Unsupervised Structural-Counterfactual Generation under Domain Shift

TL;DR

This paper introduces an unsupervised method for generating counterfactual samples across domains by disentangling domain-intrinsic and effect-intrinsic causes using causal graphs and neural causal models, without requiring parallel data.

Contribution

It presents a novel framework combining causal graph integration, a new loss function, and neural causal models for cross-domain counterfactual generation under domain shift.

Findings

Accurately generates target domain counterfactuals closely matching ground truth.

Effectively disentangles domain-intrinsic and effect-intrinsic causes.

Framework aligns with conditional optimal transport when only causal mechanisms change.

Abstract

Motivated by the burgeoning interest in cross-domain learning, we present a novel generative modeling challenge: generating counterfactual samples in a target domain based on factual observations from a source domain. Our approach operates within an unsupervised paradigm devoid of parallel or joint datasets, relying exclusively on distinct observational samples and causal graphs for each domain. This setting presents challenges that surpass those of conventional counterfactual generation. Central to our methodology is the disambiguation of exogenous causes into effect-intrinsic and domain-intrinsic categories. This differentiation facilitates the integration of domain-specific causal graphs into a unified joint causal graph via shared effect-intrinsic exogenous variables. We propose leveraging Neural Causal models within this joint framework to enable accurate counterfactual generation under standard identifiability assumptions. Furthermore, we introduce a novel loss function that effectively segregates effect-intrinsic from domain-intrinsic variables during model training. Given a factual observation, our framework combines the posterior distribution of effect-intrinsic variables from the source domain with the prior distribution of domain-intrinsic variables from the target domain to synthesize the desired counterfactuals, adhering to Pearl's causal hierarchy. Intriguingly, when domain shifts are restricted to alterations in causal mechanisms without accompanying covariate shifts, our training regimen parallels the resolution of a conditional optimal transport problem. Empirical evaluations on a synthetic dataset show that our framework generates counterfactuals in the target domain that very closely resemble the ground truth.