Variational message-passing: extension to continuous variables and applications in multi-target tracking

This dissertation focuses on both the application and development of variational inference algorithms for probabilistic graphical models. First, we propose a new application of graphical models and approximate inference in the multi-target tracking domain. By constructing a factor graph representation of the track-oriented multiple hypothesis tracker, we enable the application of variational inference algorithms to efficiently estimate marginal probabilities of possible tracks. We then show that these track marginals are the key ingredient in a multi-target generalization of the standard expectation-maximization algorithm used for parameter estimation in single-target tracking. The resulting online estimation algorithm makes the tracker robust to parameter misspecification and can improve performance in settings with non-stationary target dynamics. Next, we develop a general framework to extend algorithms for approximate marginalization in discrete systems to work with continuous-valued graphical models. We extend the particle belief propagation algorithm, which uses importance sampling to lift the sum and product operations of belief propagation from a variable's continuous domain into an importance-reweighted particle domain. We demonstrate that this framework admits other variational inference algorithms such as mean field and tree-reweighted belief propagation, and that they confer similar qualitative benefits to continuous-valued models as in the discrete domain.