Parallel and distributed MCMC inference using Julia

Abstract

Machine learning algorithms are often computationally intensive and operate on large datasets. Being able to eciently learn models on large datasets holds the future of machine learning. As the speed of serial computation stalls, it is necessary to utilize the power of parallel computing in order to better scale with the growing complexity of algorithms and the growing size of datasets. In this thesis, we explore the use of Julia, a fairly new high level programming language that lends itself to easy parallelization over multiple CPU cores as well as multiple machines, on Markov chain Monte Carlo (MCMC) inference algorithms. First, we take existing algorithms and implement them in Julia. We focus on MCMC inference using Continuous Piecewise-Affine Based (CPAB) transformations and a parallel MCMC sampler for Dirichlet Process Mixture Models (DPMM). Instead of parallelizing over multiple cores on a single machine, our Julia implementations extend existing implementations by parallelizing over multiple machines. We compare our implementation with these existing implementations written in more traditional programming languages. Next, we develop a model Projections Dirichlet Process Gaussian Mixture Model (PDP-GMM) which relaxes the assumption that the draws from a Dirichlet Process Gaussian Mixture Model (DP-GMM) are directly observed. We extend our DPMM Julia implementation and present a few applications of this model.