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Neural Computation

April 2007, Vol. 19, No. 4, Pages 1097-1111
(doi: 10.1162/neco.2007.19.4.1097)
© 2007 Massachusetts Institute of Technology
State-Space Models: From the EM Algorithm to a Gradient Approach
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Slow convergence is observed in the EM algorithm for linear state-space models. We propose to circumvent the problem by applying any off-the-shelf quasi-Newton-type optimizer, which operates on the gradient of the log-likelihood function. Such an algorithm is a practical alternative due to the fact that the exact gradient of the log-likelihood function can be computed by recycling components of the expectation-maximization (EM) algorithm. We demonstrate the efficiency of the proposed method in three relevant instances of the linear state-space model. In high signal-to-noise ratios, where EM is particularly prone to converge slowly, we show that gradient-based learning results in a sizable reduction of computation time.