Abstract:We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference. We propose two diffusion-guided estimators based on semiparametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores. The estimators combine causal nuisance adjustment with geometry-adaptive localization driven by diffusion score information, removing first-order nuisance bias while aligning smoothing with local outcome geometry. We establish asymptotic expansions, risk bounds, and inference procedures for smoothed density and score-based targets, with ambient density inference obtained under additional approximation conditions. Under structural geometry conditions, the leading stochastic error is governed by an effective dimension induced by the diffusion-guided kernel, rather than by the ambient dimension. Semi-synthetic experiments based on CelebA show steeper error decay for geometry-adaptive methods, supporting the proposed effective-dimension theory.
| Subjects: | Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2605.25811 [stat.ME] |
| (or arXiv:2605.25811v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25811 arXiv-issued DOI via DataCite (pending registration) |
From: Kwangho Kim [view email]
[v1]
Mon, 25 May 2026 13:02:56 UTC (4,103 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。