Part mutual information for quantifying direct associations in networks.
Quantitatively identifying direct dependencies between variables is an important task in data analysis, in particular for reconstructing various types of networks and causal relations in science and engineering. One of the most widely used criteria is partial correlation, but it can only measure linearly direct association and miss nonlinear associations. However, based on conditional independence, conditional mutual information (CMI) is able to quantify nonlinearly direct relationships among variables from the observed data, superior to linear measures, but suffers from a serious problem of underestimation, in particular for those variables with tight associations in a network, which severely limits its applications. In this work, we propose a new concept, "partial independence," with a new measure, "part mutual information" (PMI), which not only can overcome the problem of CMI but also retains the quantification properties of both mutual information (MI) and CMI. Specifically, we first defined PMI to measure nonlinearly direct dependencies between variables and then derived its relations with MI and CMI. Finally, we used a number of simulated data as benchmark examples to numerically demonstrate PMI features and further real gene expression data from Escherichia coli and yeast to reconstruct gene regulatory networks, which all validated the advantages of PMI for accurately quantifying nonlinearly direct associations in networks.
Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, University of the Chinese Academy of Sciences, Shanghai 200031, China;
Juan
J
Zhao
Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, University of the Chinese Academy of Sciences, Shanghai 200031, China; School of Life Science and Technology, ShanghaiTech University, Shanghai 200031, China;
Yiwei
Y
Zhou
Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, University of the Chinese Academy of Sciences, Shanghai 200031, China;
Xiujun
X
Zhang
Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, University of the Chinese Academy of Sciences, Shanghai 200031, China; School of Life Science and Technology, ShanghaiTech University, Shanghai 200031, China; Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo 113-8654, Japan lnchen@sibs.ac.cn.
Luonan
L
Chen
D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008954:Models, Biological; D015233:Models, Statistical
conditional independence; conditional mutual information; network inference; systems biology