Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression
This work provides a theoretically grounded approach for causal inference with continuous treatments, a known bottleneck in nonparametric causal effect estimation.
The authors propose a two-stage kernel ridge regression method for estimating continuous treatment effects, addressing confounding by correcting for distribution shift. Their method achieves provable adaptivity to overlap and kernel regularity.
We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on covariates, creating selection bias that makes direct regression of the response on treatment unreliable. To address this issue, we propose a two-stage kernel ridge regression method. In the first stage, we learn a model for the response as a function of both treatment and covariates; in the second stage, we use this model to construct pseudo-outcomes that correct for distribution shift, and then fit a second model to estimate the treatment effect. Although the response varies with both treatment and covariates, the induced effect function obtained by averaging over covariates is typically much simpler, and our estimator adapts to this structure. Furthermore, we introduce a fully data-driven model selection procedure that achieves provable adaptivity to both the unknown degree of overlap and the regularity (eigenvalue decay) of the underlying kernel.