CATE Lasso: Conditional Average Treatment Effect Estimation with
  High-Dimensional Linear Regression
Masahiro Kato Masaaki Imaizumi
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.