Differential networking with path weights in Gaussian trees

Marginal and partial correlations quantify the strength of the associations represented by the edges of a graphical Gaussian model. The identification of changes in these quantities across different multivariate distributions, defined on the same vector of random variables, is often used to analyze regulatory networks in molecular biology, doing what is popularly known as differential networking, or differential coexpression analysis. However, the strength of associations along the paths of a graphical model has remained largely unexplored in this type of analysis. Here we investigate how to quantify this strength over the paths of a Gaussian tree, leading to a factorization of what we shall call path weights. We show that tree structures allow for an intuitive interpretation of path weights and that the proposed factorization conveys information that is not captured by marginal or partial correlations alone. Path weights can help to improve our understanding of a multivariate system under study and provide a new tool for differential coexpression analysis.

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