提出首个自适应数据收集下的分布效应分析方法，可精准捕捉均值与高阶矩变化。
Kernel Treatment Effects with Adaptively Collected Data
- 用核方法在再生核希尔伯特空间中建模干预后分布差异
- 在自适应实验中保持类型一错误率，对均值和高阶矩变化均有效
- 适合需要分析复杂分布变化的因果推断场景
自适应实验通过根据历史结果调整处理分配来提升效率，但这种自适应性破坏了经典渐近理论依赖的独立同分布假设。同时，许多关注问题属于分布层面，超越平均效应。核处理效应（KTE）通过在再生核希尔伯特空间（RKHS）中表示干预后结果分布，并利用核距离进行比较，提供了一种灵活的框架。本文首次构建了在自适应数据收集下进行分布推断的核方法。该方法结合双重稳健的RKHS评分与在某一折上学习的见证函数，使用投影且逐次标准化的标量统计量在另一折上进行推断，保证了有效的类型一误差控制。实验表明，该方法在均值变化和高阶矩差异检测上均表现良好，优于仅限于标量效应的自适应基线方法。
原文摘要 · Abstract (English)
Adaptive experiments improve efficiency by adjusting treatment assignments based on past outcomes, but this adaptivity breaks the i.i.d.\ assumptions that underpin classical asymptotics. At the same time, many questions of interest are distributional, extending beyond average effects. Kernel treatment effects (KTE) provide a flexible framework by representing interventional outcome distributions in an RKHS and comparing them via kernel distances. We present the first kernel-based framework for distributional inference under adaptive data collection. Our method combines doubly robust RKHS scores with a witness function learned on one fold, and performs inference on a second fold using a projected, sequentially normalized scalar statistic with valid type-I error. Experiments show that the resulting procedure is well calibrated and effective for both mean shifts and higher-moment differences, outperforming adaptive baselines limited to scalar effects.
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