Building complex networks through classical and Bayesian statistics - a comparison

TL;DR

This paper compares classical and Bayesian methods for constructing complex networks, introducing a new local partial correlation technique to improve network building with limited observations, and finds Bayesian inference preferable in small-sample scenarios.

Contribution

It introduces a novel local partial correlation methodology and compares classical and Bayesian network construction methods, highlighting Bayesian inference's advantages with fewer observations.

Findings

Bayesian inference outperforms classical methods with limited data.

Both methods perform well with sufficient observations.

The proposed local partial correlation improves network estimation.

Abstract

This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Inverse Wishart conjugate prior). In this current work, in order to solve the problem of having less observations than variables, we propose a new methodology called local partial correlation, which consists of selecting, for each pair of variables, the other variables most correlated to the pair.We applied these methods on simulated data and compared them through ROC curves. The most attractive result is that, even though it has high computational costs, to use Bayesian inference on trees is better when we have less observations than variables. In other cases, both approaches present satisfactory results.