Neural Permutation Processes

Ari Pakman, Yueqi Wang, Liam Paninski

Keywords: amortized inference, permutations, deep sets

TL;DR: A novel neural architecture for efficient amortized inference over latent permutations

Abstract: We introduce a neural architecture to perform amortized approximate Bayesian inference over latent random permutations of two sets of objects. The method involves approximating permanents of matrices of pairwise probabilities using recent ideas on functions defined over sets. Each sampled permutation comes with a probability estimate, a quantity unavailable in MCMC approaches. We illustrate the method in sets of 2D points and MNIST images.