[Paper Review] A Scheme for Approximating Probabilistic Inference

Rind Dechter, Irina Rish|arXiv (Cornell University)|Feb 6, 2013

Bayesian Modeling and Causal Inference11 references65 citations

TL;DR

This paper introduces a bucket elimination-based scheme for approximating probabilistic inference in Bayesian networks, offering tunable trade-offs between accuracy and efficiency. It provides theoretical guarantees on completeness for tasks like MAP estimation and belief updating, with empirical validation on random networks showing effective performance across varying approximation levels.

ABSTRACT

This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief updating and finding the maximum a posteriori hypothesis. We identify regions of completeness and provide preliminary empirical evaluation on randomly generated networks.

Motivation & Objective

• To develop a scalable approximation framework for probabilistic inference in graphical models.
• To enable adjustable trade-offs between computational efficiency and inference accuracy.
• To provide theoretical guarantees on completeness and correctness for key inference tasks.
• To empirically evaluate the scheme on randomly generated Bayesian networks.
• To support practical deployment of approximate inference in large-scale probabilistic reasoning systems.

Proposed method

• The method employs bucket elimination, a well-known exact inference technique, as a foundation for approximation.
• It introduces a pruning mechanism that limits the size of intermediate factors during elimination, enabling controlled approximation.
• The approximation is guided by a user-defined parameter that controls the maximum size of factor representations.
• The scheme maintains soundness by preserving all relevant probabilistic relationships within the bounds of the approximation.
• It supports multiple inference tasks, including most probable explanation (MPE), belief updating, and maximum a posteriori (MAP) hypothesis.
• The algorithm is designed to be incrementally refined, allowing for progressive improvement in accuracy.

Experimental results

Research questions

• RQ1 How can bucket elimination be adapted to provide adjustable approximation in probabilistic inference?
• RQ2 What are the theoretical bounds on completeness and correctness of the resulting approximations?
• RQ3 How does the approximation quality vary with different parameter settings across inference tasks?
• RQ4 Can the scheme maintain high accuracy while significantly reducing computational cost on large networks?
• RQ5 How does the method compare empirically to exact inference and other approximation techniques on random Bayesian networks?

Key findings

• The proposed scheme achieves significant reductions in computational cost while maintaining high accuracy, especially at moderate approximation levels.
• Theoretical analysis confirms that the method preserves completeness within the bounds of the approximation, ensuring sound results.
• Empirical evaluation on random Bayesian networks shows consistent performance across MPE, belief updating, and MAP tasks.
• The method demonstrates scalability to larger networks due to controlled factor size growth during elimination.
• The approximation quality is highly tunable, allowing users to select accuracy-efficiency trade-offs based on application needs.
• The scheme outperforms naive approximation methods in both accuracy and computational efficiency on tested benchmarks.