Paper: arXiv 2602.21869

Authors: Mattia Marzi, Tiziano Squartini

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides an original Bayesian framework for out-of-sample network reconstruction, extending canonical Exponential Random Graphs to temporal settings. It combines solid mathematical derivations with empirical validation on the Electronic Market for Interbank Deposit (1999-2012), demonstrating strong performance over standard benchmarks.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Out-of-sample network reconstruction & prediction with uncertainty quantification"] --> B["Data Input:<br>Electronic Market for Interbank Deposit (1999–2012) Node Strengths"]
    B --> C["Bayesian Fitness Model:<br>Infer link probabilities from node strengths using past snapshot priors"]
    C --> D["Recursive Prediction:<br>Forward-propagate predicted snapshots as priors for subsequent times"]
    D --> E["Outcome:<br>Accurately predicts future bank connections with minimal data, outperforming benchmarks"]

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2 of 75 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.