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Aggregation and constraint processing in lifted probabilistic inference Kisynski, Jacek Jerzy


Representations that mix graphical models and first-order logic - called either first-order or relational probabilistic models — were proposed nearly twenty years ago and many more have since emerged. In these models, random variables are parameterized by logical variables. One way to perform inference in first-order models is to propositionalize the model, that is, to explicitly consider every element from the domains of logical variables. This approach might be intractable even for simple first-order models. The idea behind lifted inference is to carry out as much inference as possible without propositionalizing. An exact lifted inference procedure for first-order probabilistic models was developed by Poole [2003] and later extended to a broader range of problems by de Salvo Braz et al. [2007]. The C-FOVE algorithm by Milch et al. [2008] expanded the scope of lifted inference and is currently the state of the art in exact lifted inference. In this thesis we address two problems related to lifted inference: aggregation in directed first-order probabilistic models and constraint processing during lifted inference. Recent work on exact lifted inference focused on undirected models. Directed first-order probabilistic models require an aggregation operator when a parent random variable is parameterized by logical variables that are not present in a child random variable. We introduce a new data structure, aggregation parfactors, to describe aggregation in directed first-order models. We show how to extend the C-FOVE algorithm to perform lifted inference in the presence of aggregation parfactors. There are cases where the polynomial time complexity (in the domain size of logical variables) of the C-FOVE algorithm can be reduced to logarithmic time complexity using aggregation parfactors. First-order models typically contain constraints on logical variables. Constraints are important for capturing knowledge regarding particular individuals. However, the impact of constraint processing on computational efficiency of lifted inference has been largely overlooked. In this thesis we develop an efficient algorithm for counting the number of solutions to the constraint satisfaction problems encountered during lifted inference. We also compare, both theoretically and empirically, different ways of handling constraints during lifted inference.

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