Optimal-transport Network Inference for Distributional Data

We propose a network-based framework grounded in optimal transport to analyze relationships among distributional data. Unlike traditional approaches based on scalar or vector variables, our method represents each node as a probability distribution. We infer two complementary networks: a similarity network, constructed from Wasserstein distances, and a regression network, based on Wasserstein barycenters, capturing directional dependencies among distributions. Statistical validation is achieved through permutation testing in the optimal transport space. Applied to data from the European Social Survey, the framework models the joint distributions of citizens’ satisfaction with the economy and attitudes toward immigration across countries. The resulting networks reveal clusters of nations with similar attitudinal geometries, as well as directional structures capturing patterns of alignment in public opinion. Overall, the approach provides a graphical and interpretable representation of complex distributional relationships in multivariate social data.