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Issue No. 04 - July-Aug. (2012 vol. 9)
ISSN: 1545-5963
pp: 1203-1211
E. Serpedin , Dept. of Electr. & Comput. Eng., Texas A& M Univ., College Station, TX, USA
A. Noor , Dept. of Electr. & Comput. Eng., Texas A& M Univ., College Station, TX, USA
M. Nounou , Chem. Eng. Dept., Texas A&M Univ. at Qatar, Doha, Qatar
Hazem N. Nounou , Electr. Eng. Dept., Texas A&M Univ. at Qatar, Doha, Qatar
This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.
time series, bioinformatics, cellular biophysics, genetics, Kalman filters, least squares approximations, sparse structure, gene regulatory network, nonlinear state space models, sparsity exploitation, gene expression time series data, particle filter-based state estimation algorithm, parameter vector, microarray data, LASSO-based least squares regression, extended Kalman filter, unscented Kalman filter, mean square error, fidelity criterion, particle filter-based network inference algorithm, Kalman filters, Mathematical model, Data models, Estimation, Approximation algorithms, Gene expression, Noise, LASSO., Gene regulatory network, particle filter, Kalman filter, parameter estimation

E. Serpedin, A. Noor, M. Nounou and H. N. Nounou, "Inferring Gene Regulatory Networks via Nonlinear State-Space Models and Exploiting Sparsity," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. , pp. 1203-1211, 2012.
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