We propose a nonparametric procedure to achieve fast inference in generative
graphical models when the number of latent states is very large. The approach
is based on iterative latent variable preselection, where we alternate between
learning a 'selection function' to reveal the relevant latent variables, and
use this to obtain a compact approximation of the posterior distribution for
EM; this can make inference possible where the number of possible latent states
is e.g. exponential in the number of latent variables, whereas an exact
approach would be computationally unfeasible. We learn the selection function
entirely from the observed data and current EM state via Gaussian process
regression. This is by contrast with earlier approaches, where selection
functions were manually-designed for each problem setting. We show that our
approach performs as well as these bespoke selection functions on a wide
variety of inference problems: in particular, for the challenging case of a
hierarchical model for object localization with occlusion, we achieve results
that match a customized state-of-the-art selection method, at a far lower
computational cost
