Dynamic Message-Passing Equations and Applications to Inference of Epidemic Origin

Andrey Lokhov (Université Paris-Sud, LPTMS)

Abstract.  Understanding and quantifying the out-of-equilibrium dynamics is one of the major tasks of today's science. Using dynamic cavity method on time trajectories, we show how to derive dynamic message-passing (DMP) equations for a large class of models with irreversible dynamics - the key point that makes the problem solvable. These equations are asymptotically exact for locally tree-like graphs and generally provide a good approximation for real-world networks. We illustrate the approach by applying the DMP equations for susceptible-infected-recovered (SIR) model to the problem of inference of epidemic origin.