Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects
Abstract
Estimating causal effects with continuous treatments in observational studies is challenging due to confounding, model misspecification, and high-dimensional covariates. We propose the Weighted Spline-Expanded Network (WSENet), an end-to-end neural framework that addresses these challenges by combining covariate balancing, structured treatment embedding, and bias-corrected outcome estimation. WSENet first applies Distance Covariate Optimal Weights to induce distributional independence between covariates and treatment without relying on parametric models. It then learns the conditional outcome via a structured network that fuses outcome-relevant representations of covariates with a spline-expanded treatment input, enabling smooth and flexible modeling of the dose-response relationship. To mitigate residual bias, we introduce Weighted Targeted Regularization, a correction technique based on efficient influence functions that yields a doubly robust estimator. Extensive evaluations on semi-synthetic and real-world datasets, including high-dimensional genomic and environmental health data, demonstrate that WSENet consistently outperforms existing baselines in both accuracy and stability.
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BibTeX
@misc{liu2026weighted,
title = {{Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects}},
author = {Shucheng Liu and Chan Park and Guanhua Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33740},
eprint = {2609.33740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33740},
}
RIS
TY - UNPB
TI - Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects
AU - Shucheng Liu
AU - Chan Park
AU - Guanhua Chen
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33740
UR - https://arxiv.org/abs/2609.33740
AB - Estimating causal effects with continuous treatments in observational studies is challenging due to confounding, model misspecification, and high-dimensional covariates. We propose the Weighted Spline-Expanded Network (WSENet), an end-to-end neural framework that addresses these challenges by combining covariate balancing, structured treatment embedding, and bias-corrected outcome estimation. WSENet first applies Distance Covariate Optimal Weights to induce distributional independence between covariates and treatment without relying on parametric models. It then learns the conditional outcome via a structured network that fuses outcome-relevant representations of covariates with a spline-expanded treatment input, enabling smooth and flexible modeling of the dose-response relationship. To mitigate residual bias, we introduce Weighted Targeted Regularization, a correction technique based on efficient influence functions that yields a doubly robust estimator. Extensive evaluations on semi-synthetic and real-world datasets, including high-dimensional genomic and environmental health data, demonstrate that WSENet consistently outperforms existing baselines in both accuracy and stability.
ER -