# A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment

arXiv: https://arxiv.org/abs/2111.13226 · HTML: https://mlsanity.com/paper/2111.13226/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 25 Nov 2021.

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

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [Parameterizing and Simulating from Causal Models](https://mlsanity.com/paper/2109.03694/) (2021)
- [Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs](https://mlsanity.com/paper/1302.1566/) (2013)
- [Revisiting the g-null paradox](https://mlsanity.com/paper/2103.03857/) (2021)
- [A quantile-based g-computation approach to addressing the effects of exposure mixtures](https://mlsanity.com/paper/1902.04200/) (2019)

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

- [An Overview of Causal Inference using Kernel Embeddings](https://mlsanity.com/paper/2410.22754/) (2024)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting](https://mlsanity.com/paper/2511.10130/) (2025)

## Abstract (arXiv)

Causal inference grows increasingly complex as the number of confounders increases. Given treatments X, confounders Z and outcomes Y, we develop a non-parametric method to test the textitdo-null hypothesis H0:; p(y|it do(X=x))=p(y) against the general alternative. Building on the Hilbert Schmidt Independence Criterion (HSIC) for marginal independence testing, we propose backdoor-HSIC (bd-HSIC) and demonstrate that it is calibrated and has power for both binary and continuous treatments under a large number of confounders. Additionally, we establish convergence properties of the estimators of covariance operators used in bd-HSIC. We investigate the advantages and disadvantages of bd-HSIC against parametric tests as well as the importance of using the do-null testing in contrast to marginal independence testing or conditional independence testing. A complete implementation can be found at hyperlinkhttps://github.com/MrHuff/kgformulatexttthttps://github.com/MrHuff/kgformula.