# Conditional independence testing under misspecified inductive biases

arXiv: https://arxiv.org/abs/2307.02520 · HTML: https://mlsanity.com/paper/2307.02520/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [On the Generalization Benefit of Noise in Stochastic Gradient Descent](https://mlsanity.com/paper/2006.15081/) (2020)
- [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)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Testing Conditional Independence in Supervised Learning Algorithms](https://mlsanity.com/paper/1901.09917/) (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)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Floodgate: inference for model-free variable importance](https://mlsanity.com/paper/2007.01283/) (2020)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [On conditional parity as a notion of non-discrimination in machine learning](https://mlsanity.com/paper/1706.08519/) (2017)
- [Testing Conditional Independence on Discrete Data using Stochastic Complexity](https://mlsanity.com/paper/1903.04829/) (2019)
- [A unified framework for dataset shift diagnostics](https://mlsanity.com/paper/2205.08340/) (2022)

## Built on by (most cited first, 7 of 7)

- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [MinShap: A Shapley-Based Framework for Feature Redundancy](https://mlsanity.com/paper/2604.15107/) (2026)
- [Closing the Expression Gap in LLM Instructions via Socratic Questioning](https://mlsanity.com/paper/2510.27410/) (2025)
- [Sequential Kernel-based Conditional Independence Testing via Adaptive Betting](https://mlsanity.com/paper/2606.18993/) (2026)

## Abstract (arXiv)

Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes predictors as an intermediate step; we refer to this class of tests as regression-based tests. Although these methods are guaranteed to control Type-I error when the supervised learning methods accurately estimate the regression functions or Bayes predictors of interest, their behavior is less understood when they fail due to misspecified inductive biases; in other words, when the employed models are not flexible enough or when the training algorithm does not induce the desired predictors. Then, we study the performance of regression-based CI tests under misspecified inductive biases. Namely, we propose new approximations or upper bounds for the testing errors of three regression-based tests that depend on misspecification errors. Moreover, we introduce the Rao-Blackwellized Predictor Test (RBPT), a regression-based CI test robust against misspecified inductive biases. Finally, we conduct experiments with artificial and real data, showcasing the usefulness of our theory and methods.