[Paper Review] Particle Gibbs with Ancestor Sampling for Probabilistic Programs

Jan-Willem van de Meent, Hongseok Yang+2 more|arXiv (Cornell University)|Jan 27, 2015

Bayesian Modeling and Causal Inference7 references15 citations

TL;DR

This paper introduces Particle Gibbs with Ancestor Sampling (PGAS) adapted for probabilistic programming, enabling efficient posterior inference in complex models with early-sampled variables. By combining prefix and suffix execution histories via a formalized resampling mechanism, PGAS achieves significantly higher effective sample sizes and faster convergence than standard particle MCMC, even with fewer particles, due to improved mixing for variables generated early in program execution.

ABSTRACT

Particle Markov chain Monte Carlo techniques rank among current state-of-the-art methods for probabilistic program inference. A drawback of these techniques is that they rely on importance resampling, which results in degenerate particle trajectories and a low effective sample size for variables sampled early in a program. We here develop a formalism to adapt ancestor resampling, a technique that mitigates particle degeneracy, to the probabilistic programming setting. We present empirical results that demonstrate nontrivial performance gains.

Motivation & Objective

• To address particle degeneracy in particle MCMC methods for probabilistic programs, especially for variables sampled early in execution.
• To extend ancestor sampling—a technique that improves mixing in particle Gibbs—to higher-order, recursive, and memoized probabilistic programs.
• To develop a formalism for safely merging execution prefixes and suffixes while preserving correct probabilities and avoiding redundant recomputation.
• To empirically evaluate PGAS against standard particle MCMC (ICSMC) in terms of statistical efficiency and computational cost.
• To demonstrate that PGAS can outperform ICSMC in effective sample size and convergence speed, even with a small number of particles.

Proposed method

• Proposes a formalism for traced execution that tracks upstream dependencies to enable consistent regeneration of particle trajectories.
• Introduces a mechanism to combine a partial execution prefix with a previously completed suffix, ensuring correct probability updates and state consistency.
• Uses ancestor resampling to mitigate particle degeneracy by reweighting trajectories based on ancestry, improving mixing for early variables.
• Employs a traced evaluation strategy that avoids full re-execution of the suffix by reusing existing computation where possible.
• Implements a hybrid approach combining SMC for proposal generation and MCMC for refinement, enhancing mixing compared to standard SMC or MH.
• Applies the method within a probabilistic programming framework supporting recursion, higher-order functions, and memoization.

Experimental results

Research questions

• RQ1 Can ancestor sampling be effectively adapted to probabilistic programs with dynamic structure, recursion, and memoization?
• RQ2 Does PGAS improve mixing for variables sampled early in a program compared to standard particle MCMC methods like ICSMC?
• RQ3 Can PGAS achieve higher effective sample sizes with fewer particles than ICSMC, despite increased computational cost per sweep?
• RQ4 How does the computational cost of PGAS compare to ICSMC when normalized by statistical efficiency (e.g., ESS per unit time)?
• RQ5 Can the traced execution formalism avoid unnecessary recomputation while maintaining correctness in complex program structures?

Key findings

• PGAS achieves a stable effective sample size (ESS) across all time steps, while ICSMC shows a sharp decline in ESS for early-sampled variables, indicating poor mixing.
• With only 10 particles, PGAS matches the ESS performance of ICSMC with 500 particles for estimating the parameter q, demonstrating superior statistical efficiency.
• The standard deviation of posterior estimates for ω and q converges faster under PGAS than under ICSMC, indicating better convergence per sweep.
• Despite higher computational cost per sweep, PGAS achieves better effective sample size per unit time for state estimates below t ≈ 50, indicating net performance gains.
• The ESS of PGAS fluctuates by approximately 15% across independent runs, suggesting sensitivity to prior probabilities of latent transitions, but remains consistently higher than ICSMC for early times.
• The formalism successfully avoids unnecessary recomputation during regeneration by tracking upstream dependencies, reducing computational overhead compared to naive re-execution.