Puli Aahlad, Perotte Adler J, Ranganath Rajesh
Computer Science, New York University, New York, NY 10011.
Biomedical Informatics, Columbia University, New York, NY 10032.
Adv Neural Inf Process Syst. 2020 Dec;33:5115-5125.
Causal inference relies on two fundamental assumptions: and . We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting EFC. In this setting ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called and a sufficient condition for effect estimation of these interventions called . Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE's effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC.
和 。当真实混杂因素值可以表示为观测数据的函数时，我们研究因果推断；我们将这种情况称为EFC。在这种情况下，可忽略性得到满足，但正性被违反，一般来说因果推断是不可能的。我们考虑两种因果效应可估计的情况。首先，我们讨论对称为 的部分处理的干预以及这些干预效应估计的一个充分条件，称为 。其次，我们基于函数混杂因素和真实结果函数的梯度场，为非参数效应估计制定条件。为了在这些条件下估计效应，我们开发了水平集正交下降估计（LODE）。此外，我们证明了LODE效应估计的误差界，在模拟数据和真实数据上评估我们的方法，并通过实证证明了EFC的价值。
