Complex network is a powerful tool to discover important information from various types of big data. Although substantial studies have been conducted for the development of stock relation networks, correlation coefficient is dominantly used to measure the relationship between stock pairs. Information theory is much less discussed for this important topic, though mutual information is able to measure nonlinear pairwise relationship. In this work we propose to use part mutual information for developing stock networks. The path-consistency algorithm is used to filter out redundant relationships. Using the Australian stock market data, we develop four stock relation networks using different orders of part mutual information. Compared with the widely used planar maximally filtered graph (PMFG), we can generate networks with cliques of large size. In addition, the large cliques show consistency with the structure of industrial sectors. We also analyze the connectivity and degree distributions of the generated networks. Analysis results suggest that the proposed method is an effective approach to develop stock relation networks using information theory.

Recent advances in experimental biology studies have produced large amount of molecular activity data. In particular, individual patient data provide non-time series information for the molecular activities in disease conditions. The challenge is how to design effective algorithms to infer regulatory networks using the individual patient datasets and consequently address the issue of network symmetry. This work is aimed at developing an efficient pipeline to reverse-engineer regulatory networks based on the individual patient proteomic data. The first step uses the SCOUT algorithm to infer the pseudo-time trajectory of individual patients. Then the path-consistent method with part mutual information is used to construct a static network that contains the potential protein interactions. To address the issue of network symmetry in terms of undirected symmetric network, a dynamic model of ordinary differential equations is used to further remove false interactions to derive asymmetric networks. In this work a dataset from triple-negative breast cancer patients is used to develop a protein-protein interaction network with 15 proteins.

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One of the key challenges in systems biology and molecular sciences is how to infer regulatory relationships between genes and proteins using high-throughout omics datasets. Although a wide range of methods have been designed to reverse engineer the regulatory networks, recent studies show that the inferred network may depend on the variable order in the dataset. In this work, we develop a new algorithm, called the statistical path-consistency algorithm (SPCA), to solve the problem of the dependence of variable order. This method generates a number of different variable orders using random samples, and then infers a network by using the path-consistent algorithm based on each variable order. We propose measures to determine the edge weights using the corresponding edge weights in the inferred networks, and choose the edges with the largest weights as the putative regulations between genes or proteins. The developed method is rigorously assessed by the six benchmark networks in DREAM challenges, the mitogen-activated protein (MAP) kinase pathway, and a cancer-specific gene regulatory network. The inferred networks are compared with those obtained by using two up-to-date inference methods. The accuracy of the inferred networks shows that the developed method is effective for discovering molecular regulatory systems.