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Title: Weighted dynamic multi-layer networks via latent Gaussian processes Authors:  Christian Carmona - University of Oxford (United Kingdom) [presenting]
Serafin Martinez-Jaramillo - Center for Latin American Monetary Studies (Mexico)
Abstract: A general network model suited for longitudinal data of multi-layer networks with directed and weighted edges is proposed. The formulation combines relevant features from existing network models, creating one that is able to capture simultaneously the characteristics of such complex networks. The model is built upon the \emph{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 mixture between a Gaussian component and a point-mass probability at zero. 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 (code available in the supplement). The performance of the model is measured 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.