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Stein Discrepancy

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Recently, Stein discrepancy-based methods have become popular tools for machine learning applications, including verifying the convergence of MCMC [1], goodness-of-fit tests [2][3], and variational inference [4][5]. Although Stein’s method has been long-known, widespread use was limited by an intractable optimization over a difficult function space. However, the recent development of the kernelized Stein discrepancy (KSD) [2][3] has circumvented this difficulty. Our talk will give a theoretical introduction to the Stein discrepancy and KSD . We will then introduce two recent applications of the Stein discrepancy to machine learning problems. The first of these, Stein variational gradient descent (SVGD) [4], shows how to apply the KSD to variational inference. We conclude by discussing the Stein variational autoencoder (Stein VAE ) [5], which applies SVGD to VAE learning.

Papers that are important for the talk:

[2] Chwialkowski, K., Strathmann, H., and Gretton, A. A kernel test of goodness of fit. In ICML , 2016. https://arxiv.org/abs/1602.02964

[4] Liu, Q. and Wang, D. Stein variational gradient descent: A general purpose Bayesian inference algorithm. In NIPS , 2016. https://arxiv.org/abs/1608.04471

Additional Recommended reading:

[1] Gorham, J. and Mackey, L. Measuring sample quality with Stein’s method. In NIPS , pp. 226-234, 2015. https://arxiv.org/abs/1506.03039 —Note: we will only be discussing up to and including section 3

[3] Liu, Q., Lee, J., and Jordan, M. I. A kernelized Stein discrepancy for goodness-of-fit tests. In ICML , 2016. https://arxiv.org/abs/1602.03253 —Note: this is essentially the same paper as [2], which is what we will present

[5] Pu, Y., Gan, Z., Henao, R., Li, C., Han, S., and Carin, L. VAE learning with Stein variational gradient descent. In NIPS , 2017. https://arxiv.org/abs/1704.05155

This talk is part of the Machine Learning Reading Group @ CUED series.

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