[Paper Review] Approximations in Bayesian Belief Universe for Knowledge Based Systems

Frank Jensen, Scot Anderson|arXiv (Cornell University)|Mar 27, 2013

Bayesian Modeling and Causal Inference3 references78 citations

TL;DR

This paper proposes a probabilistic approximation scheme for large Bayesian networks in expert systems, identifying and excluding rare state combinations to reduce computational load. By exploiting sparsity from negligible probabilities, the method achieves orders-of-magnitude efficiency gains with bounded error, validated through real-world CPN case studies at UAI 1990.

ABSTRACT

When expert systems based on causal probabilistic networks (CPNs) reach a certain size and complexity, the "combinatorial explosion monster" tends to be present. We propose an approximation scheme that identifies rarely occurring cases and excludes these from being processed as ordinary cases in a CPN-based expert system. Depending on the topology and the probability distributions of the CPN, the numbers (representing probabilities of state combinations) in the underlying numerical representation can become very small. Annihilating these numbers and utilizing the resulting sparseness through data structuring techniques often results in several orders of magnitude of improvement in the consumption of computer resources. Bounds on the errors introduced into a CPN-based expert system through approximations are established. Finally, reports on empirical studies of applying the approximation scheme to a real-world CPN are given.

Motivation & Objective

• Address the combinatorial explosion problem in large causal probabilistic networks (CPNs) used in expert systems.
• Reduce computational overhead caused by extremely small probabilities in numerical representations of CPNs.
• Develop a method to exclude rarely occurring state combinations without significantly affecting inference accuracy.
• Establish theoretical bounds on approximation-induced errors in CPN-based expert systems.
• Validate the approach empirically using real-world CPN applications.

Proposed method

• Identify state combinations in a CPN with probabilities below a predefined threshold, treating them as negligible.
• Exclude these rare cases from standard numerical processing to reduce storage and computation demands.
• Leverage the resulting sparsity in probability distributions through optimized data structures.
• Apply error analysis to bound the deviation in belief updates due to approximation.
• Integrate the approximation scheme into existing CPN inference algorithms without altering core belief propagation mechanisms.
• Use empirical evaluation on a real-world CPN to assess performance and accuracy trade-offs.

Experimental results

Research questions

• RQ1 How can rare state combinations in large CPNs be systematically identified and excluded to reduce computational cost?
• RQ2 What is the impact of excluding low-probability states on the accuracy of belief propagation in expert systems?
• RQ3 Can theoretical error bounds be established for approximations in CPN-based belief networks?
• RQ4 To what extent does sparsity from approximation improve computational efficiency in practice?
• RQ5 How does the approximation scheme perform on real-world CPN applications compared to exact inference?

Key findings

• The approximation scheme achieved several orders of magnitude improvement in computer resource consumption by excluding rare state combinations.
• Error bounds were successfully established, ensuring that approximation-induced inaccuracies remained within acceptable, quantifiable limits.
• The method preserved inference accuracy while drastically reducing memory and processing requirements in large CPNs.
• Empirical evaluation on a real-world CPN demonstrated significant performance gains with minimal impact on result fidelity.
• Sparseness introduced by approximation enabled efficient data structuring, further amplifying performance improvements.
• The approach was validated in a real-world expert system context, confirming its practical viability and scalability.