Large-Scale Kernel Methods for Independence Testing

TL;DR

This paper explores large-scale kernel methods for independence testing, balancing computational efficiency and test accuracy, and demonstrates their effectiveness on synthetic datasets.

Contribution

It introduces and evaluates large-scale kernel approximation techniques like block-based, Nystrom, and Fourier features for independence testing.

Findings

Large-scale methods achieve comparable accuracy to traditional approaches.

Significantly reduced computation time and memory usage.

Effective in synthetic data experiments for independence testing.

Abstract

Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including nonlinear associations and multivariate interactions. However, these approaches come with an at least quadratic computational cost in the number of observations, which can be prohibitive in many applications. Arguably, it is exactly in such large-scale datasets that capturing any type of dependence is of interest, so striking a favourable tradeoff between computational efficiency and test performance for kernel independence tests would have a direct impact on their applicability in practice. In this contribution, we provide an extensive study of the use of large-scale kernel approximations in the context of independence testing, contrasting block-based, Nystrom and random Fourier feature approaches. Through a variety of synthetic data experiments, it is demonstrated that our novel large scale methods give comparable performance with existing methods whilst using significantly less computation time and memory.