A New Approach to Probabilistic Programming Inference (1507.00996v2)

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.

• The paper proposes a novel PMCMC method that integrates Particle filters with MCMC to efficiently sample execution traces in probabilistic programs.
• It demonstrates significant efficiency gains, including up to 100x speed improvements over earlier interpreted versions in the Anglican system.
• The approach enables robust multivariate updates in models with complex dependencies, laying the groundwork for further parallel and algorithmic advancements.

Overview of "A New Approach to Probabilistic Programming Inference"

The paper presents a novel method for probabilistic programming inference using Particle Markov Chain Monte Carlo (PMCMC) techniques. Traditionally, inference in probabilistic programming involves characterizing the conditional distribution of variables within a probabilistic model given certain observed data. This paper leverages PMCMC—an approach combining Markov chain sampling strategies with particle filters—to effectively sample and characterize execution traces in a Turing-complete probabilistic programming language, particularly the Anglican system.

Key Contributions:

1. Integration with Probabilistic Programming: The authors propose using PMCMC to explore probabilistic programs' execution traces, offering a method easily implementable and parallelizable. This integration supports rigorous inference in models utilizing complex control flows or nonparametric Bayesian statistics, overcoming limitations of earlier inference methods like single-site Metropolis-Hastings (MH) sampling.
2. Language Evolution: This work was originally demonstrated on an interpreted variant of Anglican with a now-deprecated syntax resembling Scheme/Lisp. Since then, the language has evolved to a compiled version using Clojure-style syntax, offering significantly increased performance—achieving speeds up to a hundredfold faster than the interpreted predecessor.
3. Algorithmic Development: PMCMC, particularly in the version of Particle-Gibbs (PG) presented, offers a robust sampling technique with potentially higher efficacy and efficiency than traditional MH methods. Notably, PMCMC facilitates multivariate updates, enhancing its performance on models with dense conditional dependencies and expressive probabilistic structures.

Experimental Results:

To validate the approach, the authors conduct comprehensive experiments comparing PMCMC to a traditional random database (RDB) MH sampling method across various test scenarios including a Hidden Markov Model (HMM), a Dirichlet Process (DP) Gaussian Mixture, and models with deterministic branching and recursion. Results indicate quicker convergence and superior inference accuracy of PMCMC, particularly in complex model scenarios.

Implications and Future Directions:

The research showcases PMCMC's potential in improving inference within probabilistic programming environments, suggesting several implications:

• Increased Efficiency for Complex Models: PMCMC's ability to handle models with intricate dependency structures more efficiently than existing methods highlights its utility in real-world probabilistic program applications needing fine-grained analysis over large parameter spaces.
• Parallelization Opportunities: Although PMCMC already shows promise as a single-threaded approach, the algorithm's inherent parallel-friendly nature hints at further performance gains achievable through optimized multi-threaded implementations.
• Program Structuring Influence: The authors demonstrate that program structuring (e.g., the order of observe statements) affects PMCMC efficiency, pointing towards possible methodologies for automatic restructuring that could further enhance inference efficacy.

Speculation on Future AI Developments:

The application of PMCMC within probabilistic programming languages like Anglican may pave the way for more sophisticated AI systems capable of performing advanced statistical inference on complex, real-world data distributions. There may also be scope for hybrid methods, incorporating PMCMC with other algorithms for even more robust inference performance.

In conclusion, this paper contributes a significant advancement in the field of probabilistic programming by introducing PMCMC as a viable and efficient inference mechanism. This work provides a foundation for further exploration into how particle methods can enhance computational tasks within AI research and beyond.