Learning and Reasoning in Hybrid Structured Spaces

Many real world AI applications involve reasoning on both continuous and discrete variables, while requiring some level of symbolic reasoning that can provide guarantees on the system's behaviour. Unfortunately, most of the existing probabilistic models do not efficiently support hard constraints or they are limited to purely discrete or continuous scenarios. Weighted Model Integration (WMI) is a recent and general formalism that enables probabilistic modeling and inference in hybrid structured domains. A difference of WMI-based inference algorithms with respect to most alternatives is that probabilities are computed inside a structured support involving both logical and algebraic relationships between variables. While some progress has been made in the last years and the topic is increasingly gaining interest from the community, research in this area is at an early stage. These aspects motivate the study of hybrid and symbolic probabilistic models and the development of scalable inference procedures and effective learning algorithms in these domains. This PhD Thesis embodies my effort in studying scalable reasoning and learning techniques in the context of WMI.