Data quality for the inverse lsing problem

There are many methods proposed for inferring parameters of the Ising modelfrom given data, that is a set of configurations generated according to themodel itself. However little attention has been paid until now to the data, e.g.how the data is generated, whether the inference error using one set of datacould be smaller than using another set of data, etc. In this paper we discussthe data quality problem in the inverse Ising problem, using as a benchmarkthe kinetic Ising model. We quantify the quality of data using effective rank ofthe correlation matrix, and show that data gathered in a out-of-equilibriumregime has a better quality than data gathered in equilibrium for couplingreconstruction. We also propose a matrix-perturbation based method for tun-ing the quality of given data and for removing bad-quality(i.e. redundant)configurations from data.