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

Causal effect estimation has been studied by many researchers when only
observational data is available. Sound and complete algorithms have been
developed for pointwise estimation of identifiable causal queries. For
non-identifiable causal queries, researchers developed polynomial programs to
estimate tight bounds on causal effect. However, these are computationally
difficult to optimize for variables with large support sizes. In this paper, we
analyze the effect of "weak confounding" on causal estimands. More
specifically, under the assumption that the unobserved confounders that render
a query non-identifiable have small entropy, we propose an efficient linear
program to derive the upper and lower bounds of the causal effect. We show that
our bounds are consistent in the sense that as the entropy of unobserved
confounders goes to zero, the gap between the upper and lower bound vanishes.
Finally, we conduct synthetic and real data simulations to compare our bounds
with the bounds obtained by the existing work that cannot incorporate such
entropy constraints and show that our bounds are tighter for the setting with
weak confounders.

本文分析了 “弱混淆” 的因果估计结果，提出了一种有效的线性规划方法来确定因果效应的上下界，并展示了与现有方法相比更紧密的界限，这些方法不能纳入熵限制。