Stein Point Markov Chain Monte Carlo
Wilson Ye Chen, Alessandro Barp, Francois-Xavier Briol, Jackson Gorham, Mark Girolami, Lester Mackey, Chris Oates
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.
BibTeX
@InProceedings{pmlr-v97-chen19b,
title = {Stein Point {M}arkov Chain {M}onte {C}arlo},
author = {Chen, Wilson Ye and Barp, Alessandro and Briol, Francois-Xavier and Gorham, Jackson and Girolami, Mark and Mackey, Lester and Oates, Chris},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {1011--1021},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/chen19b/chen19b.pdf},
url = {https://proceedings.mlr.press/v97/chen19b.html},
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.}
}