| |
The Variational Kalman
Smoother
Matthew J. Beal and Zoubin Ghahramani
Gatsby Computational Neuroscience Unit
GCNU TR 2001-003
Abstract
In this note we outline the derivation of the
variational Kalman smoother, in the context of Bayesian Linear Dynamical Systems.
The smoother is an ecient algorithm for the E-step in the Expectation-Maximisation
(EM) algorithm for linear-Gaussian state-space models. However, inference
approximations are required if we hold distributions over parameters. We derive the E-step
updates for the hidden states (the variational smoother), and the M-step updates for the
parameter distributions. We show that inference of the hidden state is tractable for any
distribution over parameters, provided the expectations of certain quantities are
available, analytically or otherwise.
Download: [ps.gz] or [pdf]
last revision 6 April 2001
|