Impact of network characteristics on network reconstruction

TL;DR

This paper investigates how local network features affect the likelihood of false positives and negatives in network inference, proposing methods to estimate confidence levels and improve reconstruction accuracy.

Contribution

It introduces the influence of local connectivity measures on error probabilities and suggests using these measures to enhance network reconstruction without prior knowledge of the true network.

Findings

False positive and negative rates depend on local network measures.

Local measures like shortest path and detour degree can estimate confidence levels.

Enhanced link thresholding improves network reconstruction accuracy.

Abstract

When a network is inferred from data, two types of errors can occur: false positive and false negative conclusions about the presence of links. We focus on the influence of local network characteristics on the probability $\alpha$ - of type I false positive conclusions, and on the probability $\beta$ - of type II false negative conclusions, in the case of networks of coupled oscillators. We demonstrate that false conclusion probabilities are influenced by local connectivity measures such as the shortest path length and the detour degree, which can also be estimated from the inferred network when the true underlying network is not known a priory. These measures can then be used for quantification of the confidence level of link conclusions, and for improving the network reconstruction via advanced concepts of link thresholding.