Inference with Seperately Specified Sets of Probabilities in Credal Networks

TL;DR

This paper introduces new algorithms for inference in credal networks, which are graphical models with sets of probabilities, focusing on reducing computational complexity especially in polytrees.

Contribution

The paper develops a theory of credal networks with separately specified probability sets and proposes techniques to improve inference efficiency, notably in polytrees.

Findings

Inference with credal networks is NP-hard in polytrees.

New algorithms exploit separability of credal sets to reduce computational effort.

Theoretical framework for credal networks based on strong independence relations.

Abstract

We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a theory of credal networks based on separately specified sets of probabilities. We also show that inference with polytrees is NP-hard in this setting. We then introduce new techniques that reduce the computational effort demanded by inference, particularly in polytrees, by exploring separability of credal sets.