## 1 Introduction  
A gene regulatory network (GRN) is a collection of molecular regulators that interact with each other and other substances in the cell to govern the gene expression levels of mRNA and proteins. Uncovering the underlying interactions genetic from a time series gene expression dataset is a network inference or reverse engineering problem, and many methods have been proposed to address it. Specifically, in this problem the goal involves finding a set of regulatory genes for each target gene as well as inferring the regulatory rules between genes. Data-driven methods are a class of GRN reconstruction methods that estimate gene dependencies directly from the data. Within this class, the correlation score is widely used to associate a pair of vector-valued measurements. Weighted gene co-expression network analysis (WGCNA) [1] is a well known correlation score-based method that shows consistently reliable performance. However, the correlation coefficients fail to capture more complex statistical dependencies, e.g., non-linear ones, between expression patterns. To resolve this limitation, the mutual information (MI) has been used as an alternative. MI is an efficient information-theoretic score that has been frequently used in the determination of regulatory relations. The relevance network is the simplest model based on this measure; it computes MI between all pairs of genes and infers the presence of a regulatory interaction when the MI is larger than a given threshold. The context likelihood of relatedness (CLR) algorithm [2] is an extension of the relevance network approach used to replace the probability distributions of all MI scores with empirical distributions. CLR applies an adaptive background correction step to eliminate false correlations and indirect influences. The algorithm for the reconstruction of accurate cellular networks (ARACNE) [3] is another information-theoretic algorithm for reverse engineering transcriptional networks from microarray data. ARACNE defines an edge as an irreducible statistical dependency between gene expression profiles that cannot be explained as an artifact of other statistical dependencies in the network. Finally, minimum redundancy networks (MRNET) [4] use an effective information-theoretic technique for feature selection based on a maximum relevance/minimum redundancy criterion. Despite promising results, computational complexity remains a major limitation. Another limitation is that most of these methods are only applicable to smaller networks. In order to reduce computational complexity and speed up running time, many methods to transform real-valued gene expression data into binary data have been widely used. These binarized expression data are then used as an input for inferring systems. The best fit [5] is an example method that considers the consistency as well as best-fit extension problems in the context of inferring networks from discretized data. Another example of using binary data [6] is to infer a Boolean network (BN) model of a GRN from limited transcriptomic or proteomic time series data. This method is able to illustrate the inference of a BN from limited time series data with constraints on connectivity that explain the observed state transitions. The mutual information-based Boolean network inference (MIBNI) method [7] uses Boolean data discretized from time series expression data as an input for inferring regulatory networks. MIBNI first identifies a set of initial regulatory genes using mutual information-based feature selection, then improves the dynamics prediction accuracy by iteratively swapping a pair of genes between sets of the selected regulatory genes and the other genes. A genetic algorithm-based Boolean network inference (GABNI) method [8] is an upgraded approach from MIBNI. GABNI applies a genetic algorithm (GA) to search an optimal set of regulatory genes in a wider solution space when MIBNI fails to find an optimal solution in a small-scale inference problem.