# Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves

arXiv: https://arxiv.org/abs/2010.04855 · HTML: https://mlsanity.com/paper/2010.04855/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 30 of 36)

- [Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm](https://mlsanity.com/paper/2312.07186/) (2023)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Minimax Optimal Kernel Operator Learning via Multilevel Training](https://mlsanity.com/paper/2209.14430/) (2022)
- [Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms](https://mlsanity.com/paper/2405.14778/) (2024)
- [Dynamics Within Latent Chain-of-Thought: An Empirical Study of Causal Structure](https://mlsanity.com/paper/2602.08783/) (2026)
- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [A Neural Mean Embedding Approach for Back-door and Front-door Adjustment](https://mlsanity.com/paper/2210.06610/) (2022)
- [Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension](https://mlsanity.com/paper/2102.11076/) (2021)
- [Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency](https://mlsanity.com/paper/2301.06240/) (2023)
- [Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients](https://mlsanity.com/paper/2402.05639/) (2024)
- [An Overview of Causal Inference using Kernel Embeddings](https://mlsanity.com/paper/2410.22754/) (2024)
- [Unveiling and Causalizing CoT: A Causal Pespective](https://mlsanity.com/paper/2502.18239/) (2025)
- [Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves](https://mlsanity.com/paper/2111.03950/) (2021)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Kernel methods for long term dose response curves](https://mlsanity.com/paper/2201.05139/) (2022)
- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [Moments of Causal Effects](https://mlsanity.com/paper/2505.04971/) (2025)
- [Doubly-Robust Estimation of Counterfactual Policy Mean Embeddings](https://mlsanity.com/paper/2506.02793/) (2025)
- [Sources of Gain: Decomposing Performance in Conditional Average Dose Response Estimation](https://mlsanity.com/paper/2406.08206/) (2024)
- [Automatic debiasing of neural networks via moment-constrained learning](https://mlsanity.com/paper/2409.19777/) (2024)
- [Conditional Outcome Equivalence: A Quantile Alternative to CATE](https://mlsanity.com/paper/2410.12454/) (2024)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [Interventional Processes for Causal Uncertainty Quantification](https://mlsanity.com/paper/2410.14483/) (2024)
- [All Models Are Miscalibrated, But Some Less So: Comparing Calibration with Conditional Mean Operators](https://mlsanity.com/paper/2502.11465/) (2025)
- [Kernel Treatment Effects with Adaptively Collected Data](https://mlsanity.com/paper/2510.10245/) (2025)
- [Leveraging semantic similarity for experimentation with AI-generated treatments](https://mlsanity.com/paper/2510.21119/) (2025)
- [Density Ratio-Free Doubly Robust Proxy Causal Learning](https://mlsanity.com/paper/2505.19807/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Estimating Aleatoric Uncertainty in the Causal Treatment Effect](https://mlsanity.com/paper/2602.08461/) (2026)

## Abstract (arXiv)

We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a decomposition property specific to the RKHS, our estimators have simple closed form solutions. We prove uniform consistency with finite sample rates via original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training program for disadvantaged youths.