# Deep Nonparametric Conditional Independence Tests for Images

arXiv: https://arxiv.org/abs/2411.06140 · HTML: https://mlsanity.com/paper/2411.06140/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 95 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 30 of 34)

- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [FastSurfer -- A fast and accurate deep learning based neuroimaging pipeline](https://mlsanity.com/paper/1910.03866/) (2019)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Testing Conditional Independence in Supervised Learning Algorithms](https://mlsanity.com/paper/1901.09917/) (2019)
- [Two-sample Testing Using Deep Learning](https://mlsanity.com/paper/1910.06239/) (2019)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Transfer Learning in Magnetic Resonance Brain Imaging: a Systematic Review](https://mlsanity.com/paper/2102.01530/) (2021)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Fast Conditional Independence Test for Vector Variables with Large Sample Sizes](https://mlsanity.com/paper/1804.02747/) (2018)
- [The Projected Covariance Measure for assumption-lean variable significance testing](https://mlsanity.com/paper/2211.02039/) (2022)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [A Tour of Unsupervised Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1812.07715/) (2018)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [On boosting the power of Chatterjee's rank correlation](https://mlsanity.com/paper/2108.06828/) (2021)

## Built on by (most cited first, 3 of 3)

- [Embedded Conditional Independence Tests for Large Language Model Generated Text with an Application to German Parliament Speeches](https://mlsanity.com/paper/2609.00946/) (2026)
- [Interpreting Protein Language Model Embeddings via Orthogonal Projection for Protein Fitness Prediction](https://mlsanity.com/paper/2608.25548/) (2026)
- [ICON decomposition: Multivariate concept auditing reveals shortcuts that neural networks rely on](https://mlsanity.com/paper/2608.26083/) (2026)

## Abstract (arXiv)

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.