Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if ?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is in general not identifiable from the observed factual distribution. Nevertheless, in this work, we show that under the assumption that the main latent contributors to the treatment responses are categorical, the counterfactuals can be still reliably predicted. Building upon this assumption, we introduce CounterFactual Query Prediction (CFQP), a novel method to infer counterfactuals from continuous observations when the background variables are categorical. We show that our method significantly outperforms previously available deep-learning-based counterfactual methods, both theoretically and empirically on time series and image data. Our code is available at https://github.com/edebrouwer/cfqp.

翻译：反事实质问通常会问“如果呢?”追溯性的问题。估计反事实的标准方法在于使用准确反映基本数据生成过程的结构等式模型。然而,这些模型在实践中很少,通常希望仅从观测数据中推断出来。不幸的是,正确的结构等式模型一般无法从观察到的事实分布中识别出来。然而,在这项工作中,我们表明,假设治疗答复的主要潜在贡献者是绝对的,反事实仍然可以可靠地预测。基于这一假设,我们引入了反事实询问预测(CFQP),这是在背景变量明确时从持续观察中推断反事实的一种新颖方法。我们表明,我们的方法在理论上和经验上明显地超越了以往在时间序列和图像数据上基于深学习的反事实方法。我们的代码可以在https://github.com/edebroewer/cfqp上查阅。