Conditional Generative Models are Sufficient to Sample from Any Causal
  Effect Estimand
Md Musfiqur Rahman Matt Jordan Murat Kocaoglu
Causal inference from observational data has recently found many applications
in machine learning. While sound and complete algorithms exist to compute
causal effects, many of these algorithms require explicit access to conditional
likelihoods over the observational distribution, which is difficult to estimate
in the high-dimensional regime, such as with images. To alleviate this issue,
researchers have approached the problem by simulating causal relations with
neural models and obtained impressive results. However, none of these existing
approaches can be applied to generic scenarios such as causal graphs on image
data with latent confounders, or obtain conditional interventional samples. In
this paper, we show that any identifiable causal effect given an arbitrary
causal graph can be computed through push-forward computations of conditional
generative models. Based on this result, we devise a diffusion-based approach
to sample from any (conditional) interventional distribution on image data. To
showcase our algorithm's performance, we conduct experiments on a Colored MNIST
dataset having both the treatment ($X$) and the target variables ($Y$) as
images and obtain interventional samples from $P(y|do(x))$. As an application
of our algorithm, we evaluate two large conditional generative models that are
pre-trained on the CelebA dataset by analyzing the strength of spurious
correlations and the level of disentanglement they achieve.