# Model-Powered Conditional Independence Test

arXiv: https://arxiv.org/abs/1709.06138 · HTML: https://mlsanity.com/paper/1709.06138/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 30 of 43)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Mutual Information Estimation via Normalizing Flows](https://mlsanity.com/paper/2403.02187/) (2024)
- [Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression](https://mlsanity.com/paper/2305.08013/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Auditing for Human Expertise](https://mlsanity.com/paper/2306.01646/) (2023)
- [Out-of-Distribution Generalization Analysis via Influence Function](https://mlsanity.com/paper/2101.08521/) (2021)
- [Composite Feature Selection using Deep Ensembles](https://mlsanity.com/paper/2211.00631/) (2022)
- [Demystifying amortized causal discovery with transformers](https://mlsanity.com/paper/2405.16924/) (2024)
- [Diffeomorphic Information Neural Estimation](https://mlsanity.com/paper/2211.10856/) (2022)
- [Less is More: Mitigate Spurious Correlations for Open-Domain Dialogue Response Generation Models by Causal Discovery](https://mlsanity.com/paper/2303.01962/) (2023)
- [Conditional Independence Testing via Latent Representation Learning](https://mlsanity.com/paper/2209.01547/) (2022)
- [High-Dimensional Smoothed Entropy Estimation via Dimensionality Reduction](https://mlsanity.com/paper/2305.04712/) (2023)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [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)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [CausalScore: An Automatic Reference-Free Metric for Assessing Response Relevance in Open-Domain Dialogue Systems](https://mlsanity.com/paper/2406.17300/) (2024)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [FairICP: Encouraging Equalized Odds via Inverse Conditional Permutation](https://mlsanity.com/paper/2404.05678/) (2024)
- [DIET: Conditional independence testing with marginal dependence measures of residual information](https://mlsanity.com/paper/2208.08579/) (2022)
- [A survey of some recent developments in measures of association](https://mlsanity.com/paper/2211.04702/) (2022)
- [A Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2404.17644/) (2024)
- [Deep Nonparametric Conditional Independence Tests for Images](https://mlsanity.com/paper/2411.06140/) (2024)
- [PPFS: Predictive Permutation Feature Selection](https://mlsanity.com/paper/2110.10713/) (2021)
- [Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimation](https://mlsanity.com/paper/2110.14122/) (2021)
- [Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Data](https://mlsanity.com/paper/2206.08448/) (2022)

## Abstract (arXiv)

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution f(x,y,z) of continuous random vectors X,Y and Z, we determine whether X perp Y | Z. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution fCI(x,y,z) = f(x|z)f(y|z)f(z) -- the joint distribution if and only if X perp Y | Z. -- when given access only to i.i.d. samples from the true joint distribution f(x,y,z). To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to fCI in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d near-independent samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.