Granger causality and the inverse Ising problem

by Sebastiano Stramaglia (Univ. of Bari and INFN, Sezione di Bari)

Tuesday 4 Dec 2012, 13:30 → 14:30 Europe/Stockholm

122:026

Inverse Ising problem is the prototypical example of inference of dynamical networks from data, a topic which is widely studied due to the fact that dynamical networks model physical and biological behavior in many applications. We show that autoregressive methods, like Granger causality, may be used to learn the couplings of an Ising model, also in the case of asymmetric connections and for multi-spin interactions. We find that, for each link, the linear Granger causality is two times the corresponding transfer entropy (i.e. the information flow on that link) in the weak coupling limit. For sparse connections and a low number of samples, the L1 regularized least squares method can be used to detect the interacting pairs of spins. Nonlinear Granger causality is related to multispin interactions. We also describe applications in Neuroscience, in particular to the estimation of effective connectivity in the brain.