Bayesian networks are widely applied to a variety of domains such as business, engineering, and medicine [1]. The networks can be used to make optimal inference decisions based on Bayesian theory as well as to find the causal relationship between different entities as a graph model.

To perform an efficient inference and correct representation of the dependency relationship, an optimal structure is constructed to maximize the probabilistic fitness to the given data. Determining the optimal network through learning structures of Bayesian networks has been explored over the last decade, which contains the development of searching and scoring schemes. The searching is to find the structure that has the highest score among all possible ones. Since the searching space grows exponentially when the number of variables (nodes) increases, it is known as NP hard [2]. The scoring computes the score of a structure to evaluate how well it fits a given data.

Until now, several scoring functions have been developed including the well known Cooper-Herskovits scoring function as in K2 algorithm [3], the likelihood equivalence Bayesian Dirichlet (BDe) scoring function [4], and the minimum description length (MDL) scoring function [5]. In addition to serving as a scoring function, the K2 algorithm [3] functioning as a searching method has attracted attention from researchers due to its performance and efficiency till quite recently. However, the assumption of K2 algorithm is that the order of variables is correctly known. In other words, the performance highly depends on if the variables are well ordered. With regard to structure learning, Hill-Climbing greedy algorithm was used as a searching algorithm in [6]. Conditional independence property and mutual information were also employed for structure learning [7].

The goal of this study is to infer the proteomic signaling pathways affected by DNA damage, DNA repair, cell cycle checkpoints, and cell apoptosis under the influence of different radiation dosages. An emerging protein microarray technology, called the revers-phase protein microarray (RPPM), in conjunction with the quantum dots (Qdot) nano-technology, is used as the detection system. We study the proteomic responses at different time points (1h, 6h, 24h, 48h, and 72h) under different dosages (4 cGy, 10 cGy, 50 cGy, 1 Gy, and 5 Gy).

To infer the signaling pathways under different radiation dosages, in this paper we propose a new Bayesian network structure learning algorithm using the mutual information, conditional independence, and property of immorality in graph. Our method has two important features. First, the algorithm does not provide the direction for every edge in a predicted network. Since a signaling pathway is composed of successive and oriented interactions of molecules, even a small number of edges that have incorrect directions can cause significant effect in biological network analysis. To avoid a misleading result, therefore, we aim to report the most trusted edges, though a complete directed graph is not produced. Second, we focus on reducing wrong edges even though price for missing edges is paid. In other words, reliable, though not complete, information is reported as opposed to complete but uncertain information. To achieve these two goals, we initially exclude edges with low mutual information, and strictly carry out conditional independence test and immorality test for each candidate edge in order to remove incorrect edges. In the following sections, we first introduce the main steps of the proposed methodology. Then we use well known standard networks to evaluate the performance of the algorithm. Finally proteomic networks for ATM cell lines under different radiation dosages are presented.