Logistic部分线性模型的双/去偏机器学习
Double/Debiased Machine Learning for Logistic Partially Linear Model
摘要：
我们提出了双/去偏机器学习方法来推断（在参数率）的Logistic部分线性模型的参数组件与二进制响应以下的条件Logistic模型的低维线性参数函数的一些关键（暴露）协变量和非参数函数调整其他协变量的混杂效应。我们考虑一个内曼正交（双鲁棒）评分方程组成的两个滋扰功能：非参数组件的logistic模型和条件平均值的暴露在其他协变量和响应固定。为了估计滋扰模型，我们分别考虑使用高维（HD）稀疏参数模型和更一般的（通常是非参数的）机器学习（ML）方法。在HD的情况下，我们推导出一定的矩方程来校准的滋扰模型的一阶偏差，并授予我们的方法模型的双重鲁棒性的意义上说，我们的估计达到理想的速率时，至少有一个滋扰模型是正确指定的，他们都是超稀疏的。在ML情况下，logit链接的非线性使得使用任意条件均值学习算法来估计逻辑模型的干扰分量比部分线性设置要困难得多。我们通过一种新的完整模型改装过程来处理这个障碍，该过程易于实现，并且便于在我们的框架中使用非参数ML算法。我们的ML估计器在与Escherichukov等人相同的意义上具有双重鲁棒性。（2018 a）。我们通过模拟研究评估了我们的方法，并将其应用于评估紧急避孕药（EC）对早期妊娠胎儿的影响，并于2008年在智利进行了政策改革（Bentancor和Clarke，2017）。
英文摘要：
We propose double/debiased machine learning approaches to infer (at the parametric rate) the parametric component of a logistic partially linear model with the binary response following a conditional logistic model of a low dimensional linear parametric function of some key (exposure) covariates and a nonparametric function adjusting for the confounding effect of other covariates. We consider a Neyman orthogonal (doubly robust) score equation consisting of two nuisance functions: nonparametric component in the logistic model and conditional mean of the exposure on the other covariates and with the response fixed. To estimate the nuisance models, we separately consider the use of high dimensional (HD) sparse parametric models and more general (typically nonparametric) machine learning (ML) methods. In the HD case, we derive certain moment equations to calibrate the first-order bias of the nuisance models and grant our method a model double robustness property in the sense that our estimator achieves the desirable rate when at least one of the nuisance models is correctly specified and both of them are ultra-sparse. In the ML case, the non-linearity of the logit link makes it substantially harder than the partially linear setting to use an arbitrary conditional mean learning algorithm to estimate the nuisance component of the logistic model. We handle this obstacle through a novel full model refitting procedure that is easy-to-implement and facilitates the use of nonparametric ML algorithms in our framework. Our ML estimator is rate doubly robust in the same sense as Chernozhukov et al. (2018a). We evaluate our methods through simulation studies and apply them in assessing the effect of emergency contraceptive (EC) pill on early gestation foetal with a policy reform in Chile in 2008 (Bentancor and Clarke, 2017).
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