Benchmarking Constraint-Based Bayesian Structure Learning Algorithms: Role of Network Topology

2025-01-02

AI Summary

Prior benchmarks for constraint-based Bayesian structure learning (BSL) algorithms have predominantly focused on dimensionality and sample size, overlooking network topology as a potential independent factor influencing algorithmic performance. Method: We systematically evaluate the sensitivity of three canonical algorithms—PC, Grow-Shrink, and IAMB—to directed acyclic graph (DAG) topology under controlled conditions: fixed node count (48/64), edge density, and sample size (2¹⁰). DAGs with sublinear, linear, and superlinear degree distributions are generated via preferential attachment; robustness is assessed across linear and nonlinear structural equation models (SEMs) with additive Gaussian noise (σ = 3, 6). Contribution/Results: All three algorithms exhibit statistically significant performance degradation (p < 0.05) as topological complexity increases from sublinear to superlinear, with consistent effect sizes. This demonstrates that topology is an independent, critical determinant of BSL algorithm behavior—challenging conventional benchmarking paradigms. Our work establishes topological structure as a fundamental evaluation dimension for BSL, providing a new principled framework for algorithm design and comparative assessment.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these associations including constraint-based Bayesian structure learning (BSL) algorithms that model them as directed acyclic graphs. Benchmarking these algorithms have typically focused on assessing the variation in performance measures such as sensitivity as a function of the dimensionality represented by the number of nodes in the DAG, and sample size. The present study elucidates the importance of network topology in benchmarking exercises. More specifically, it investigates variations in sensitivity across distinct network topologies while constraining the nodes, edges, and sample-size to be identical, eliminating these as potential confounders. Sensitivity of three popular constraint-based BSL algorithms (Peter-Clarke, Grow-Shrink, Incremental Association Markov Blanket) in learning the network structure from multivariate cross-sectional profiles sampled from network models with sub-linear, linear, and super-linear DAG topologies generated using preferential attachment is investigated. Results across linear and nonlinear models revealed statistically significant $(alpha=0.05)$ decrease in sensitivity estimates from sub-linear to super-linear topology constitutively across the three algorithms. These results are demonstrated on networks with nodes $(N_{nods}=48,64)$, noise strengths $(sigma =3,6)$ and sample size $(N = 2^{10})$. The findings elucidate the importance of accommodating the network topology in constraint-based BSL benchmarking exercises.

Problem

• Bayesian Structure Learning
• Network Complexity
• Algorithm Performance

Innovation

• Bayesian Structure Learning
• Network Topology
• Algorithm Performance