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September 2013 Learning local directed acyclic graphs based on multivariate time series data
Wanlu Deng, Zhi Geng, Hongzhe Li
Ann. Appl. Stat. 7(3): 1663-1683 (September 2013). DOI: 10.1214/13-AOAS635

Abstract

Multivariate time series (MTS) data such as time course gene expression data in genomics are often collected to study the dynamic nature of the systems. These data provide important information about the causal dependency among a set of random variables. In this paper, we introduce a computationally efficient algorithm to learn directed acyclic graphs (DAGs) based on MTS data, focusing on learning the local structure of a given target variable. Our algorithm is based on learning all parents (P), all children (C) and some descendants (D) (PCD) iteratively, utilizing the time order of the variables to orient the edges. This time series PCD-PCD algorithm (tsPCD-PCD) extends the previous PCD-PCD algorithm to dependent observations and utilizes composite likelihood ratio tests (CLRTs) for testing the conditional independence. We present the asymptotic distribution of the CLRT statistic and show that the tsPCD-PCD is guaranteed to recover the true DAG structure when the faithfulness condition holds and the tests correctly reject the null hypotheses. Simulation studies show that the CLRTs are valid and perform well even when the sample sizes are small. In addition, the tsPCD-PCD algorithm outperforms the PCD-PCD algorithm in recovering the local graph structures. We illustrate the algorithm by analyzing a time course gene expression data related to mouse T-cell activation.

Citation

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Wanlu Deng. Zhi Geng. Hongzhe Li. "Learning local directed acyclic graphs based on multivariate time series data." Ann. Appl. Stat. 7 (3) 1663 - 1683, September 2013. https://doi.org/10.1214/13-AOAS635

Information

Published: September 2013
First available in Project Euclid: 3 October 2013

zbMATH: 06237192
MathSciNet: MR3127963
Digital Object Identifier: 10.1214/13-AOAS635

Keywords: Bayesian network , composite likelihood ratio test , genetic network , PCD-PCD algorithm

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 3 • September 2013
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