Abstract:
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To understand the gene regulatory network on a genome-wide scale, we proposed a two-stage penalized least squares method to study interactions between a huge number of genes, and then constructed reciprocal graphical models on the basis of simultaneous equation models. At each stage, a single regression model for each gene is fitted. While L2 penalty is employed at the first stage to obtain consistent estimation of surrogate variables, L1 penalty is utilized at the second stage to select the regulatory genes from a large number of candidates. The estimates of the regulatory effects enjoy the oracle properties. In addition, the method is computationally fast and permits parallel implementation. We demonstrated the effectiveness of the method by simulation studies, and applied it to construct a yeast gene regulatory network.
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