A numerically efficient implementation of the expectation maximization algorithm for state space models

Empirical time series are subject to observational noise. Naïve approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error-in-variables challenge. State space models (SSM) explicitly include observational noise. Applying the expectation maximiza...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 241; pp. 222 - 232
Main Authors Mader, Wolfgang, Linke, Yannick, Mader, Malenka, Sommerlade, Linda, Timmer, Jens, Schelter, Björn
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2014
Subjects
Algorithms
Computation
Estimates
Expectation–maximization algorithm
Kalman filter
Mathematical models
Maximization
Noise
Parameter estimation
State space models
State-space model
Time series
Parameter estimation
Expectation–maximization algorithm
State-space model
Kalman filter
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Summary:Empirical time series are subject to observational noise. Naïve approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error-in-variables challenge. State space models (SSM) explicitly include observational noise. Applying the expectation maximization (EM) algorithm together with the Kalman filter constitute a robust iterative procedure to estimate model parameters in the SSM as well as an approach to denoise the signal. The EM algorithm provides maximum likelihood parameter estimates at convergence. The drawback of this approach is its high computational demand. Here, we present an optimized implementation and demonstrate its superior performance to naïve algorithms or implementations.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.05.021