Variational Russian Roulette for Deep Bayesian Nonparametrics
Kai Xu, Akash Srivastava, Charles Sutton
Abstract
Bayesian nonparametric models provide a principled way to automatically adapt the complexity of a model to the amount of the data available, but computation in such models is difficult. Amortized variational approximations are appealing because of their computational efficiency, but current methods rely on a fixed finite truncation of the infinite model. This truncation level can be difficult to set, and also interacts poorly with amortized methods due to the over-pruning problem. Instead, we propose a new variational approximation, based on a method from statistical physics called Russian roulette sampling. This allows the variational distribution to adapt its complexity during inference, without relying on a fixed truncation level, and while still obtaining an unbiased estimate of the gradient of the original variational objective. We demonstrate this method on infinite sized variational auto-encoders using a Beta-Bernoulli (Indian buffet process) prior.
BibTeX
@InProceedings{pmlr-v97-xu19e,
title = {Variational Russian Roulette for Deep {B}ayesian Nonparametrics},
author = {Xu, Kai and Srivastava, Akash and Sutton, Charles},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {6963--6972},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/xu19e/xu19e.pdf},
url = {https://proceedings.mlr.press/v97/xu19e.html},
abstract = {Bayesian nonparametric models provide a principled way to automatically adapt the complexity of a model to the amount of the data available, but computation in such models is difficult. Amortized variational approximations are appealing because of their computational efficiency, but current methods rely on a fixed finite truncation of the infinite model. This truncation level can be difficult to set, and also interacts poorly with amortized methods due to the over-pruning problem. Instead, we propose a new variational approximation, based on a method from statistical physics called Russian roulette sampling. This allows the variational distribution to adapt its complexity during inference, without relying on a fixed truncation level, and while still obtaining an unbiased estimate of the gradient of the original variational objective. We demonstrate this method on infinite sized variational auto-encoders using a Beta-Bernoulli (Indian buffet process) prior.}
}