B1647
Title: Deep nonparametric conditional independence tests for images
Authors: Marco Simnacher - Humboldt-Universität zu Berlin (Germany) [presenting]
Xiangnan Xu - Humboldt University of Berlin (Germany)
Hani Park - Hasso-Plattner-Institut (Germany)
Christoph Lippert - Hasso-Plattner-Institut (Germany)
Sonja Greven - Humboldt University of Berlin (Germany)
Abstract: Medical imaging is increasingly employed to study complex health outcomes visible in images ranging from brain MRI scans to chest X-rays. Often, causal relationships of such health outcomes with genetic information, environmental exposures and other variables are of interest. Conditional independence tests (CITs) are commonly used in the discovery of causal structures. Many recent nonparametric CITs have been developed to test for conditional independence between two scalars or vectors given potential confounders. However, testing conditional independence between an image and a scalar given a vector of confounders is not addressed in the existing literature. To fill this gap, we propose novel deep nonparametric CITs, which combine nonparametric CITs applicable to vector-valued data and deep learning models to extract feature representations of images. The application of existing nonparametric CITs to these feature representations is studied and used as a benchmark, and modified CITs based on kernels, knockoffs, classifiers and supervised learning models are introduced. Moreover, theoretical criteria towards optimal feature representations of images are derived. The tests' sensitivity to features, confounder dimensions, signal-to-noise ratio, and functional relationships between the objects are explored via extensive simulations. The novel tests are applied to test the dependence between brain MRI scans and genetic data given confounders.
