# Learning to Increase the Power of Conditional Randomization Tests

arXiv: https://arxiv.org/abs/2207.01022 · HTML: https://mlsanity.com/paper/2207.01022/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 3 Jul 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Removing Spurious Features can Hurt Accuracy and Affect Groups Disproportionately](https://mlsanity.com/paper/2012.04104/) (2020)
- [Achieving Equalized Odds by Resampling Sensitive Attributes](https://mlsanity.com/paper/2006.04292/) (2020)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [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)
- [Deep Direct Likelihood Knockoffs](https://mlsanity.com/paper/2007.15835/) (2020)
- [Feature Selection using Stochastic Gates](https://mlsanity.com/paper/1810.04247/) (2018)
- [Relative Feature Importance](https://mlsanity.com/paper/2007.08283/) (2020)
- [Knockoffs for the mass: new feature importance statistics with false discovery guarantees](https://mlsanity.com/paper/1807.06214/) (2018)
- [Causal Inference in Genetic Trio Studies](https://mlsanity.com/paper/2002.09644/) (2020)

## Built on by (most cited first, 2 of 2)

- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [A Model-free Closeness-of-influence Test for Features in Supervised Learning](https://mlsanity.com/paper/2306.11855/) (2023)

## Abstract (arXiv)

The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I error rates. An appealing advantage of this test is that it can work with any machine learning model to design powerful test statistics. In turn, the common practice in the model-X literature is to form a test statistic using machine learning models, trained to maximize predictive accuracy with the hope to attain a test with good power. However, the ideal goal here is to drive the model (during training) to maximize the power of the test, not merely the predictive accuracy. In this paper, we bridge this gap by introducing, for the first time, novel model-fitting schemes that are designed to explicitly improve the power of model-X tests. This is done by introducing a new cost function that aims at maximizing the test statistic used to measure violations of conditional independence. Using synthetic and real data sets, we demonstrate that the combination of our proposed loss function with various base predictive models (lasso, elastic net, and deep neural networks) consistently increases the number of correct discoveries obtained, while maintaining type-I error rates under control.