# Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing

arXiv: https://arxiv.org/abs/2401.15447 · HTML: https://mlsanity.com/paper/2401.15447/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 27 Jan 2024.

## Builds on (most cited first, 16 of 16)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [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)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Training for the Future: A Simple Gradient Interpolation Loss to Generalize Along Time](https://mlsanity.com/paper/2108.06721/) (2021)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Adversarial Balancing for Causal Inference](https://mlsanity.com/paper/1810.07406/) (2018)
- [Generalization bounds and algorithms for estimating conditional average treatment effect of dosage](https://mlsanity.com/paper/2205.14692/) (2022)

## Built on by (most cited first, 7 of 7)

- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [PairNet: Training with Observed Pairs to Estimate Individual Treatment Effect](https://mlsanity.com/paper/2406.03864/) (2024)
- [Sources of Gain: Decomposing Performance in Conditional Average Dose Response Estimation](https://mlsanity.com/paper/2406.08206/) (2024)
- [Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time](https://mlsanity.com/paper/2507.07271/) (2025)
- [Disentangled Representation via Variational AutoEncoder for Continuous Treatment Effect Estimation](https://mlsanity.com/paper/2406.02310/) (2024)
- [Leveraging a Simulator for Learning Causal Representations from Post-Treatment Covariates for CATE](https://mlsanity.com/paper/2502.05037/) (2025)
- [A Computational Theory for Efficient Mini Agent Evaluation with Causal Guarantees](https://mlsanity.com/paper/2503.21138/) (2025)

## Abstract (arXiv)

We address the Individualized continuous treatment effect (ICTE) estimation problem where we predict the effect of any continuous-valued treatment on an individual using observational data. The main challenge in this estimation task is the potential confounding of treatment assignment with an individual's covariates in the training data, whereas during inference ICTE requires prediction on independently sampled treatments. In contrast to prior work that relied on regularizers or unstable GAN training, we advocate the direct approach of augmenting training individuals with independently sampled treatments and inferred counterfactual outcomes. We infer counterfactual outcomes using a two-pronged strategy: a Gradient Interpolation for close-to-observed treatments, and a Gaussian Process based Kernel Smoothing which allows us to downweigh high variance inferences. We evaluate our method on five benchmarks and show that our method outperforms six state-of-the-art methods on the counterfactual estimation error. We analyze the superior performance of our method by showing that (1) our inferred counterfactual responses are more accurate, and (2) adding them to the training data reduces the distributional distance between the confounded training distribution and test distribution where treatment is independent of covariates. Our proposed method is model-agnostic and we show that it improves ICTE accuracy of several existing models.