Modular Learning of Deep Causal Generative Models for High-dimensional
  Causal Inference
Md Musfiqur Rahman Murat Kocaoglu
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.