Abstract
Many data generating processes involve latent random variables over discrete
combinatorial spaces whose size grows factorially with the dataset. In these
settings, existing posterior inference methods can be inaccurate and/or very
slow. In this work we develop methods for efficient amortized approximate
Bayesian inference over discrete combinatorial spaces, with applications to
probabilistic clustering (such as Dirichlet process mixture models),random
communities (such as stochastic block models) and random permutations. The
approach exploits the exchangeability of the generative models and is based on
mapping distributed, permutation-invariant representations of discrete
arrangements into conditional probabilities. The resulting algorithms
parallelize easily, yield iid samples from the approximate posteriors along
with a probability estimate of each sample (a quantity generally unavailable
using Markov Chain Monte Carlo) and can easily be applied to both conjugate and
non-conjugate models, as training only requires samples from the generative
model. As a scientific application, we present a novel approach to spike
sorting for high-density multielectrode probes.
Users
Please
log in to take part in the discussion (add own reviews or comments).