An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

翻译：因果推断中一个基础且具有挑战性的问题是从观测数据中估计因果效应。当存在未观测混杂变量时，该问题变得更加困难。前门调整是处理未观测混杂变量的一种实用方法。然而，标准前门调整的限制条件在实践中难以满足。本文通过提出条件前门（CFD）调整概念，放宽了部分限制条件，并建立了确保CFD调整因果效应可识别性的定理。此外，由于实践中通常无法直接获得CFD变量，因此需要从数据中学习该变量。我们利用深度生成模型的能力，提出CFDiVAE方法，通过可识别变分自编码器直接从数据中学习CFD调整变量的表示，并形式化证明了模型的可识别性。在合成数据集上的大量实验验证了CFDiVAE的有效性及其相较于现有方法的优越性。实验结果还表明，CFDiVAE的性能对未观测混杂变量的因果强度敏感性较低。我们进一步将CFDiVAE应用于真实数据集，展示了其潜在的应用价值。