提出新方法精准估计治疗效果的分布差异。
Conditional Counterfactual Mean Embeddings: Doubly Robust Estimation and Learning Rates
- 将反事实结果分布嵌入核空间，构建可学习的统计框架。
- 三种具体算法均具备双重稳健性，收敛速度快于现有方法。
- 适合因果推断、医疗决策等需分析个体化效果的场景。
理解异质性治疗效应的关键在于刻画潜在结果的完整条件分布。为此，我们提出条件反事实均值嵌入（CCME）框架，将反事实结果的条件分布嵌入再生核希尔伯特空间（RKHS）。在此框架下，我们设计一种两阶段元估计器，支持任意RKHS值回归。基于该元估计器，开发了三种实用的CCME估计器：(1) 岭回归估计器，(2) 深度特征估计器（用神经网络参数化特征映射），(3) 神经-核估计器（以神经网络参数化系数进行RKHS值回归）。我们为所有估计器提供了有限样本收敛率，证明其具备双重稳健性。实验表明，这些估计器能准确恢复包括多模态结构在内的条件反事实分布特征。
原文摘要 · Abstract (English)
A complete understanding of heterogeneous treatment effects involves characterizing the full conditional distribution of potential outcomes. To this end, we propose the Conditional Counterfactual Mean Embeddings (CCME), a framework that embeds conditional distributions of counterfactual outcomes into a reproducing kernel Hilbert space (RKHS). Under this framework, we develop a two-stage meta-estimator for CCME that accommodates any RKHS-valued regression in each stage. Based on this meta-estimator, we develop three practical CCME estimators: (1) Ridge Regression estimator, (2) Deep Feature estimator that parameterizes the feature map by a neural network, and (3) Neural-Kernel estimator that performs RKHS-valued regression, with the coefficients parameterized by a neural network. We provide finite-sample convergence rates for all estimators, establishing that they possess the double robustness property. Our experiments demonstrate that our estimators accurately recover distributional features including multimodal structure of conditional counterfactual distributions.
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