To reach human level intelligence, learning algorithms need to incorporate causal reasoning. But identifying causality, and particularly counterfactual reasoning, remains elusive. In this paper, we make progress on counterfactual inference in nonseparable outcome models by utilizing instrumental variables (IVs). IVs are a classic tool for mitigating bias from unobserved confounders when estimating causal effects. While IV methods for effect estimation have been extended to nonseparable outcome models under different assumptions, existing IV approaches to counterfactual prediction typically assume one-dimensional outcomes and additive noise. In this paper, we show that under standard IV assumptions, along with the assumption that the outcome function is invertible and has a triangular structure, then the treatment-outcome relationship becomes identifiable from observed data. We furthermore propose a method to learn the outcome function utilizing normalizing flows. This outcome function estimator can then be used to perform counterfactual inference. We refer to the method as Flow IV.

翻译：为达到人类水平的智能，学习算法需要融入因果推理能力。但识别因果关系，尤其是反事实推理，仍然难以实现。本文通过利用工具变量（IVs），在非可分结果模型的反事实推断方面取得了进展。工具变量是估计因果效应时缓解未观测混杂因素偏差的经典工具。尽管在不同假设下，用于效应估计的IV方法已扩展到非可分结果模型，但现有的反事实预测IV方法通常假设一维结果和加性噪声。本文证明，在标准IV假设以及结果函数可逆且具有三角结构的前提下，处理-结果关系可从观测数据中识别。此外，我们提出了一种利用归一化流学习结果函数的方法。该结果函数估计器随后可用于执行反事实推断。我们将该方法称为Flow IV。