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Relating balance and conditional independence in graphical models

Alberto Zenere, Erik G. Larsson, and Claudio Altafini*

  • Department of Electrical Engineering, Linköping University, SE-58183 Linköping, Sweden

  • *Corresponding author: claudio.altafini@liu.se
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Phys. Rev. E 106, 044309 – Published 28 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044309

Abstract

When data are available for all nodes of a Gaussian graphical model, then, it is possible to use sample correlations and partial correlations to test to what extent the conditional independencies that encode the structure of the model are indeed verified by the data. In this paper, we give a heuristic rule useful in such a validation process: When the correlation subgraph involved in a conditional independence is balanced (i.e., all its cycles have an even number of negative edges), then a partial correlation is usually a contraction of the corresponding correlation, which often leads to conditional independence. In particular, the contraction rule can be made rigorous if we look at concentration subgraphs rather than correlation subgraphs. The rule is applied to real data for elementary gene regulatory motifs.

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Phys. Rev. E 106, 044309– Published 28 October, 2022
  • Received 29 March 2022
  • Accepted 13 September 2022
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