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.

提出了名为 Modular-DCM 的算法，利用预训练模型可以可靠地对高维数据进行因果查询，并从可识别的干预和反事实分布中采样。

高维因果推断的深层因果生成模型的模块化学习

Modular Learning of Deep Causal Generative Models for High-dimensional  Causal Inference

We propose a formalization of the three-tier causal hierarchy of association,
intervention, and counterfactuals as a series of probabilistic logical
languages. Our languages are of strictly increasing expressivity, the first
capable of expressing quantitative probabilistic reasoning -- including
conditional independence and Bayesian inference -- the second encoding
do-calculus reasoning for causal effects, and the third capturing a fully
expressive do-calculus for arbitrary counterfactual queries. We give a
corresponding series of finitary axiomatizations complete over both structural
causal models and probabilistic programs, and show that satisfiability and
validity for each language are decidable in polynomial space.

本研究将 3 层因果关系层次结构分为概率逻辑语言模型，第一层表达定量概率推断，第二层编码用于因果效应的 do-calculus 推理，第三层捕捉任意反事实查询。相关的公理化表达完全考虑了因果模型和概率编程，并证明了每种语言的可满足性和有效性都可以在多项式空间内可判定。