CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression
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CATE Lasso：高维线性回归中的条件平均处理效应估计
- 研究问题
- 当两个潜在结果的线性模型参数高维且各自不稀疏时，能否利用共同参数在差分中抵消的结构，一致估计条件平均处理效应？
- 方法与思路
- 作者将参数分为处理特有部分和两模型相同的共同部分，以效应差异的隐式稀疏性为基础，构造专门估计CATE的Lasso方法。
- 材料陈述的贡献
- 摘要称，在所提出的隐式稀疏性下，无需两个潜在结果模型的参数分别稀疏，也能得到CATE估计的一致性，并提供模拟检验。
- 阅读关注点
- 应核对隐式稀疏性的精确定义、处理分配与潜在结果识别条件，以及高维设计、惩罚参数和共同参数估计对一致性的要求。
- 阅读边界
- 这是arXiv预印本，同行评审或接收状态未核实；摘要未说明处理效应的识别假设、误差界及非线性情况下的适用范围。
原文摘要
In causal inference about two treatments, Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect, defined as a difference between the expected outcomes of the two treatments conditioned on covariates. This study assumes two linear regression models between a potential outcome and covariates of the two treatments and defines CATEs as a difference between the linear regression models. Then, we propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters. In our study, we demonstrate that desirable theoretical properties, such as consistency, remain attainable even without assuming sparsity explicitly if we assume a weaker assumption called implicit sparsity originating from the definition of CATEs. In this assumption, we suppose that parameters of linear models in potential outcomes can be divided into treatment-specific and common parameters, where the treatment-specific parameters take difference values between each linear regression model, while the common parameters remain identical. Thus, in a difference between two linear regression models, the common parameters disappear, leaving only differences in the treatment-specific parameters. Consequently, the non-zero parameters in CATEs correspond to the differences in the treatment-specific parameters. Leveraging this assumption, we develop a Lasso regression method specialized for CATE estimation and present that the estimator is consistent. Finally, we confirm the soundness of the proposed method by simulation studies.