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Testing (conditional) independence of multivariate random variables is a taskcentral to statistical inference and modelling in general - thoughunfortunately one for which to date there does not exist a practicableworkflow. State-of-art workflows suffer from the need for heuristic orsubjective manual choices, high computational complexity, or strong parametricassumptions.  We address these problems by establishing a theoretical link betweenmultivariate/conditional independence testing, and model comparison in themultivariate predictive modelling aka supervised learning task. This linkallows advances in the extensively studied supervised learning workflow to bedirectly transferred to independence testing workflows - including automatedtuning of machine learning type which addresses the need for a heuristicchoice, the ability to quantitatively trade-off computational demand withaccuracy, and the modern black-box philosophy for checking and interfacing.  As a practical implementation of this link between the two workflows, wepresent a python package 'pcit', which implements our novel multivariate andconditional independence tests, interfacing the supervised learning API of thescikit-learn package. Theory and package also allow for straightforwardindependence test based learning of graphical model structure.  We empirically show that our proposed predictive independence test outperformor are on par to current practice, and the derived graphical model structurelearning algorithms asymptotically recover the 'true' graph. This paper, andthe 'pcit' package accompanying it, thus provide powerful, scalable,generalizable, and easy-to-use methods for multivariate and conditionalindependence testing, as well as for graphical model structure learning.

Predictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling