Variance Reduction and Quasi-Newton for Particle-Based Variational Inference

Michael Zhu, Chang Liu, Jun Zhu
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:11576-11587, 2020.

Abstract

Particle-based Variational Inference methods (ParVIs), like Stein Variational Gradient Descent, are nonparametric variational inference methods that optimize a set of particles to best approximate a target distribution. ParVIs have been proposed as efficient approximate inference algorithms and as potential alternatives to MCMC methods. However, to our knowledge, the quality of the posterior approximation of particles from ParVIs has not been examined before for large-scale Bayesian inference problems. We conduct this analysis and evaluate the sample quality of particles produced by ParVIs, and we find that existing ParVI approaches using stochastic gradients converge insufficiently fast under sample quality metrics. We propose a novel variance reduction and quasi-Newton preconditioning framework for ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of variance reduction and quasi-Newton methods for ParVIs for accurate posterior inference in large-scale and ill-conditioned problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-zhu20b, title = {Variance Reduction and Quasi-{N}ewton for Particle-Based Variational Inference}, author = {Zhu, Michael and Liu, Chang and Zhu, Jun}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {11576--11587}, 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/zhu20b/zhu20b.pdf}, url = {https://proceedings.mlr.press/v119/zhu20b.html}, abstract = {Particle-based Variational Inference methods (ParVIs), like Stein Variational Gradient Descent, are nonparametric variational inference methods that optimize a set of particles to best approximate a target distribution. ParVIs have been proposed as efficient approximate inference algorithms and as potential alternatives to MCMC methods. However, to our knowledge, the quality of the posterior approximation of particles from ParVIs has not been examined before for large-scale Bayesian inference problems. We conduct this analysis and evaluate the sample quality of particles produced by ParVIs, and we find that existing ParVI approaches using stochastic gradients converge insufficiently fast under sample quality metrics. We propose a novel variance reduction and quasi-Newton preconditioning framework for ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of variance reduction and quasi-Newton methods for ParVIs for accurate posterior inference in large-scale and ill-conditioned problems.} }
Endnote
%0 Conference Paper %T Variance Reduction and Quasi-Newton for Particle-Based Variational Inference %A Michael Zhu %A Chang Liu %A Jun Zhu %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-zhu20b %I PMLR %P 11576--11587 %U https://proceedings.mlr.press/v119/zhu20b.html %V 119 %X Particle-based Variational Inference methods (ParVIs), like Stein Variational Gradient Descent, are nonparametric variational inference methods that optimize a set of particles to best approximate a target distribution. ParVIs have been proposed as efficient approximate inference algorithms and as potential alternatives to MCMC methods. However, to our knowledge, the quality of the posterior approximation of particles from ParVIs has not been examined before for large-scale Bayesian inference problems. We conduct this analysis and evaluate the sample quality of particles produced by ParVIs, and we find that existing ParVI approaches using stochastic gradients converge insufficiently fast under sample quality metrics. We propose a novel variance reduction and quasi-Newton preconditioning framework for ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of variance reduction and quasi-Newton methods for ParVIs for accurate posterior inference in large-scale and ill-conditioned problems.
APA
Zhu, M., Liu, C. & Zhu, J.. (2020). Variance Reduction and Quasi-Newton for Particle-Based Variational Inference. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:11576-11587 Available from https://proceedings.mlr.press/v119/zhu20b.html.

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