[Paper Review] A New Approach to Probabilistic Programming Inference

Frank Wood, Jan Willem van de Meent+1 more|arXiv (Cornell University)|Jul 3, 2015

Markov Chains and Monte Carlo Methods8 references4 citations

TL;DR

This paper introduces a particle Markov chain Monte Carlo (PMCMC) approach for probabilistic programming inference that enables efficient, parallelizable sampling in Turing-complete languages with complex control flow and Bayesian nonparametric primitives. It demonstrates faster convergence than single-site Metropolis-Hastings methods, even after normalizing for computational cost, particularly in models with dense conditional dependencies.

ABSTRACT

We introduce and demonstrate a new approach to inference in expressive probabilistic programming languages based on particle Markov chain Monte Carlo. Our approach is simple to implement and easy to parallelize. It applies to Turing-complete probabilistic programming languages and supports accurate inference in models that make use of complex control flow, including stochastic recursion. It also includes primitives from Bayesian nonparametric statistics. Our experiments show that this approach can be more efficient than previously introduced single-site Metropolis-Hastings methods.

Motivation & Objective

• To develop a scalable and efficient inference method for expressive probabilistic programming languages that support complex control flow and Bayesian nonparametric statistics.
• To enable accurate inference in models with stochastic recursion and intricate conditional dependencies, which are challenging for traditional MCMC methods.
• To improve computational efficiency over existing single-site Metropolis-Hastings samplers by leveraging particle-based MCMC techniques.
• To support practical inference in real-world models by enabling easy implementation and parallelization through repeated program simulation.

Proposed method

• The method employs particle Markov chain Monte Carlo (PMCMC), combining sequential Monte Carlo (SMC) with MCMC to explore execution traces of probabilistic programs.
• It uses a particle filter to propagate and resample execution traces, with the entire program re-executed for each particle to evaluate likelihoods.
• The approach supports both exchangeable and elementary random primitives, including nonparametric distributions like the Chinese restaurant process (CRP).
• It leverages the interpreted and later compiled versions of the Anglican probabilistic programming language to implement and evaluate the method.
• The inference engine is designed to be parallelizable, with particles executed independently across threads, though memory access patterns currently limit optimal parallelism.
• Programs are written in a Lisp/Scheme-like syntax with special forms for assume, observe, and predict, enabling trace-level observation and monitoring.

Experimental results

Research questions

• RQ1 Can PMCMC be effectively applied to Turing-complete probabilistic programs with complex control flow, such as stochastic recursion?
• RQ2 How does PMCMC performance compare to single-site Metropolis-Hastings in terms of convergence speed and computational efficiency?
• RQ3 To what extent does the ordering of program lines affect inference performance in PMCMC, and can this be exploited for optimization?
• RQ4 How does the number of particles in the SMC component influence the accuracy and efficiency of PMCMC inference?
• RQ5 Can PMCMC achieve faster convergence than RDB (rejection-based sampling) even when accounting for computational overhead?

Key findings

• PMCMC converges faster to the true conditional distribution than single-site Metropolis-Hastings methods, even after normalizing for computational cost.
• In the HMM model, PMCMC outperforms RDB when program lines are ordered to prioritize early observation, but performance degrades under adversarial ordering.
• For the DP Mixture model, PMCMC consistently outperforms RDB across all line permutations, indicating robustness to syntactic ordering.
• Increasing the number of particles improves inference performance, with significant gains observed from 100 to 500 particles in the experiments.
• Even with a single thread, PMCMC sometimes outperforms RDB in wall clock time, suggesting inherent efficiency advantages beyond parallelization.
• The method supports complex models with nonparametric priors and stochastic recursion, demonstrating its expressivity and practical applicability.