# DIET: Conditional independence testing with marginal dependence measures of residual information

arXiv: https://arxiv.org/abs/2208.08579 · HTML: https://mlsanity.com/paper/2208.08579/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Gene Hunting with Knockoffs for Hidden Markov Models](https://mlsanity.com/paper/1706.04677/) (2017)
- [Deep Direct Likelihood Knockoffs](https://mlsanity.com/paper/2007.15835/) (2020)
- [Control Function Instrumental Variable Estimation of Nonlinear Causal Effect Models](https://mlsanity.com/paper/1602.01051/) (2016)
- [Causal Inference in Genetic Trio Studies](https://mlsanity.com/paper/2002.09644/) (2020)
- [On a Nonparametric Notion of Residual and its Applications](https://mlsanity.com/paper/1409.3886/) (2014)

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

- [Robustness to Spurious Correlations Improves Semantic Out-of-Distribution Detection](https://mlsanity.com/paper/2302.04132/) (2023)
- [Explanations that reveal all through the definition of encoding](https://mlsanity.com/paper/2411.02664/) (2024)
- [Empirically Calibrated Conditional Independence Tests](https://mlsanity.com/paper/2602.21036/) (2026)

## Abstract (arXiv)

Conditional randomization tests (CRTs) assess whether a variable x is predictive of another variable y, having observed covariates z. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: F(x mid z) and F(y mid z) where F(· mid z) is a conditional cumulative distribution function (CDF). These variables are termed "information residuals." We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.