# An Overview of Causal Inference using Kernel Embeddings

arXiv: https://arxiv.org/abs/2410.22754 · HTML: https://mlsanity.com/paper/2410.22754/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 30 Oct 2024.

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

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Deconditional Downscaling with Gaussian Processes](https://mlsanity.com/paper/2105.12909/) (2021)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2102.10324/) (2021)
- [Bayesian Learning of Kernel Embeddings](https://mlsanity.com/paper/1603.02160/) (2016)
- [Hyperparameter Learning via Distributional Transfer](https://mlsanity.com/paper/1810.06305/) (2018)
- [A Neural Mean Embedding Approach for Back-door and Front-door Adjustment](https://mlsanity.com/paper/2210.06610/) (2022)
- [Neural-Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10859/) (2024)
- [Bayesian Deconditional Kernel Mean Embeddings](https://mlsanity.com/paper/1906.00199/) (2019)
- [Bayesian Kernel Two-Sample Testing](https://mlsanity.com/paper/2002.05550/) (2020)
- [A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment](https://mlsanity.com/paper/2111.13226/) (2021)

## Built on by (most cited first, 6 of 6)

- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Measuring Differences between Conditional Distributions using Kernel Embeddings](https://mlsanity.com/paper/2605.02260/) (2026)
- [Kernel Quantile Embeddings and Associated Probability Metrics](https://mlsanity.com/paper/2505.20433/) (2025)

## Abstract (arXiv)

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable flexible representations of complex relationships between variables. They serve as a mechanism for efficiently transferring the representation of a distribution downstream to other tasks, such as hypothesis testing or causal effect estimation. In the context of causal inference, the main challenges include identifying causal associations and estimating the average treatment effect from observational data, where confounding variables may obscure direct cause-and-effect relationships. Kernel embeddings provide a robust nonparametric framework for addressing these challenges. They allow for the representations of distributions of observational data and their seamless transformation into representations of interventional distributions to estimate relevant causal quantities. We overview recent research that leverages the expressiveness of kernel embeddings in tandem with causal inference.