[Paper Review] Asynchronous Distributed Gibbs Sampling

Alexander Terenin, Daniel Simpson+1 more|arXiv (Cornell University)|Sep 30, 2015

Markov Chains and Monte Carlo Methods36 references4 citations

TL;DR

This paper introduces Asynchronous Distributed Gibbs (ADG) sampling, a novel parallel MCMC method that eliminates synchronization and locking overhead by allowing asynchronous updates across distributed nodes. It achieves convergence under regularity conditions and demonstrates strong scaling in high-dimensional hierarchical models, enabling efficient large-scale Bayesian inference without performance bottlenecks.

ABSTRACT

Gibbs sampling is a widely used Markov Chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. It is widely believed that MCMC methods do not extend easily to parallel implementations, as their inherently sequential nature incurs a large synchronization cost. This means that new solutions are needed to bring Bayesian analysis fully into the era of large-scale computation. In this paper, we present a novel scheme - Asynchronous Distributed Gibbs (ADG) sampling - that allows us to perform MCMC in a parallel fashion with no synchronization or locking, avoiding the typical performance bottlenecks of parallel algorithms. Our method is especially attractive in settings, such as hierarchical random-effects modeling in which each observation has its own random effect, where the problem dimension grows with the sample size. We prove convergence under some basic regularity conditions, and discuss the proof for similar parallelization schemes for other iterative algorithms. We provide three examples that illustrate some of the algorithm's properties with respect to scaling. Because our hardware resources are bounded, we have not yet found a limit to the algorithm's scaling, and thus its true capabilities remain unknown.

Motivation & Objective

• To address the challenge of scaling Bayesian inference using MCMC methods in large-scale distributed systems.
• To eliminate synchronization and locking overhead in parallel MCMC, which traditionally limits scalability.
• To enable efficient, scalable Gibbs sampling in high-dimensional models where dimension grows with sample size, such as hierarchical random-effects models.
• To prove convergence of the asynchronous scheme under standard regularity conditions.
• To demonstrate the algorithm's practical scalability and performance on real-world examples.

Proposed method

• ADG sampling performs Gibbs updates in a fully asynchronous manner across distributed nodes, without waiting for global synchronization.
• Each node independently updates its local variables using the latest available data, even if outdated, to avoid idle waiting.
• The method relies on a randomized update order and consistent local state management to maintain convergence properties.
• Convergence is established under standard regularity conditions, extending to other iterative algorithms with similar parallelization patterns.
• The algorithm is designed to scale with increasing problem size and hardware resources, with no observed upper bound in tested configurations.

Experimental results

Research questions

• RQ1 Can Gibbs sampling be effectively parallelized without synchronization or locking to improve scalability in large-scale Bayesian inference?
• RQ2 What conditions ensure convergence of an asynchronous Gibbs sampling scheme in distributed systems?
• RQ3 How does ADG perform in scaling with increasing data size and computational resources in hierarchical models?
• RQ4 Can ADG handle high-dimensional models where the number of random effects grows with sample size?
• RQ5 What are the practical limits of scaling for this asynchronous MCMC approach?

Key findings

• ADG sampling achieves convergence under standard regularity conditions, validating its theoretical soundness.
• The algorithm scales effectively in practice, with no observed performance bottleneck or upper limit in tested configurations.
• ADG enables efficient parallelization of Gibbs sampling in high-dimensional hierarchical models, where each observation has its own random effect.
• The absence of synchronization or locking allows the method to fully utilize available hardware resources without idle waiting.
• The method demonstrates strong scaling behavior across three illustrative examples, suggesting potential for large-scale deployment.