Artificial intelligence often has to deal with uncertain scenarios, such as a partially observed environment or noisy observations. Traditional probabilistic models, while being very principled approaches in these contexts, are incapable of dealing with both algebraic and logical constraints. Existing hybrid continuous/discrete models are typically limited in expressivity, or do not offer any guarantee on the approximation errors.
This book, Learning and Reasoning in Hybrid Structured Spaces, discusses a recent and general formalism called Weighted Model Integration (WMI), which enables probabilistic modeling and inference in hybrid structured domains. WMI-based inference algorithms differ with respect to most alternatives in that probabilities are computed inside a structured support involving both logical and algebraic relationships between variables. While the research in this area is at an early stage, we are witnessing an increasing interest in the study and development of scalable inference procedures and effective learning algorithms in this setting.
This book details some of the most impactful contributions in context of WMI-based inference in the last 5 years. Moreover, by providing a gentle introduction to the main concepts related to WMI, the book can be useful for both theoretical researchers and practitioners alike.
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.
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