Hugh Dance, Johnny Xi, Peter Orbanz, Benjamin Bloem-Reddy
原文摘要
Estimating the full counterfactual distribution under an intervention is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational distributions and marginal counterfactual distributions over outcomes are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any outcome features which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.
Many causal inference problems require sampling from interventional outcome distributions rather than estimating low-dimensional summaries. Existing approaches often rely on fitting generative models of the target distribution together with additional nuisance components, which can be computationally demanding for high-dimensional outcomes. We propose Interventional Maximum Mean Discrepancy Flow (IMMD-Flow), a particle-based method that instead represents the target interventional distribution through its kernel mean embedding. This kernel embedding admits a doubly robust, Neyman-orthogonal estimator with finite-sample guarantees and can be efficiently reused to sample from the interventional distribution via MMD gradient flow. IMMD-Flow accommodates both hard and soft interventions, admits theoretical guarantees for estimation and particle approximation, and extends to high-dimensional image outcomes through frozen encoders. Across image-based benchmarks, IMMD-Flow matches or improves upon state-of-the-art generative approaches while showing significant speed advantages.