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In data science, it is often required to estimate dependencies betweendifferent data sources. These dependencies are typically calculated usingPearson's correlation, distance correlation, and/or mutual information.However, none of these measures satisfy all the Granger's axioms for an "idealmeasure". One such ideal measure, proposed by Granger himself, calculates theBhattacharyya distance between the joint probability density function (pdf) andthe product of marginal pdfs. We call this measure the mutual dependence.However, to date this measure has not been directly computable from data. Inthis paper, we use our recently introduced maximum likelihood non-parametricestimator for band-limited pdfs, to compute the mutual dependence directly fromthe data. We construct the estimator of mutual dependence and compare itsperformance to standard measures (Pearson's and distance correlation) fordifferent known pdfs by computing convergence rates, computational complexity,and the ability to capture nonlinear dependencies. Our mutual dependenceestimator requires fewer samples to converge to theoretical values, is fasterto compute, and captures more complex dependencies than standard measures.

Mutual Dependence: A Novel Method for Computing Dependencies Between Random Variables