This paper proposes a novel algorithm for inferring gene regulatory networks which makes use of cubature Kalman filter (CKF) and Kalman filter (KF) techniques in conjunction with compressed sensing methods. The gene network is described using a state-space model. A nonlinear model for the evolution of gene expression is considered, while the gene expression data is assumed to follow a linear Gaussian model. The hidden states are estimated using CKF. The system parameters are modeled as a Gauss-Markov process and are estimated using compressed sensing-based KF. These parameters provide insight into the regulatory relations among the genes. The Cramér-Rao lower bound of the parameter estimates is calculated for the system model and used as a benchmark to assess the estimation accuracy. The proposed algorithm is evaluated rigorously using synthetic data in different scenarios which include different number of genes and varying number of sample points. In addition, the algorithm is tested on the DREAM4 in silico data sets as well as the in vivo data sets from IRMA network. The proposed algorithm shows superior performance in terms of accuracy, robustness, and scalability. 1. Introduction Gene regulation is one of the most intriguing processes taking place in living cells. With hundreds of thousands of genes at their disposal, cells must decide which genes are to express at a particular time. As the cell development evolves, different needs and functions entail an efficient mechanism to turn the required genes on while leaving the others off. Cells can also activate new genes to respond effectively to environmental changes and perform specific roles. The knowledge of which gene triggers a particular genetic condition can help us ward off the potential harmful effects by switching that gene off. For instance, cancer can be controlled by deactivating the genes that cause it. Gene expression is the process of generating functional gene products, for example, mRNA and protein. The level of gene functionality can be measured using microarrays or gene chips to produce the gene expression data [1]. More accurate estimation of gene expression is now possible using the RNA-Seq method. Intelligent use of such data can help improve our understanding of how the genes are interacting in a living organism [2–4]. Gene regulation is known to exhibit several modes; a couple of important ones include transcription regulation and posttranscription regulation [5]. While the theoretical applications of gene regulation are extremely promising, it requires a thorough understanding
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