| Summary: | The central objective of this thesis is to develop new algorithms for inference in probabilistic graphical models that improve upon the state-of-the-art and lend new insight into the computational nature of probabilistic inference. The four main technical contributions of this thesis are: 1) a new framework for inference in probabilistic models based on stochastic approximation, variational methods and sequential Monte Carlo is proposed that achieves significant improvements in accuracy and reductions in variance over existing Monte Carlo and variational methods, and at a comparable computational expense, 2) for many instances of the proposed approach to probabilistic inference, constraints must be imposed on the parameters, so I describe a new stochastic approximation algorithm that adopts the methodology of primal-dual interior-point methods and handles constrained optimization problems much more robustly than existing approaches, 3) a new class of conditionally-specified variational approximations based on mean field theory is described, which, when combined with sequential Monte Carlo, overcome some of the limitations imposed by conventional variational mean field approximations, and 4) I show how recent advances in variational inference can be used to implement inference and learning in a novel contingently acyclic probabilistic relational model, a model developed for the purpose of making predictions about relationships in a social network.
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