Hybrid Probabilistic Logic Programming: Inference and Learning

TL;DR

This thesis advances probabilistic logic programming by supporting both discrete and continuous variables, introducing new algorithms for inference and learning, and addressing relational data with missing values.

Contribution

It introduces context-specific likelihood weighting, a hybrid PLP framework DC# integrating various independencies, and DiceML for learning from relational data with missing values.

Findings

CS-LW improves sampling efficiency in PLP.

DC# effectively models multiple types of independencies.

DiceML successfully learns hybrid PLP structures from incomplete data.

Abstract

This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random variables, which is necessary for applications with numeric data. The first contribution is the introduction of context-specific likelihood weighting (CS-LW), a new sampling algorithm that exploits context-specific independencies for computational gains. Next, a new hybrid PLP, DC#, is introduced, which integrates the syntax of Distributional Clauses with Bayesian logic programs and represents three types of independencies: i) conditional independencies (CIs) modeled in Bayesian networks; ii) context-specific independencies (CSIs) represented by logical rules, and iii) independencies amongst attributes of related objects in relational models expressed by combining rules. The scalable inference algorithm FO-CS-LW is introduced for DC#. Finally, the thesis addresses the lack of approaches for learning hybrid PLP from relational data with missing values and (probabilistic) background knowledge with the introduction of DiceML, which learns the structure and parameters of hybrid PLP and tackles the relational autocompletion problem. The conclusion discusses future directions and open challenges for hybrid PLP.