Learning of couplings for random asymmetric kinetic Ising models revisited: random correlation matrices and learning curves

Abstract: We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the nontrivial equal time correlations between spins induced by the dynamics for the speed of learning. These correlations become more important as the spin's stochasticity is decreased. We also analyse the deviation of the estimation error from asymptotic optimality.