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arXiv 2202.07098cs.LGstat.ME
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纵向数据自适应采样后的统计推断

Statistical Inference After Adaptive Sampling for Longitudinal Data

Harvard University(哈佛大学)

Kelly W. Zhang, Lucas Janson, Susan A. Murphy

AI总结:

针对多用户在线强化学习等自适应采样造成的纵向数据依赖,本文提出基于 Z 估计的分析方法和 adaptive 三明治方差估计量,实现一致方差估计与有效统计推断。

摘要:

在线强化学习及其他自适应采样算法正越来越多地用于数字干预实验,以便随时间推移为用户优化治疗提供方式。在本研究中,我们关注由一大类自适应采样算法收集的纵向用户数据;这些算法旨在利用来自多个用户的不断累积数据,在线优化治疗决策。跨用户合并或“汇集”数据,使自适应采样算法有可能更快学习。然而,这种汇集会使被采样的用户数据轨迹之间产生依赖;我们表明,这会导致针对独立同分布(i.i.d.)数据的标准方差估计量低估此类数据上常用估计量的真实方差。我们开发了新方法,通过 Z 估计对此类自适应采样数据执行多种统计分析。具体而言,我们提出 adaptive(自适应)三明治方差估计量,这是一种经过校正的三明治估计量,可在自适应采样下给出一致的方差估计。此外,为证明我们的结果,我们开发了用于非 i.i.d.、自适应采样纵向数据上经验过程的新理论工具,这些工具本身也可能具有独立价值。本工作的动机来自我们设计实验的实践:在这些实验中,在线强化学习算法优化治疗决策,而在实验结束后进行分析时,统计推断至关重要。

英文摘要:

Online reinforcement learning and other adaptive sampling algorithms are increasingly used in digital intervention experiments to optimize treatment delivery for users over time. In this work, we focus on longitudinal user data collected by a large class of adaptive sampling algorithms that are designed to optimize treatment decisions online using accruing data from multiple users. Combining or "pooling" data across users allows adaptive sampling algorithms to potentially learn faster. However, by pooling, these algorithms induce dependence between the sampled user data trajectories; we show that this can cause standard variance estimators for i.i.d. data to underestimate the true variance of common estimators on this data type. We develop novel methods to perform a variety of statistical analyses on such adaptively sampled data via Z-estimation. Specifically, we introduce the \textit{adaptive} sandwich variance estimator, a corrected sandwich estimator that leads to consistent variance estimates under adaptive sampling. Additionally, to prove our results we develop novel theoretical tools for empirical processes on non-i.i.d., adaptively sampled longitudinal data which may be of independent interest. This work is motivated by our efforts in designing experiments in which online reinforcement learning algorithms optimize treatment decisions, yet statistical inference is essential for conducting analyses after experiments conclude.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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