Part mutual information for quantifying direct associations in networks

Juan Zhao Chinese Academy of Sciences Yiwei Zhou Chinese Academy of Sciences Xiujun Zhang Chinese Academy of Sciences Luonan Chen Chinese Academy of Sciences

Information Theory mathscidoc:1912.19001

Proc Natl Acad Sci USA, 113, 5130-5135, 2016
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.
mutual inforamtion, statistical dependency, network, direct causality
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  title={Part mutual information for quantifying direct associations in networks},
  author={Juan Zhao, Yiwei Zhou, Xiujun Zhang, and Luonan Chen},
  booktitle={Proc Natl Acad Sci USA},
Juan Zhao, Yiwei Zhou, Xiujun Zhang, and Luonan Chen. Part mutual information for quantifying direct associations in networks. 2016. Vol. 113. In Proc Natl Acad Sci USA. pp.5130-5135.
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