Belief Updating and Learning in Semi-Qualitative Probabilistic Networks
This work addresses computational and learning challenges in probabilistic networks for domains requiring mixed information, but it appears incremental as it builds on existing qualitative and probabilistic frameworks.
The paper tackles the problem of performing exact inference and learning in semi-qualitative probabilistic networks (SQPNs), which combine numeric and qualitative information, by showing that exact inferences are NPPP-Complete and proposing methods using multilinear programming and maximum likelihood or Bayesian approaches to handle qualitative relations and generate estimates.
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.