Structured filtering

Abstract

A major challenge facing existing sequential Monte Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results with equivalent probability. We address this problem here by proposing a form of particle filtering that clusters the particles that comprise the sequential Monte Carlo approximation to the posterior before applying a resampler. Through a new graphical approach to thinking about such models, we are able to devise an artificial-intelligence based strategy that automatically learns the shape and number of the clusters in the support of the posterior. We demonstrate the power of our approach by applying it to randomized gap estimation and a form of low circuit-depth phase estimation where existing methods from the physics literature either exhibit much worse performance or even fail completely.