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Granger causality and the inverse Ising problem
We study Ising models for describing data and show that autoregressive
methods may be used to learn their connections, also in the case of asymmetric
connections and for multi-spin interactions. 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 is used to detect
the interacting pairs of spins. Nonlinear Granger causality is related to
multispin interactions.Comment: 6 pages and 8 figures. Revised version in press on Physica
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