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Stein Point Markov Chain Monte Carlo
Wilson Ye Chen · Alessandro Barp · Francois-Xavier Briol · Jackson Gorham · Mark Girolami · Lester Mackey · Chris Oates

Tue Jun 11 12:00 PM -- 12:05 PM (PDT) @ Room 101

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.

Author Information

Wilson Ye Chen (The Institute of Statistical Mathematics)
Alessandro Barp (Imperial College London)
Francois-Xavier Briol (University of Cambridge)
Jackson Gorham (OPENDOOR)
Mark Girolami (Imperial College London)
Lester Mackey (Microsoft Research)
Chris Oates (Newcastle University)

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