Network estimation in State Space Model with L1-regularization constraint

TL;DR

This paper introduces a novel method combining L1-regularization with an EM algorithm to infer sparse, dynamic gene regulatory networks from noisy, high-dimensional time-course microarray data, accounting for hidden processes.

Contribution

It develops a new approach for estimating sparse state space models with L1-regularization in high-dimensional settings, specifically applied to gene expression data.

Findings

Identified key genes with high inwards and outwards connections.

Discovered gene interactions such as Caspase 4 activating JunD.

Validated the method on T-cell microarray data.

Abstract

Biological networks have arisen as an attractive paradigm of genomic science ever since the introduction of large scale genomic technologies which carried the promise of elucidating the relationship in functional genomics. Microarray technologies coupled with appropriate mathematical or statistical models have made it possible to identify dynamic regulatory networks or to measure time course of the expression level of many genes simultaneously. However one of the few limitations fall on the high-dimensional nature of such data coupled with the fact that these gene expression data are known to include some hidden process. In that regards, we are concerned with deriving a method for inferring a sparse dynamic network in a high dimensional data setting. We assume that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some unknown or hidden process. We build an input-dependent linear state space model from these hidden states and demonstrate how an incorporated $L_{1}$ regularization constraint in an Expectation-Maximization (EM) algorithm can be used to reverse engineer transcriptional networks from gene expression profiling data. This corresponds to estimating the model interaction parameters. The proposed method is illustrated on time-course microarray data obtained from a well established T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4, CASP4, CD69, and C3X1 to have higher number of inwards directed connections and FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed connections. We recommend these genes to be object for further investigation. Caspase 4 is also found to activate the expression of JunD which in turn represses the cell cycle regulator CDC2.