The Distance Precision Matrix: computing networks from nonlinear relationships

TL;DR

This paper introduces the Distance Precision Matrix, a novel method for network reconstruction from non-linear data, extending traditional Gaussian-based approaches to handle more complex relationships.

Contribution

The paper proposes the Distance Precision Matrix, enabling network inference from non-linear associations, which improves upon Gaussian assumptions in traditional precision matrix methods.

Findings

Successfully reconstructs networks from non-linear data

Consistent performance across diverse data scenarios

Extends Gaussian-based network inference methods

Abstract

A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The precision matrix assumes Gaussian data and its entries are zero for those pairs of variable which are conditionally independent. Here, we propose the Distance Precision Matrix which is based on a measure of possibly non-linear association, the distance covarince. We provide evidence that the Distance Precision Matrix can successfully compute networks from non-linear data and does so in a very consistent manner across many data situations.