On Continuous Distributions and Parameter Estima- tion in Probabilistic Logic Programs

In the last decade remarkable progress has been made on combining statistical machine learning techniques, reasoning under uncertainty, and relational representations. The branch of Artificial Intelligence working on the synthesis of these three areas is known as statistical relational learning or probabilistic logic learning. ProbLog, one of the probabilistic frameworks developed, is an extension of the logic programming language Prolog with independent random variables that are defined by annotating logical facts with probabilities. The separation of the logical and probabilistic part of the model is based on the distribution semantics. Driven by the demand for models that are able to handle continuous values and can be automatically optimized on training data, this thesis introduces several algorithms and extensions to the ProbLog language. Continuous-valued data arise naturally in robotics, human activity recognition and bio-medical applications. Moreover, the models used are complex and the available data is often noisy and incomplete. Hence tuning a model towards the specifics of the environment can hardly be done manually. This poses two crucial challenges for probabilistic programming languages such as ProbLog: processing continuous values and being able to learn from training data. This thesis makes four main contributions to the field of probabilistic logic learning. Hybrid ProbLog is an extension for ProbLog with continuous facts that allows for exact inference. Distributional Programs combine elements of ProbLog, Hybrid ProbLog and CP-Logic into a very expressive language for dealing with continuous distributions. A sampling-based inference algorithm is used to answer conditional queries, while the deterministic information in the program guides the sampling process. LFE-ProbLog is able to learn the parameters of a ProbLog program from queries and proofs, while LFI-ProbLog is optimized to learn the parameters from partial interpretations. Together they cover the standard learning settings considered in PLL. All learning approaches have been evaluated in several relational real-world domains.