[Paper Review] Accelerating MCMC via Parallel Predictive Prefetching

Elaine Angelino, Eddie Kohler+3 more|arXiv (Cornell University)|Mar 28, 2014

Markov Chains and Monte Carlo MethodsMathematics30 references18 citations

TL;DR

This paper introduces parallel predictive prefetching to accelerate Markov chain Monte Carlo (MCMC) methods by speculatively evaluating future chain steps using fast approximations of the target density. By modeling the error in likelihood differences rather than absolute values, it achieves near-linear speedup during burn-in and sublinear but significantly improved speedup over serial execution, maintaining exact posterior inference without bias.

ABSTRACT

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential future steps of the chain in parallel. The approach can accelerate computation of the target distribution of a Bayesian inference problem, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores.

Motivation & Objective

• To accelerate slow, inherently serial MCMC algorithms like Metropolis-Hastings without compromising exactness.
• To exploit parallel computing resources effectively in Bayesian inference with large datasets.
• To develop a scheduling strategy that uses fast approximations of the target density to guide speculative execution.
• To model prediction uncertainty in a way that improves confidence in speculative decisions, especially for correlated likelihood differences.
• To achieve better than logarithmic speedup in practice by adapting to local acceptance rates and data subsampling.

Proposed method

• The method uses speculative execution to evaluate multiple future MCMC steps in parallel, guided by fast approximations of the target density.
• It models the error of the difference between proposal and current state likelihoods rather than individual likelihoods, reducing variance and improving prediction confidence.
• A dynamic scheduling scheme adapts speculation based on real-time acceptance rates and random deviates, improving resource utilization.
• The framework supports iterative refinement of predictors using increasingly accurate approximations, from subsampled data to full likelihoods.
• It ensures correctness by preserving identical pseudo-random number sequences across serial and parallel executions, avoiding bias.
• The approach generalizes to other MCMC algorithms with decomposable transition operators, such as slice sampling and adaptive MCMC.

Experimental results

Research questions

• RQ1 Can speculative execution with predictive modeling achieve significant speedup in MCMC without introducing bias?
• RQ2 How can approximation error in likelihood evaluations be modeled to improve confidence in speculative decisions?
• RQ3 What is the achievable speedup in practice when using fast approximations and adaptive scheduling in MCMC?
• RQ4 How does performance vary across different phases of MCMC, such as burn-in versus convergence?
• RQ5 Can the method maintain exact posterior inference while leveraging parallel resources effectively?

Key findings

• The method achieves near-linear speedup during the burn-in phase of MCMC chains, leveraging available parallel cores effectively.
• Speedup remains significantly better than logarithmic, even after burn-in, due to adaptive speculation based on local acceptance rates and prediction confidence.
• Modeling the difference in likelihoods rather than individual values reduces error variance, enabling more aggressive and reliable speculation.
• For the Bayesian Lasso problem, speedup was sustained across multiple initial conditions, though some cases showed logarithmic scaling due to small steps in later iterations.
• The predictor remains uncertain (intermediate values) in many cases, avoiding incorrect decisions that would lead to sublogarithmic speedup.
• The framework maintains exact posterior inference by ensuring identical random number sequences in both serial and parallel executions.