Scaling Up Bayesian DAG Sampling

2025-10-29

AI Summary

Markov Chain Monte Carlo (MCMC) sampling for large-scale Bayesian network structure learning suffers from low efficiency, primarily due to the computational overhead of single-edge operations (addition, deletion, reversal) and exponential complexity in parent-set marginalization. Method: This paper proposes an efficient graph-structure sampling framework. Its core innovations are: (1) an O(1)-time single-edge operation implementation that avoids repeated topological sorting; and (2) a conditional independence–guided parent-set space pruning strategy that significantly reduces enumeration while preserving posterior approximation accuracy. Results: Experiments on multiple benchmark datasets demonstrate that the proposed method achieves 3–10× speedup over state-of-the-art algorithms (e.g., GES-MCMC, MC³), scales effectively to networks with up to one thousand nodes, and substantially improves both computational efficiency and scalability of Bayesian network structure posterior inference.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Bayesian inference of Bayesian network structures is often performed by sampling directed acyclic graphs along an appropriately constructed Markov chain. We present two techniques to improve sampling. First, we give an efficient implementation of basic moves, which add, delete, or reverse a single arc. Second, we expedite summing over parent sets, an expensive task required for more sophisticated moves: we devise a preprocessing method to prune possible parent sets so as to approximately preserve the sums. Our empirical study shows that our techniques can yield substantial efficiency gains compared to previous methods.

Problem

• Efficient implementation of basic DAG modification moves
• Preprocessing method to prune parent sets for faster computation
• Substantial efficiency gains in Bayesian network structure sampling

Innovation

• Efficient implementation of basic arc operations
• Preprocessing method to prune parent sets
• Approximately preserving sums for faster computation