Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series
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....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-01-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/20/1/76 |
| _version_ | 1828109882885144576 |
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| author | Saïd Maanan Bogdan Dumitrescu Ciprian Doru Giurcăneanu |
| author_facet | Saïd Maanan Bogdan Dumitrescu Ciprian Doru Giurcăneanu |
| author_sort | Saïd Maanan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:11:14Z |
| format | Article |
| id | doaj.art-e4b13367850645418b95de4951ad875c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T11:11:14Z |
| publishDate | 2018-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e4b13367850645418b95de4951ad875c2022-12-22T04:27:29ZengMDPI AGEntropy1099-43002018-01-012017610.3390/e20010076e20010076Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time SeriesSaïd Maanan0Bogdan Dumitrescu1Ciprian Doru Giurcăneanu2Department of Statistics, University of Auckland, Auckland 1142, New ZealandDepartment of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Statistics, University of Auckland, Auckland 1142, New ZealandThis 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.http://www.mdpi.com/1099-4300/20/1/76maximum entropyExpectation-Maximizationgraphical modelsautoregressive modellatent variablesinformation theoretic criteriatime series |
| spellingShingle | Saïd Maanan Bogdan Dumitrescu Ciprian Doru Giurcăneanu Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series Entropy maximum entropy Expectation-Maximization graphical models autoregressive model latent variables information theoretic criteria time series |
| title | Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series |
| title_full | Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series |
| title_fullStr | Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series |
| title_full_unstemmed | Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series |
| title_short | Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series |
| title_sort | maximum entropy expectation maximization algorithm for fitting latent variable graphical models to multivariate time series |
| topic | maximum entropy Expectation-Maximization graphical models autoregressive model latent variables information theoretic criteria time series |
| url | http://www.mdpi.com/1099-4300/20/1/76 |
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