A Novel Gaussian Sum Smoother for Approximate Inference in Switching Linear Dynamical Systems
David Barber and Bertrand Mesot
In: Advances in Neural Information Processing Systems NIPS 20, Dec 2006, Vancouver, Canada.
We introduce amethod 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 only
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. Unlike the alternative Expectation Propagation procedure, our
method consists only of a single forward and backward pass and is reminiscent
of the standard smoothing ‘correction’ recursions in the simpler linear dynamical
system. The algorithm performs well on both toy experiments and in a large scale
application to noise robust speech recognition.