针对高维结果的反事实分布学习，提出几何自适应平滑方法提升稳定性与精度。
Geometry Adaptive Counterfactual Distribution Learning with Diffusion-Guided Smoothing
- 用扩散得分引导局部化，实现与结果几何结构匹配的自适应平滑
- 误差衰减更快，稳定性和精度优于传统方法，在CelebA实验中表现显著
- 适合处理高维嵌入数据的因果推断，尤其在低维流形结构上有效
我们研究高维结果反事实分布学习，其分布可能集中在低维结构附近。标准各向同性平滑忽略此几何特性，导致不良的缩放行为和不稳定的局部推断。本文提出半参数去偏、扩散引导的平滑反事实密度及其梯度估计器。这些估计器结合因果干扰项调整与由学习到的扩散得分驱动的几何自适应定位，获得二阶干扰余项，并使平滑与局部结果几何一致。我们推导了渐近展开式、集成风险界及平滑密度与史坦泛函的联合推断，扩展至环境密度与梯度目标在额外逼近条件下的情形。风险界中的方差项由平滑算子的集中性决定：合适的几何条件可实现内在而非环境尺度的缩放，而显式的漂移项量化了几何估计的成本。基于CelebA的半合成实验表明，几何自适应一步法具有更快的误差衰减和更高的稳定性，展示了其在高维嵌入中的适用性。
原文摘要 · Abstract (English)
We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure. Standard isotropic smoothing ignores this geometry, leading to unfavorable scaling and unstable local inference. We propose semiparametrically debiased, diffusion-guided estimators for smoothed counterfactual densities and their scores. These estimators combine causal nuisance adjustment with geometry-adaptive localization driven by a learned diffusion score, yielding second-order nuisance remainders while aligning smoothing with local outcome geometry. We derive asymptotic expansions, integrated risk bounds, and simultaneous inference for smoothed densities and Stein functionals, with extensions to ambient density and score targets under additional approximation conditions. The variance term in the risk bounds is governed by the concentration of the smoothing operator: suitable geometric conditions yield intrinsic rather than ambient scaling, while an explicit drift term quantifies the cost of estimating the geometry. CelebA-based semi-synthetic experiments show faster error decay and improved stability for geometry-adaptive one-step methods, illustrating their applicability to high-dimensional embeddings.
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