Chen, WY; Barp, A; Briol, F-X; Gorham, J; Girolami, M; Mackey, L; Oates, CJ; (2019) Stein Point Markov Chain Monte Carlo. In: Chaudhuri, Kamalika and Salakhutdinov, Ruslan, (eds.) Proceedings of the 36th International Conference on Machine Learning. (pp. pp. 1011-1021). Proceedings of Machine Learning Research: Long Beach, California, USA.

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Abstract

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established.

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