The Complexity of Bayesian Networks Specified by Propositional and Relational Languages

TL;DR

This paper analyzes the computational complexity of inference in Bayesian networks specified by various logical languages, covering propositional to first-order logic, and explores implications for probabilistic databases.

Contribution

It characterizes the complexity of inference across different logical representations and input scenarios, linking results to probabilistic databases and liftability.

Findings

Complexity ranges from polynomial to exponential depending on the logic and input scenario.

Connections established between Bayesian network inference and probabilistic database complexity.

Provides a comprehensive classification of inference complexity for logical Bayesian network representations.

Abstract

We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover a variety of plate models and of probabilistic relational models. We study the complexity of inferences when network, query and domain are the input (the inferential and the combined complexity), when the network is fixed and query and domain are the input (the query/data complexity), and when the network and query are fixed and the domain is the input (the domain complexity). We draw connections with probabilistic databases and liftability results, and obtain complexity classes that range from polynomial to exponential levels.