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

TL;DR

This paper analytically examines how equal-time correlations in a kinetic Ising model influence the efficiency of learning couplings from finite data, highlighting the impact of spin stochasticity on learning speed.

Contribution

It provides a detailed analysis of the learning performance considering dynamic correlations and deviation from optimality in asymmetric kinetic Ising models.

Findings

Equal-time correlations significantly affect learning speed.

Reduced spin stochasticity increases the importance of correlations.

Deviations from asymptotic optimality are characterized.

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.