Understanding and Accelerating Particle-Based Variational Inference

Chang Liu, Jingwei Zhuo, Pengyu Cheng, Ruiyi Zhang, Jun Zhu
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4082-4092, 2019.

Abstract

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-liu19i, title = {Understanding and Accelerating Particle-Based Variational Inference}, author = {Liu, Chang and Zhuo, Jingwei and Cheng, Pengyu and Zhang, Ruiyi and Zhu, Jun}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4082--4092}, 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/liu19i/liu19i.pdf}, url = {https://proceedings.mlr.press/v97/liu19i.html}, abstract = {Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.} }
Endnote
%0 Conference Paper %T Understanding and Accelerating Particle-Based Variational Inference %A Chang Liu %A Jingwei Zhuo %A Pengyu Cheng %A Ruiyi Zhang %A Jun Zhu %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-liu19i %I PMLR %P 4082--4092 %U https://proceedings.mlr.press/v97/liu19i.html %V 97 %X Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.
APA
Liu, C., Zhuo, J., Cheng, P., Zhang, R. & Zhu, J.. (2019). Understanding and Accelerating Particle-Based Variational Inference. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4082-4092 Available from https://proceedings.mlr.press/v97/liu19i.html.

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