Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand

Md Musfiqur Rahman, Matt Jordan, Murat Kocaoglu

Primary Area: causal reasoning

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Keywords: Causality, Causal inference, Structural causal models, Causal graphs, Causal effect, Generative models, Diffusion models

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TL;DR: We propose a diffusion-based approach to sample from any identifiable interventional or conditional interventional distribution given an arbitrary causal graph containing latent confounders.

Abstract: The ability to apply causal reasoning from observational data has made causal inference algorithms widely adopted in machine learning applications. While there exist sound and complete algorithms to compute causal effects, these algorithms require explicit access to conditional likelihoods over the observational distribution. In the high dimensional regime, conditional likelihoods are difficult to estimate. To alleviate this issue, researchers have approached the causal effect estimation problem by simulating causal relations with neural models. However, none of these existing approaches can be applied to generic scenarios such as causal graphs having latent confounders and obtaining conditional interventional samples. In this paper, we show that any identifiable causal effect given an arbitrary causal graph containing latent confounders can be computed through push-forward computations using trained conditional generative models. Based on this observation, we devise a diffusion-based approach to sample from any such interventional or conditional interventional distribution. To showcase our algorithm's performance, we conduct experiments on a semi-synthetic Colored MNIST dataset having both the intervention ($X$) and the target variable ($Y$) as images and present interventional image samples from $P(Y|do(X))$. We also perform a case study on a real-world COVIDx chest X-ray image dataset to demonstrate our algorithm's utility.

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Submission Number: 8014