P1: Deep Conditional Independence Tests with an Application to Imaging Genetics

Project Summary

Project P1 develops conditional independence tests (CITs) for structured data, such as images, by leveraging Deep Learning for data embedding. This approach enables statistical testing as a key inference tool for multimodal datasets. By using appropriately learned data embeddings and nonparametric adjustments for the conditioning set, the tests ensure Type I error control across large sets of the null hypothesis of conditional independence. Furthermore, we enhance statistical power through transfer learning, optimally learned embeddings, and powerful CITs tailored for these embeddings.

The tests for conditional independence will be used as input for visual explanation tests in P2, and they will also be applied in P4 and P7.

Research Questions

How can statistical testing, specifically conditional independence testing, be enabled for multimodal datasets—such as those containing images and tabular data—with a focus on the biomedical domain?

Research Framework

We will integrate learned embeddings with existing nonparametric CITs, examine the theoretical properties and performance of these tests through simulations, and benchmark them on real and artificial structured data. By developing sample size and power calculations for CITs, we aim to equip researchers with the tools to design experiments based on their scientific questions using CITs. Furthermore, we will create efficient algorithms and easy-to-use software, which will be tested on the UK Biobank to validate its applicability to large-scale biomedical datasets.

Main Contribution

Conditional independence testing for multimodal datasets in the biomedical domain.

Publications

Marco Simnacher, Xiangnan Xu, Hani Park, Christoph Lippert, Sonja Greven (2024): Deep Nonparametric Conditional Independence Tests for Images, in: arXiv