A0765
Title: Hamiltonian Monte Carlo for Bayesian nonparametric clustering via soft multinomial approximations
Authors: Shounak Chattopadhyay - University of California, Los Angeles (United States) [presenting]
Marc Suchard - University of California, Los Angeles (United States)
Abstract: Bayesian nonparametric (BNP) clustering approaches provide an elegant yet flexible framework to carry out model-based clustering. Posterior computation in such models typically involves Markov chain Monte Carlo (MCMC) algorithms such as Gibbs sampling, iteratively sampling the cluster membership variables and the model hyperparameters. Although straightforward to implement, Gibbs sampling can have poor computational scalability, particularly when the discrete cluster allocations exhibit mutual dependence. As an alternative, model-based soft-multinomial clustering is developed via a continuous approximation to the discrete multinomial variable signifying cluster membership. The use of soft-multinomials allows the implementation of general-purpose MCMC algorithms such as Hamiltonian Monte Carlo (HMC) to jointly sample the cluster memberships and the model hyperparameters. Theoretical results are provided detailing this approximation and demonstrate substantial computational improvements using soft-multinomial clustering with HMC for posterior sampling over discrete BNP clustering approaches in a variety of simulation examples and real-world data applications.
