Sampling Interventional Distributions with Orthogonal MMD Flow
Bariscan Bozkurt, Hugh Dance, Zonghao Chen, Alexandre Galashov, Arthur Gretton, Houssam Zenati
Abstract
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.