A Multi-Laplacian Prior and Augmented Lagrangian Approach to the Exploratory Analysis of Time-Varying Gene and Transcriptional Regulatory Networks for Gene Microarray Data

This paper proposes a novel multi-Laplacian prior (MLP) and augmented Lagrangian method (ALM) approach for gene interactions and putative transcription factors (TFs) identification from time-course gene microarray data. It employs a non-linear time-varying auto-regressive (N-TVAR) model and the Maximum-A-Posteriori-Probability method for incorporating the multi-Laplacian prior and the continuity constraint. The MLP allows connections to/from a gene to be better preserved for putative TF identification in non-stationarity gene regulatory network as compared with conventional
$L_1$
-based penalties. Moreover, the ALM allows the resultant non-smooth
$L_1$
-based penalties to be decoupled from the remaining smooth terms, so that the former and latter can be efficiently solved using a low-complexity proximity operator and smooth optimization technique, respectively. Synthetic and real time-course gene microarray datasets are tested to evaluate the performance of the proposed method. Experimental results show that the proposed method gives better accuracy and higher computational speed than our previous work using smoothed approximation. Moreover, its performance, without the use of ChIP-chip data, is found to be highly comparable with other state-of-the-art methods integrating both ChIP-chip and gene microarray data. It suggests that the proposed method may serve as a useful exploratory tool for putative TF identification with reduced experimental cost.