Large-Scale Kernel Methods for Independence Testing - Zhang,Q; Filippi,S; Gretton,A; Sejdinovic,D (Statistics and Computing, 2017)
Representations of probability measures in reproducing kernel Hilbert spacesprovide a flexible framework for fully nonparametric hypothesis tests ofindependence, which can capture any type of departure from independence,including nonlinear associations and multivariate interactions. However, theseapproaches come with an at least quadratic computational cost in the number ofobservations, which can be prohibitive in many applications. Arguably, it isexactly in such large-scale datasets that capturing any type of dependence isof interest, so striking a favourable tradeoff between computational efficiencyand test performance for kernel independence tests would have a direct impacton their applicability in practice. In this contribution, we provide anextensive study of the use of large-scale kernel approximations in the contextof independence testing, contrasting block-based, Nystrom and random Fourierfeature approaches. Through a variety of synthetic data experiments, it isdemonstrated that our novel large scale methods give comparable performancewith existing methods whilst using significantly less computation time andmemory.