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Applied Mathematics and Computation, Volume 241, 2014, Pages 222–232.
Wolfgang Mader1, 2, Yannick Linke1, 2, Malenka Mader1,2,3, Linda Sommerlade4, Jens Timmer1,2, Björn Schelter4.
- Institute for Physics, University of Freiburg, Germany and
- Freiburg Centre for Data Analysis and Modeling (FDM), University of Freiburg, Germany and
- Department of Neuropediatrics and Muscular Disease, University Medical Center of Freiburg, Germany and
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, UK
Abstract
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.
Significance statement:
The expectation maximization (EM) algorithm is a tool to reliably estimate parameters in the linear state space model. Exploiting the assumption that data is stationary on the time scale of the observation, we present run-time optimizations to alleviate the high computational demand of the approach. The source code accompanying the publication has evolved into a shared C++ library featuring python bindings, and is now hosted on github (https://github.com/ReedWood/fdmb).
