Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression
线性回归预测条件平均处理效应中的良性过拟合AI 解读 ↓
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线性回归预测条件平均处理效应中的良性过拟合
- 研究问题
- 在维度不断增长且处理分配改变样本分布时，完全拟合样本的线性模型能否准确预测条件平均处理效应，不同学习器表现如何？
- 方法与思路
- 作者将良性过拟合理论用于过参数化线性处理效应预测，比较分别拟合处理组的 T-learner 与基于倾向得分的 IPW-learner。
- 材料陈述的贡献
- 摘要称其设定下 T-learner 除随机分配外不一致，而已知倾向得分时 IPW-learner 风险可趋零，并以协方差特征子空间解释差异。
- 阅读关注点
- 应核对协方差谱与维度增长条件、风险的定义，以及已知倾向得分结论是否能够延伸至实际估计倾向得分的情形。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核验；摘要未列出完整定理条件，不能将结论推广为所有过参数化因果学习器的规律。
原文摘要
We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE), with linear regression models. As the development of machine learning for causal inference, a wide range of large-scale models for causality are gaining attention. One problem is that suspicions have been raised that the large-scale models are prone to overfitting to observations with sample selection, hence the large models may not be suitable for causal prediction. In this study, to resolve the suspicious, we investigate on the validity of causal inference methods for overparameterized models, by applying the recent theory of benign overfitting (Bartlett et al., 2020). Specifically, we consider samples whose distribution switches depending on an assignment rule, and study the prediction of CATE with linear models whose dimension diverges to infinity. We focus on two methods: the T-learner, which based on a difference between separately constructed estimators with each treatment group, and the inverse probability weight (IPW)-learner, which solves another regression problem approximated by a propensity score. In both methods, the estimator consists of interpolators that fit the samples perfectly. As a result, we show that the T-learner fails to achieve the consistency except the random assignment, while the IPW-learner converges the risk to zero if the propensity score is known. This difference stems from that the T-learner is unable to preserve eigenspaces of the covariances, which is necessary for benign overfitting in the overparameterized setting. Our result provides new insights into the usage of causal inference methods in the overparameterizated setting, in particular, doubly robust estimators.