Covariance and correlation estimators in bipartite complex systems with a double heterogeneity

TL;DR

This paper introduces weighted covariance and correlation estimators for bipartite complex systems with double heterogeneity, effectively removing bias present in traditional unweighted estimators and improving analysis accuracy.

Contribution

The paper proposes novel weighted estimators that eliminate bias in covariance and correlation measurements for bipartite systems with heterogeneity, enhancing analysis reliability.

Findings

Weighted estimators remove bias in bipartite systems.

Application to social and biological systems demonstrates improved accuracy.

Unweighted estimators exhibit significant bias in real data.

Abstract

We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance and correlation can be shown to possess a bias. Indeed, such a bias affects real bipartite systems, and, for example, we report its effects on two empirical systems, one social and the other biological. On the contrary, our newly proposed weighted estimators remove the bias and are better suited to describe such systems.