# Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression

arXiv: https://arxiv.org/abs/2207.09139 · HTML: https://mlsanity.com/paper/2207.09139/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 96 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 30 of 44)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [An Attentive Survey of Attention Models](https://mlsanity.com/paper/1904.02874/) (2019)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Using Embeddings to Correct for Unobserved Confounding in Networks](https://mlsanity.com/paper/1902.04114/) (2019)
- [Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects](https://mlsanity.com/paper/2111.07966/) (2021)
- [Causal Decision Making and Causal Effect Estimation Are Not the Same... and Why It Matters](https://mlsanity.com/paper/2104.04103/) (2021)
- [On Locality of Local Explanation Models](https://mlsanity.com/paper/2106.14648/) (2021)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Transfer Learning for Estimating Causal Effects using Neural Networks](https://mlsanity.com/paper/1808.07804/) (2018)

## Built on by (most cited first, 4 of 4)

- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Zero-shot causal learning](https://mlsanity.com/paper/2301.12292/) (2023)
- [BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect](https://mlsanity.com/paper/2211.10793/) (2022)
- [Towards a Relationship-Aware Transformer for Tabular Data](https://mlsanity.com/paper/2512.07310/) (2025)

## Abstract (arXiv)

A new method for estimating the conditional average treatment effect is proposed in the paper. It is called TNW-CATE (the Trainable Nadaraya-Watson regression for CATE) and based on the assumption that the number of controls is rather large whereas the number of treatments is small. TNW-CATE uses the Nadaraya-Watson regression for predicting outcomes of patients from the control and treatment groups. The main idea behind TNW-CATE is to train kernels of the Nadaraya-Watson regression by using a weight sharing neural network of a specific form. The network is trained on controls, and it replaces standard kernels with a set of neural subnetworks with shared parameters such that every subnetwork implements the trainable kernel, but the whole network implements the Nadaraya-Watson estimator. The network memorizes how the feature vectors are located in the feature space. The proposed approach is similar to the transfer learning when domains of source and target data are similar, but tasks are different. Various numerical simulation experiments illustrate TNW-CATE and compare it with the well-known T-learner, S-learner and X-learner for several types of the control and treatment outcome functions. The code of proposed algorithms implementing TNW-CATE is available in https://github.com/Stasychbr/TNW-CATE.