Stein Point Markov Chain Monte Carlo

Understand

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.