Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments
Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments
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发表时间：
2020-12
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通讯作者：
Rahul Singh
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作者：
Rahul Singh
负性控制是在存在未测量的混杂因素的情况下，了解治疗与结果之间因果关系的一种策略。然而，如果有两个辅助变量可用，则可以确定治疗效果：负控制治疗（对实际结果没有影响）和负控制治疗（不受实际治疗影响）。这些辅助变量也可以看作是一组传统控制变量的代理，它们与工具变量相似。我提出了一组基于核脊回归的算法，用于学习具有负控制的非参数处理效果。例子包括剂量响应曲线、分布移位的剂量响应曲线和非均质治疗效果。数据可以是离散的或连续的，也可以是低维、高维或无限维的。我证明了一致的一致性，并提供了有限的样本收敛率。我估计了吸烟对婴儿出生体重的剂量反应曲线，调整了由于家庭收入引起的未观察到的混淆，使用了1989年至1991年宾夕法尼亚州单胎出生的数据集。
Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regression for learning nonparametric treatment effects with negative controls. Examples include dose response curves, dose response curves with distribution shift, and heterogeneous treatment effects. Data may be discrete or continuous, and low, high, or infinite dimensional. I prove uniform consistency and provide finite sample rates of convergence. I estimate the dose response curve of cigarette smoking on infant birth weight adjusting for unobserved confounding due to household income, using a data set of singleton births in the state of Pennsylvania between 1989 and 1991.