Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series
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Department of Statistics, University of Auckland, Auckland 1142, New Zealand
2
Department of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(1), 76; https://doi.org/10.3390/e20010076
Received: 8 December 2017
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Revised: 14 January 2018
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Accepted: 16 January 2018
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Published: 19 January 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the inverse of spectral density matrix. When applied to a given time series, the algorithm produces a set of candidate models. Various information theoretic (IT) criteria are employed for deciding the winner. A novel IT criterion, which is tailored to our model selection problem, is introduced. Some options for reducing the computational burden are proposed and tested via numerical examples. We conduct an empirical study in which the algorithm is compared with the state-of-the-art. The results are good, and the major advantage is that the subjective choices made by the user are less important than in the case of other methods.
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Keywords:
maximum entropy; Expectation-Maximization; graphical models; autoregressive model; latent variables; information theoretic criteria; time series
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MDPI and ACS Style
Maanan, S.; Dumitrescu, B.; Giurcăneanu, C.D. Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series. Entropy 2018, 20, 76. https://doi.org/10.3390/e20010076
AMA Style
Maanan S, Dumitrescu B, Giurcăneanu CD. Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series. Entropy. 2018; 20(1):76. https://doi.org/10.3390/e20010076
Chicago/Turabian StyleMaanan, Saïd, Bogdan Dumitrescu, and Ciprian D. Giurcăneanu. 2018. "Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series" Entropy 20, no. 1: 76. https://doi.org/10.3390/e20010076
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