Wasserstein barycenter for link prediction in temporal networks

We propose a flexible link forecast methodology for weighted temporal networks. Our probabilistic model estimates the evolving link dynamics among a set of nodes through Wasserstein barycentric coordinates arising within the optimal transport theory. Optimal transport theory is employed to interpolate among network evolution sequences and to compute the probability distribution of forthcoming links. Besides generating point link forecasts for weighted networks, the methodology provides the probability that a link attains weights in a certain interval, namely a quantile of the weights distribution. We test our approach to forecast the link dynamics of the worldwide Foreign Direct Investments network and of the World Trade Network, comparing the performance of the proposed methodology against several alternative models. The performance is evaluated by applying non-parametric diagnostics derived from binary classifications and error measures for regression models. We find that the optimal transport framework outperforms all the competing models when considering quantile forecast. On the other hand, for point forecast, our methodology produces accurate results that are comparable with the best performing alternative model. Results also highlight the role played by model constraints in the determination of future links emphasising that weights are better predicted when accounting for geographical rather than economic distance.