Deep Nonparametric Conditional Independence Tests for Images

TL;DR

This paper introduces deep nonparametric conditional independence tests (DNCITs) that leverage learned feature embeddings for high-dimensional data like images, enabling more effective dependence testing in complex scenarios.

Contribution

The paper develops a novel framework combining embedding maps with nonparametric CITs, applicable to high-dimensional data, and provides theoretical properties, simulations, and real-world applications.

Findings

DNCITs outperform existing tests in high-dimensional settings.

Application to UK Biobank data confirms null results in personality studies.

Potential for reduced confounder dimensions with improved confounder control.

Abstract

Conditional independence tests (CITs) test for conditional dependence between random variables. As existing CITs are limited in their applicability to complex, high-dimensional variables such as images, we introduce deep nonparametric CITs (DNCITs). The DNCITs combine embedding maps, which extract feature representations of high-dimensional variables, with nonparametric CITs applicable to these feature representations. For the embedding maps, we derive general properties on their parameter estimators to obtain valid DNCITs and show that these properties include embedding maps learned through (conditional) unsupervised or transfer learning. For the nonparametric CITs, appropriate tests are selected and adapted to be applicable to feature representations. Through simulations, we investigate the performance of the DNCITs for different embedding maps and nonparametric CITs under varying confounder dimensions and confounder relationships. We apply the DNCITs to brain MRI scans and behavioral traits, given confounders, of healthy individuals from the UK Biobank (UKB), confirming null results from a number of ambiguous personality neuroscience studies with a larger data set and with our more powerful tests. In addition, in a confounder control study, we apply the DNCITs to brain MRI scans and a confounder set to test for sufficient confounder control, leading to a potential reduction in the confounder dimension under improved confounder control compared to existing state-of-the-art confounder control studies for the UKB. Finally, we provide an R package implementing the DNCITs.