Variational Russian Roulette for Deep Bayesian Nonparametrics

Kai Xu, Akash Srivastava, Charles Sutton
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6963-6972, 2019.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Variational Russian Roulette for Deep Bayesian Nonparametrics %A Kai Xu %A Akash Srivastava %A Charles Sutton %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-xu19e %I PMLR %P 6963--6972 %U https://proceedings.mlr.press/v97/xu19e.html %V 97 %X 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.
APA
Xu, K., Srivastava, A. & Sutton, C.. (2019). Variational Russian Roulette for Deep Bayesian Nonparametrics. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6963-6972 Available from https://proceedings.mlr.press/v97/xu19e.html.

Related Material