Particle Filters, Variational methods and Importance Sampling

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at Machine Learning and Perception Group, Microsoft Research, Cambridge, U.K. on Mar 24, 2003
Neil D. Lawrence, University of Sheffield

Abstract

Particle filters allow tracking of systems with highly non-linear, multi-modal posterior distributions, however they are prone to failure when model likelihoods are sharply peaked or state spaces are high dimensional. This failure is caused by a mismatch between the proposal distribution and the true posterior. The number of particles of samples then required to accurately represent the posterior increases dramatically and with it the computational demands of the algorithm. By formulating the problem within the framework of variational inference we derive an algorithm in which the proposal naturally adapts to more accurately reflect the true posterior. This is achieved by replacing intractable moment evaluations, arising from the highly non-linear nature of the likelihood functions, with sample based approximations. In this talk we shall first introduce the approach in a static setting: Bayesian processing of cDNA microarray images. We will then add dynamics to the model and demonstrate a marked improvement over standard approaches on both synthetic and real-world tracking examples.