Hybrid Probabilistic Logic Programming: Inference and Learning
It addresses the problem of modeling uncertainty and relations in hybrid data for AI applications, though it appears incremental by building on existing PLP frameworks.
This thesis tackled the challenge of extending probabilistic logic programming (PLP) to handle both discrete and continuous variables for applications with numeric data, resulting in the introduction of new algorithms like CS-LW and FO-CS-LW for scalable inference and DiceML for learning hybrid PLP from relational data with missing values.
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.