Nonparametric belief propagation

Continuous quantities are ubiquitous in models of real-world phenomena, but are surprisingly difficult to reason about automatically. Probabilistic graphical models such as Bayesian networks and Markov random fields, and algorithms for approximate inference such as belief propagation (BP), have proven to be powerful tools in a wide range of applications in statistics and artificial intelligence. However, applying these methods to models with continuous variables remains a challenging task. In this work we describe an extension of BP to continuous variable models, generalizing particle filtering, and Gaussian mixture filtering techniques for time series to more complex models. We illustrate the power of the resulting nonparametric BP algorithm via two applications: kinematic tracking of visual motion and distributed localization in sensor networks.