Convolutional neural networks (CNN) have been successful in machine learning applications. Their success relies on their ability to consider space invariant local features. We consider the use of CNN to fit nuisance models in semiparametric estimation of the average causal effect of a treatment. In this setting, nuisance models are functions of pre-treatment covariates that need to be controlled for. In an application where we want to estimate the effect of early retirement on a health outcome, we propose to use CNN to control for time-structured covariates. Thus, CNN is used when fitting nuisance models explaining the treatment and the outcome. These fits are then combined into an augmented inverse probability weighting estimator yielding efficient and uniformly valid inference. Theoretically, we contribute by providing rates of convergence for CNN equipped with the rectified linear unit activation function and compare it to an existing result for feedforward neural networks. We also show when those rates guarantee uniformly valid inference. A Monte Carlo study is provided where the performance of the proposed estimator is evaluated and compared with other strategies. Finally, we give results on a study of the effect of early retirement on hospitalization using data covering the whole Swedish population.

翻译：卷积神经网络（CNN）在机器学习应用中取得了成功。其成功依赖于其能够考虑空间不变局部特征的能力。我们考虑利用CNN来拟合半参数估计中的干扰模型，以估计治疗的平均因果效应。在此背景下，干扰模型是需控制的前处理协变量的函数。在一项旨在估计提前退休对健康结果影响的应用中，我们提出使用CNN来控制时间结构化协变量。因此，在拟合解释治疗和结果的干扰模型时使用CNN。这些拟合结果随后被整合到增广逆概率加权估计量中，从而得到高效且一致有效的推断。在理论方面，我们贡献了配备整流线性单元激活函数的CNN的收敛速率，并将其与前馈神经网络的现有结果进行了比较。我们还展示了这些速率何时能保证一致有效推断。通过蒙特卡罗研究评估了所提议估计量的性能，并与其他策略进行了比较。最后，我们使用覆盖整个瑞典人口的数据，报告了关于提前退休对住院治疗影响的研究结果。