HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Ghahramani, Z. Articles by Hinton, G. E. Search for Related Content PubMed PubMed Citation Articles by Ghahramani, Z. Articles by Hinton, G. E.

Variational Learning for Switching State-Space Models

Gatsby Computational Neuroscience Unit, University College London, London WC1N 3AR, U.K.

Geoffrey E. Hinton

Gatsby Computational Neuroscience Unit, University College London, London WC1N 3AR, U.K.

We introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time-series models—hidden Markov models and linear dynamical systems—and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs, Jordan, Nowlan, & Hinton, 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact expectation maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log-likelihood and makes use of both the forward and backward recursions for hidden Markov models and the Kalman filter recursions for linear dynamical systems. We tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

This article has been cited by other articles:

				E. MCDERMOTT and A. NAKAMURA Production-Oriented Models for Speech Recognition IEICE Trans D: Information, March 1, 2006; E89-D(3): 1006 - 1014. [Abstract] [PDF]