CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression

• URL: http://arxiv.org/abs/2310.16819v1
• Date: Wed, 25 Oct 2023 17:51:07 GMT
• Title: CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression
• Authors: Masahiro Kato and Masaaki Imaizumi
• Abstract summary: Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect. We propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters.
• Score: 18.628644958430076
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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