A Bayesian approach to out-of-sample network reconstruction

TL;DR

This paper introduces a Bayesian method for predicting future network structures from past snapshots, effectively quantifying uncertainty and outperforming existing benchmarks in out-of-sample network reconstruction.

Contribution

It develops a Bayesian framework that leverages past network data to inform priors for predicting future network configurations, with a specific implementation using a fitness model.

Findings

Accurately predicts the number of connections in interbank networks over time.

Outperforms existing probabilistic benchmarks in link prediction tasks.

Enables self-sustained, out-of-sample network reconstruction with minimal data.

Abstract

Networks underpin systems that range from finance to biology, yet their structure is often only partially observed. Current reconstruction methods typically fit the parameters of a model anew to each snapshot, thus offering no guidance to predict future configurations. Here, we develop a Bayesian approach that uses the information about past network snapshots to inform a prior and predict the subsequent ones, while quantifying uncertainty. Instantiated with a single-parameter fitness model, our method infers link probabilities from node strengths and carries information forward in time. When applied to the Electronic Market for Interbank Deposit across the years 1999-2012, our method accurately recovers the number of connections per bank at subsequent times, outperforming probabilistic benchmarks designed for analogous, link prediction tasks. Notably, each predicted snapshot serves as a reliable prior for the next one, thus enabling self-sustained, out-of-sample reconstruction of evolving networks with a minimal amount of additional data.