Diffusion Model in Causal Inference with Unmeasured Confounders

TL;DR

This paper extends diffusion-based causal models to handle unmeasured confounders in observational data, improving the accuracy of counterfactual distribution estimation in causal inference.

Contribution

We propose the Backdoor Criterion based DCM (BDCM), an extension of the diffusion model that accounts for unmeasured confounders using the Backdoor criterion.

Findings

BDCM outperforms DCM in synthetic experiments with unmeasured confounders.

BDCM more accurately captures counterfactual distributions.

The model demonstrates robustness to unmeasured confounding in causal inference.

Abstract

We study how to extend the use of the diffusion model to answer the causal question from the observational data under the existence of unmeasured confounders. In Pearl's framework of using a Directed Acyclic Graph (DAG) to capture the causal intervention, a Diffusion-based Causal Model (DCM) was proposed incorporating the diffusion model to answer the causal questions more accurately, assuming that all of the confounders are observed. However, unmeasured confounders in practice exist, which hinders DCM from being applicable. To alleviate this limitation of DCM, we propose an extended model called Backdoor Criterion based DCM (BDCM), whose idea is rooted in the Backdoor criterion to find the variables in DAG to be included in the decoding process of the diffusion model so that we can extend DCM to the case with unmeasured confounders. Synthetic data experiment demonstrates that our proposed model captures the counterfactual distribution more precisely than DCM under the unmeasured confounders.