Learning of Weighted Multi-layer Networks via Dynamic Social Spaces, with Application to Financial Interbank Transactions

Abstract

We propose a general network model suited for longitudinal data of multi-layer networks with directed and weighted edges. Our formulation built upon the latent social space representation of networks. It consists of a hierarchical formulation: deep levels of the model represent latent coordinates of agents in the social space, evolving in continuous time via Gaussian Processes; meanwhile, top levels jointly manage incidence and strength of interactions by considering a Zero-Inflated Gaussian response. Learning of the model is performed through Bayesian Inference. We develop an efficient MCMC algorithm targeting the posterior distribution of model parameters and missing data (available in GitHub). The motivation for our model lies in the context of Financial Networks, specifically the analysis of transactions between commercial banks. We evaluate the model in synthetic data, as well as our main case study: the network of inter-bank transactions in the Mexican financial system. Accurate predictions are obtained in both cases estimating out-of-sample link incidence and link strength.