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

arXiv: https://arxiv.org/abs/2310.16819 · HTML: https://mlsanity.com/paper/2310.16819/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 77 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Open Bandit Dataset and Pipeline: Towards Realistic and Reproducible Off-Policy Evaluation](https://mlsanity.com/paper/2008.07146/) (2020)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems](https://mlsanity.com/paper/1304.0282/) (2013)
- [Post-Selection Inference for Generalized Linear Models with Many Controls](https://mlsanity.com/paper/1304.3969/) (2013)
- [Semi-parametric efficiency bounds for high-dimensional models](https://mlsanity.com/paper/1601.00815/) (2016)
- [A Tree-based Semi-Varying Coefficient Model for the COM-Poisson Distribution](https://mlsanity.com/paper/2004.11810/) (2020)

## Built on by (most cited first, 2 of 2)

- [Triple/Debiased Lasso for Statistical Inference of Conditional Average Treatment Effects](https://mlsanity.com/paper/2403.03240/) (2024)
- [Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression](https://mlsanity.com/paper/2602.18958/) (2026)

## Abstract (arXiv)

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.