PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Expectation Correction for smoothing in Switching Linear Gaussian State Space models
David Barber
Journal of Machine Learning Research Volume 7, pp. 2515-2540, 2005. ISSN 1533-7928

Abstract

We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman ‘Filter’ and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard Kim smoothing approach by dispensing with one of the key approximations, thus making fuller use of the available future information. Whilst the central assumption required is projection to a mixture of Gaussians, we show that an additional conditional independence assumption results in a simpler but accurate alternative. Our method consists of a single Forward and Backward Pass and is reminiscent of the standard smoothing ‘correction’ recursions in the simpler linear dynamical system. The method is numerically stable and compares favourably against alternative approximations, both in cases where a single mixture component provides a good posterior approximation, and where a multimodal approximation is required. Keywords: Gaussian sum smoother, switching Kalman filter, switching linear dynamical system, expectation propagation, expectation correction

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3795
Deposited By:David Barber
Deposited On:25 February 2008