Pearl's causal hierarchy establishes a clear separation between observational, interventional, and counterfactual questions. Researchers proposed sound and complete algorithms to compute identifiable causal queries at a given level of the hierarchy using the causal structure and data from the lower levels of the hierarchy. However, most of these algorithms assume that we can accurately estimate the probability distribution of the data, which is an impractical assumption for high-dimensional variables such as images. On the other hand, modern generative deep learning architectures can be trained to learn how to accurately sample from such high-dimensional distributions. Especially with the recent rise of foundation models for images, it is desirable to leverage pre-trained models to answer causal queries with such high-dimensional data. To address this, we propose a sequential training algorithm that, given the causal structure and a pre-trained conditional generative model, can train a deep causal generative model, which utilizes the pre-trained model and can provably sample from identifiable interventional and counterfactual distributions. Our algorithm, called Modular-DCM, uses adversarial training to learn the network weights, and to the best of our knowledge, is the first algorithm that can make use of pre-trained models and provably sample from any identifiable causal query in the presence of latent confounders with high-dimensional data. We demonstrate the utility of our algorithm using semi-synthetic and real-world datasets containing images as variables in the causal structure.

翻译：Pearl因果层次结构明确了观察性、干预性与反事实问题之间的清晰界限。研究者提出了利用低层级因果结构及数据来计算层级中可识别因果查询的完备算法。然而，多数算法假设能准确估计数据的概率分布，这对图像等高维变量而言是不切实际的。另一方面，现代生成式深度学习架构可通过训练准确学习从这类高维分布中采样。特别是随着图像基础模型的兴起，利用预训练模型处理高维数据的因果查询成为迫切需求。为此，我们提出一种序列训练算法：给定因果结构和预训练条件生成模型后，可训练深度因果生成模型，该模型能利用预训练模型并可从可识别的干预分布与反事实分布中可证明地采样。该算法称为Modular-DCM，采用对抗训练学习网络权重，据我们所知，这是首个能利用预训练模型、在高维数据存在潜在混淆变量的情况下可证明地从任何可识别因果查询中采样的算法。我们通过包含图像变量的半合成与真实世界数据集，展示了该算法的实用性。