Data quality for the inverse Ising problem

TL;DR

This paper investigates how the quality of data affects the accuracy of inferring Ising model parameters, proposing metrics and methods to improve data quality for better coupling reconstruction.

Contribution

It introduces the use of effective rank to quantify data quality and presents a matrix-perturbation method to enhance data sets for inverse Ising inference.

Findings

Out-of-equilibrium data yields better inference accuracy than equilibrium data.

Effective rank correlates with the quality of data for coupling reconstruction.

A method to remove redundant configurations improves inference results.

Abstract

There are many methods proposed for inferring parameters of the Ising model from given data, that is a set of configurations generated according to the model 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 data could be smaller than using another set of data, etc. In this paper we address the data quality problem in the kinetic inverse Ising problem. We quantify the quality of data using effective rank of the correlation matrix, and show that data gathered in a out of-equilibrium regime has a better quality than data gathered in equilibrium for coupling reconstruction. We also propose a matrix-perturbation based method for tuning the quality of given data and for removing bad-quality (i.e. redundant) configurations from data.