Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. $\sqrt{n}$-consistent and asymptotically normal estimation of the object of interest requires debiasing to reduce the effects of regularization and/or model selection on the object of interest. Debiasing is typically achieved by adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality. We implement an automatic debiasing procedure based on automatically learning the Riesz representation of the linear functional using Neural Nets and Random Forests. Our method only relies on black-box evaluation oracle access to the linear functional and does not require knowledge of its analytic form. We propose a multitasking Neural Net debiasing method with stochastic gradient descent minimization of a combined Riesz representer and regression loss, while sharing representation layers for the two functions. We also propose a Random Forest method which learns a locally linear representation of the Riesz function. Even though our method applies to arbitrary functionals, we experimentally find that it performs well compared to the state of art neural net based algorithm of Shi et al. (2019) for the case of the average treatment effect functional. We also evaluate our method on the problem of estimating average marginal effects with continuous treatments, using semi-synthetic data of gasoline price changes on gasoline demand.
翻译:利益的许多因果关系和政策影响是由高维或非参数回归功能的线性功能界定的。 $\ sqrt{n} 美元一致且无症状地正常估计利息对象要求降低调整和(或)模式选择对利息对象的影响。 降低偏差通常通过在功能的插座估计器中添加一个修正术语来实现,该术语导致半参数效率、双强性和尼曼或直角性等属性。 我们根据自动学习神经网和随机森林线性功能的Riesz价格变化的自动脱差处理程序。 我们的方法仅依赖于黑箱评价和(或)线性功能选择模式的影响,并不要求了解其分析形式。 我们建议采用多功能性内线性网络脱差方法,将利兹代表的混合性梯度降为最小化,同时为两种功能共享代表层。 我们还建议一种随机森林方法,通过直线性法学习线性功能变化的Ries 直径直线性分析法。 我们用直径直径直径直的直径直径直径直线方法, 也用直径直径直径直径直对内等的直线性实验进行。