噪声分布影响因果推断效果，非高斯噪声下新方法更优
It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation
- 提出基于累积量的新型估计器，提升对干扰项误差的鲁棒性
- 在非高斯噪声下，新方法比传统双机器学习更优，理论最优
- 适用于对干扰项估计不敏感的场景，适合因果推断研究者
结构无关因果推断研究在仅能获得黑箱机器学习估计的干扰函数（如混杂因素对处理和结果的影响）时，如何准确估计处理效应。本文发现，答案意外地依赖于处理噪声的分布。聚焦于Robinson（1988）提出的部分线性模型，我们首先证明广泛采用的双机器学习（DML）估计器在高斯处理噪声下达到极小极大率最优，解决了Mackey等（2018）提出的开放问题。而在独立非高斯处理噪声下，我们构造出新的实际可行方法，具有更高阶鲁棒性，可实现对干扰项误差的r阶不敏感性，只要第(r+1)阶处理累积量非零。我们还为二值处理情形在部分线性模型中给出了新颖的极小极大保证。最后，通过合成需求估计实验，展示了高阶鲁棒估计器的实际优势。
原文摘要 · Abstract (English)
Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the answer depends in a surprising way on the distribution of the treatment noise. Focusing on the partially linear model of \citet{robinson1988root}, we first show that the widely adopted double machine learning (DML) estimator is minimax rate-optimal for Gaussian treatment noise, resolving an open problem of \citet{mackey2018orthogonal}. Meanwhile, for independent non-Gaussian treatment noise, we show that DML is always suboptimal by constructing new practical procedures with higher-order robustness to nuisance errors. These \emph{ACE} procedures use structure-agnostic cumulant estimators to achieve $r$-th order insensitivity to nuisance errors whenever the $(r+1)$-st treatment cumulant is non-zero. We complement these core results with novel minimax guarantees for binary treatments in the partially linear model. Finally, using synthetic demand estimation experiments, we demonstrate the practical benefits of our higher-order robust estimators.
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