A Maximum A Posteriori Probability and Time-Varying Approach for Inferring Gene Regulatory Networks from Time Course Gene Microarray Data

Unlike most conventional techniques with static model assumption, this paper aims to estimate the time-varying model parameters and identify significant genes involved at different timepoints from time course gene microarray data. We first formulate the parameter identification problem as a new maximum a posteriori probability estimation problem so that prior information can be incorporated as regularization terms to reduce the large estimation variance of the high dimensional estimation problem. Under this framework, sparsity and temporal consistency of the model parameters are imposed using L-1-regularization and novel continuity constraints, respectively. The resulting problem is solved using the L-BFGS method with the initial guess obtained from the partial least squares method. A novel forward validation measure is also proposed for the selection of regularization parameters, based on both forward and current prediction errors. The proposed method is evaluated using a synthetic benchmark testing data and a publicly available yeast Saccharomyces cerevisiae cell cycle microarray data. For the latter particularly, a number of significant genes identified at different timepoints are found to be biological significant according to previous findings in biological experiments. These suggest that the proposed approach may serve as a valuable tool for inferring time-varying gene regulatory networks in biological studies.