Learning Bayesian and Markov Networks with an Unreliable Oracle

TL;DR

This paper investigates the robustness of structure learning algorithms for Bayesian and Markov networks when the independence oracle is unreliable, revealing conditions for identifiability and providing algorithms under certain assumptions.

Contribution

It introduces new theoretical insights into the conditions under which network structures can be learned reliably despite oracle errors and proposes algorithms for such scenarios.

Findings

Markov networks can be uniquely identified with bounded oracle errors under certain path conditions.

Bayesian networks cannot tolerate any errors for guaranteed structure identification.

Algorithms are provided for structure learning when the network structure is identifiable.

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.