[论文解读] A Bayesian approach to out-of-sample network reconstruction

Mattia Marzi, Squartini, Tiziano|arXiv (Cornell University)|Feb 25, 2026

Complex Systems and Time Series Analysis被引用 0

一句话总结

该论文建立了一个贝叶斯框架，利用过去的快照作为先验来重建和预测不断演化的网络，从而实现带有量化不确定性的样本外推断，并在 eMID 同业拆借市场上进行了演示。

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.

研究动机与目标

• Motivate the reconstruction of partially observed networks and the need for out-of-sample predictions.
• Propose a Bayesian extension of the Undirected Binary Configuration Model to propagate information over time.
• Introduce a single-parameter Bayesian models (BERM and BFM) to infer future link probabilities from past data.
• Demonstrate the approach on the eMID interbank market to predict future topology and assess uncertainty.

提出的方法

• Transform the Undirected Binary Configuration Model into a Bayesian framework using P(x|A) and the posterior predictive distribution P(A_{t+1}|A_t).
• Derive analytical expressions for edge-conditional probabilities q_{ij}^{t+1} under marginalization over z, enabling forward inference (Eq. 9).
• Instantiate the Bayesian Erdős–Rényi Model (BERM) with Beta priors to obtain a Beta-Binomial predictive for L_{t+1}.
• Instantiate the Bayesian Fitness Model (BFM) based on the density-corrected Gravity Model with node strengths as fitnesses and a prior on z derived from empirical history.

实验结果

研究问题

• RQ1 How can past network snapshots inform priors for predicting future network configurations?
• RQ2 Can a Bayesian formulation enable reliable out-of-sample network reconstruction with uncertainty quantification?
• RQ3 Do single-parameter, heterogeneous models (BERM and BFM) outperform in-sample methods in predicting future links and preserving degree sequences?
• RQ4 How does self-sustained inference perform when the model uses only its own past predictions as priors?
• RQ5 What is the comparative predictive performance of Bayesian approaches versus in-sample dcGM on real financial network data?

主要发现

• Both BERM and BFM recover the total number of links over time; the BFM better captures degree heterogeneity.
• BFM provides non-trivial link ranking enabling ROC/AUROC and Jaccard index based evaluation, unlike BERM which treats pairs uniformly.
• BFM achieves higher accuracy and better degree sequence recovery than BERM, with ACC around 0.80 on average but higher ranking metrics for BFM.
• Self-sustained inference, where priors evolve from predicted ensembles rather than observed networks, yields predictions close to those using true adjacency matrices.
• Compared to in-sample dcGM, the Bayesian predictor matches performance on average and outperforms it on a substantial share of snapshots, especially for edge-level metrics.