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This article is part of the supplement: The 2010 International Conference on Bioinformatics and Computational Biology (BIOCOMP 2010): Systems Biology

Open Access Open Badges Research article

State Space Model with hidden variables for reconstruction of gene regulatory networks

Xi Wu1, Peng Li2, Nan Wang1, Ping Gong3, Edward J Perkins4, Youping Deng5 and Chaoyang Zhang1*

Author Affiliations

1 School of Computing, University of Southern Mississippi, Hattiesburg, MS 39406, USA

2 Laboratory of Molecular Immunology, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, MD 20892, USA

3 Environmental Services, SpecPro Inc., San Antonio, TX 78216, USA

4 Environmental Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USA

5 Department of Internal Medicine, Rush University Medical Center, Chicago, IL 60612, USA

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BMC Systems Biology 2011, 5(Suppl 3):S3  doi:10.1186/1752-0509-5-S3-S3

Published: 23 December 2011



State Space Model (SSM) is a relatively new approach to inferring gene regulatory networks. It requires less computational time than Dynamic Bayesian Networks (DBN). There are two types of variables in the linear SSM, observed variables and hidden variables. SSM uses an iterative method, namely Expectation-Maximization, to infer regulatory relationships from microarray datasets. The hidden variables cannot be directly observed from experiments. How to determine the number of hidden variables has a significant impact on the accuracy of network inference. In this study, we used SSM to infer Gene regulatory networks (GRNs) from synthetic time series datasets, investigated Bayesian Information Criterion (BIC) and Principle Component Analysis (PCA) approaches to determining the number of hidden variables in SSM, and evaluated the performance of SSM in comparison with DBN.


True GRNs and synthetic gene expression datasets were generated using GeneNetWeaver. Both DBN and linear SSM were used to infer GRNs from the synthetic datasets. The inferred networks were compared with the true networks.


Our results show that inference precision varied with the number of hidden variables. For some regulatory networks, the inference precision of DBN was higher but SSM performed better in other cases. Although the overall performance of the two approaches is compatible, SSM is much faster and capable of inferring much larger networks than DBN.


This study provides useful information in handling the hidden variables and improving the inference precision.