The Distance Precision Matrix: Computing networks from non-linear relationships

Abstract

Motivation Full-order partial correlation, a fundamental approach for network reconstruction, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the covariance matrix) as an indicator of which variables are directly associated. The precision matrix assumes Gaussian linear data and its entries are zero for pairs of variables that are independent given all other variables. However, there is still very little theory on network reconstruction under the assumption of non-linear interactions among variables. Results We propose Distance Precision Matrix, a network reconstruction method aimed at both linear and non-linear data. Like partial distance correlation, it builds on distance covariance, a measure of possibly non-linear association, and on the idea of full-order partial correlation, which allows to discard indirect associations. We provide evidence that the Distance Precision Matrix method can successfully compute networks from linear and non-linear data, and consistently so across different datasets, even if sample size is low. The method is fast enough to compute networks on hundreds of nodes.