We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in high-dimensional settings. To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting, using a conditional density ratio estimator. Using this transformation, we successfully estimate nonparametric functions defined under conditional moment restrictions. Our proposed framework is general and can be applied to a wide range of methods, including neural networks. We analyze the estimation error, providing theoretical support for our proposed method. In experiments, we confirm the soundness of our proposed method.
翻译:我们考虑在有条件时刻限制下学习因果关系。与无条件时刻限制下的因果关系推断不同,有条件时刻限制对因果关系推断构成严重的挑战,特别是在高维环境中。为了解决这一问题,我们提议了一种方法,通过重量加权将有条件时刻限制转化为无条件时刻限制,使用一个有条件密度比率估计仪。我们利用这种转变,成功地估计了有条件时刻限制下定义的非参数功能。我们提议的框架是一般性的,可以适用于包括神经网络在内的多种方法。我们分析了估算错误,为拟议方法提供了理论支持。在实验中,我们确认了我们拟议方法的健全性。