Inferring propagation paths for sparsely observed perturbations on complex networks

FRANCESCO ALESSANDRO MASSUCCI; JONATHAN WHEELER; RAÚL BELTRÁN-DEBÓN; JORGE JOVEN; MARTA SALES-PARDO; ROGER GUIMERÀ

Science Advances

AAAS

Año: 2016 vol. 2

2375-2548

In a complex system, perturbations propagate by following paths on the network of interactions among the system?s units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very sparse in time (there is a single observation of the perturbed system) and in ?space? (only a few perturbed and unperturbed units are observed). A major challenge in many areas, from biology to the social sciences, is to inferthe propagation paths from observations of the effects of perturbation under these sparsity conditions. We address this problem and show that it is possible to go beyond the usual approach of using the shortest paths connectingthe known perturbed nodes. Specifically, we show that a simple and general probabilistic model, which we solved using belief propagation, provides fast and accurate estimates of the probabilities of nodes being perturbed.