Scalable Monte Carlo for Bayesian Learning

TL;DR

This paper introduces scalable Monte Carlo methods for Bayesian learning, focusing on recent advances in MCMC algorithms that handle large data and high-dimensional problems efficiently.

Contribution

It provides a comprehensive overview of recent scalable MCMC techniques, including stochastic gradient, non-reversible, and continuous-time methods, with emphasis on their theoretical and practical developments.

Findings

Recent scalable MCMC algorithms improve efficiency in high-dimensional Bayesian inference.

New convergence assessment techniques enhance reliability of Monte Carlo methods.

Advances support large-scale machine learning and AI applications.

Abstract

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment) have emerged as recently as the last decade, and have driven substantial recent practical and theoretical advances in the field. A particular focus is on methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI.