Belief Updating and Learning in Semi-Qualitative Probabilistic Networks

TL;DR

This paper investigates semi-qualitative probabilistic networks, analyzing their computational complexity, and proposes methods for inference and learning that combine qualitative and quantitative information.

Contribution

It demonstrates the NPPP-Completeness of exact inference in SQPNs and introduces multilinear programming for qualitative reasoning and set-valued learning methods.

Findings

Exact inference in SQPNs is NPPP-Complete.

Multilinear programming effectively handles qualitative relations.

Bayesian learning with the Imprecise Dirichlet Model provides set-valued estimates.

Abstract

This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesian-minded method that employs the Imprecise Dirichlet Model to generate set-valued estimates.