Learning Bayesian and Markov Networks with an Unreliable Oracle

2026-03-10

AI Summary

This study addresses the problem of reliably learning the structures of Markov networks and Bayesian networks when conditional independence tests are subject to bounded errors. The work proposes a fault-tolerant structure learning algorithm based on graph-theoretic analysis and constraint satisfaction, tailored for an independence oracle that may err but with a limited number of mistakes. The main contributions include establishing that Markov networks remain robustly identifiable under exponentially many errors when the number of vertex-disjoint paths is bounded, while demonstrating that Bayesian networks cannot tolerate arbitrary errors even under structural constraints such as bounded treewidth. Furthermore, under conditions ensuring unique identifiability, the paper provides an efficient learning algorithm for Markov networks and establishes their theoretical identifiability in the presence of numerous errors for specific graph structures.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

We study constraint-based structure learning of Markov networks and Bayesian networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For Markov networks, we observe that a low maximum number of vertex-wise disjoint paths implies that the structure is uniquely identifiable even if the number of errors is (moderately) exponential in the number of vertices. For Bayesian networks, however, we prove that one cannot tolerate any errors to always identify the structure even when many commonly used graph parameters like treewidth are bounded. Finally, we give algorithms for structure learning when the structure is uniquely identifiable.

Problem

• Bayesian Networks
• Markov Networks
• Structure Learning
• Conditional Independence Oracle
• Unreliable Oracle

Innovation

• structure learning
• unreliable oracle
• Markov networks
• Bayesian networks
• conditional independence