The Reciprocal Influence Criterion: An Upgrade of the Information Quality Ratio

Understanding and quantifying the mutual influence between systems remain crucial but challenging tasks in any scientific enterprise. The Pearson correlation coefficient, the mutual information, and the information quality ratio are the most widely used indicators, only the last two being valid for nonlinear interactions. Given their limitations, a new criterion is proposed, the reciprocal influence criterion, which is very simple conceptually and does not make any assumption about the statistics of the stochastic variables involved. In addition to being normalised as the information quality ratio, it provides a much better resilience to noise and much higher stability to the issues related to the determination of the involved probability distribution functions. A conditional version, to counteract the effects of confounding variables, has also been developed, showing the same advantages compared to the more traditional indicators. A series of systematic tests with numerical examples is reported, to compare the properties of the new indicator with the more traditional ones, proving its clear superiority in practically all respects.