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

Jul 12, 2020

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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 challenging, large-scale Bayesian inference problems. In this paper, we find that existing ParVI approaches converge insufficiently fast under sample quality metrics, and we propose a novel variance reduction and quasi-Newton preconditioning framework for all ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of ParVIs for accurate posterior inference in large-scale and ill-conditioned problems.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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