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State-Space Models: From the EM Algorithm to a Gradient Approach

rko{at}imm.dtu.dk

Kaare Brandt Petersen

kbp{at}epital.dk

Tue Lehn-Schiøler

tls{at}imm.dtu.dk Technical University of Denmark, 2800 Kongens Lyngby, Denmark

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.