Hamilton Monte Carlo with discrete categorical parameters using the Concrete distribution

Jakob Torgander, Måns Magnusson, Jonas Wallin

Keywords: Hamiltonian Monte Carlo, MCMC, Probabilistic machine learning, Gumbel max trick

TL;DR: We introduce a method to enable Hamiltonian Monte Carlo (HMC) to simulate from mixed continuous and discrete posterior distributions.

Abstract:

We introduce a method to enable Hamiltonian Monte Carlo (HMC) to simulate from mixed
continuous and discrete posterior distributions. In particular, we show how the ”Gumbel
Max Trick” and the Concrete (Gumbel-softmax) distribution can be used for constructing
a continuous approximation of a categorical discrete distribution, and how this distribution
can be efficiently implemented for HMC. We also illustrate how the Concrete distribution
can be incorporated into a latent discrete parameter model, resulting in the Concrete
Mixture model.

Submission Number: 13