Network Reconstruction via Jeffreys Prior under Missing Sufficient Statistics

TL;DR

This paper introduces a novel network reconstruction method using Jeffreys prior to handle missing block-specific densities, improving accuracy in economic trade network modeling with limited data.

Contribution

It extends the Fitness-Corrected Block Model by incorporating Jeffreys prior to estimate heterogeneous densities without empirical block-specific data.

Findings

The method outperforms baseline Fitness Model in various trade datasets.

It sometimes surpasses the more data-intensive FCBM in accuracy.

The approach reduces overfitting risk in network reconstruction.

Abstract

The modeling and reconstruction of economic networks from aggregate information has important implications for counterfactual analysis and policymaking. The traditional Fitness Model (FM) achieves good performance by using node-specific variables that are easily accessible (e.g., GDP for countries or total assets for banks or firms) and the overall link density as the only sufficient statistic. However, it often ignores additional contextual or mesoscopic features which may be more difficult to observe. In this paper, we extend the framework by incorporating block structure as in the Fitness-Corrected Block Model (FCBM), which allows for heterogeneous densities within and across blocks, but in the more challenging setting where such block-specific densities are not empirically available. Our method compensates for the absence of empirical information about the sufficient statistics by using a Jeffreys prior to average, in the most unbiased way, over all compatible solutions that are otherwise left unidentified. We evaluate the method on three international trade datasets across different product classes, including fresh products, common products, geographically specific products, and high-technology products. The underlying block structure is represented by economic regions as defined by the World Bank, and we only assume empirical knowledge of the total GDPs and the overall link density. The new method systematically outperforms the baseline Block-Agnostic FM (which uses the same input information) and sometimes even the FCBM (despite the latter uses more information), thereby suggesting reduced overfitting risk.