Effects of hidden nodes on network structure inference

TL;DR

This paper investigates how hidden nodes affect the accuracy of network structure inference in a disordered Ising model, revealing that hidden nodes generally impair inference quality, but certain conditions can mitigate this effect.

Contribution

It provides analytical and numerical insights into the impact of hidden nodes on network inference, highlighting factors that improve or worsen inference accuracy.

Findings

Inference quality decreases as the number of hidden nodes increases.

Increasing hidden node field variance improves coupling inference but worsens field inference.

Attenuated couplings involving hidden nodes lead to better coupling inference quality.

Abstract

Effects of hidden nodes on inference quality of observed network structure are explored based on a disordered Ising model with hidden nodes. We first study analytically small systems consisting of a few nodes, and find that the magnitude of the effective coupling grows as the coupling strength from the hidden common input nodes increases, while the field strength of the input node has opposite effects. Insights gained from analytic results of small systems are confirmed in numerical simulations of large systems. We also find that the inference quality deteriorates as the number of hidden nodes increases. Furthermore, increasing field variance of hidden nodes improves the inference quality of the effective couplings, but worsens the quality for the effective fields. In addition, attenuated coupling strengths involved in at least one hidden node lead to high quality of coupling inference.