用两阶段核岭回归估计连续处理效应，避免混淆偏差。
Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression
- 先建模响应与处理、协变量的关系，再构造伪结果修正分布偏移。
- 无需估计条件处理密度，学习误差更优，可适应重叠度和核谱衰减。
- 适合处理存在复杂协变量依赖的连续干预效应分析。
我们研究连续处理效应函数的估计问题，该函数将每个处理值映射到总体平均结果。核心挑战是混淆：处理分配常依赖于协变量，导致选择偏差，使响应对处理的直接回归不可靠。为此，我们提出两阶段核岭回归方法。第一阶段学习响应作为处理和协变量函数的模型；第二阶段利用该模型构建纠正分布偏移的伪结果，并拟合第二个模型以估计处理效应。尽管响应同时依赖处理和协变量，但对协变量平均后的效应函数通常更简单，我们的估计器能自适应这一结构。最优学习界在不估计条件处理密度的前提下实现，从而绕过现有方法的主要瓶颈。此外，我们引入完全数据驱动的模型选择过程，可证明地适应未知重叠程度和底层核的谱衰减。
原文摘要 · Abstract (English)
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. Our optimal learning bounds are achieved without estimating the conditional treatment density, thereby bypassing a major bottleneck in existing methods. Furthermore, we introduce a fully data-driven model selection procedure that achieves provable adaptivity to both the unknown degree of overlap and the spectral decay of the underlying kernel.
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