {Black-box variational inference tries to approximate a complex target distribution through a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the target is M-Lipschitz smooth, then so is the “energy” part of the variational objective. The key proof idea is to describe gradients in a certain inner-product space, thus permitting the use of Bessel’s inequality. This result gives bounds on the location of the optimal parameters, and is a key ingredient for convergence guarantees.}
}