Title: Predictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling,
Abstract: Testing (conditional) independence of multivariate random variables is a task
central to statistical inference and modelling in general - though
unfortunately one for which to date there does not exist a practicable
workflow. State-of-art workflows suffer from the need for heuristic or
subjective manual choices, high computational complexity, or strong parametric
assumptions.
We address these problems by establishing a theoretical link between
multivariate/conditional independence testing, and model comparison in the
multivariate predictive modelling aka supervised learning task. This link
allows advances in the extensively studied supervised learning workflow to be
directly transferred to independence testing workflows - including automated
tuning of machine learning type which addresses the need for a heuristic
choice, the ability to quantitatively trade-off computational demand with
accuracy, and the modern black-box philosophy for checking and interfacing.
As a practical implementation of this link between the two workflows, we
present a python package 'pcit', which implements our novel multivariate and
conditional independence tests, interfacing the supervised learning API of the
scikit-learn package. Theory and package also allow for straightforward
independence test based learning of graphical model structure.
We empirically show that our proposed predictive independence test outperform
or are on par to current practice, and the derived graphical model structure
learning algorithms asymptotically recover the 'true' graph. This paper, and
the 'pcit' package accompanying it, thus provide powerful, scalable,
generalizable, and easy-to-use methods for multivariate and conditional
independence testing, as well as for graphical model structure learning.