CIF: EAGER: Statistical Inference and Decision-Making With Sequential Samples

现代世界拥有丰富的数据来源，这些数据为潜在的随机现象提供了宝贵的见解。然而，由于测量限制或隐私保护，这些数据通常只提供关于潜在现象的间接或不精确的信息。该项目开发了有效的算法，使用顺序样本来推断隐藏的随机现象，并使用这些知识来做出决策。该项目的成果将提高数据驱动的决策和推理的效率和准确性，广泛应用于营销和推荐系统、云计算、制造业和医疗保健等领域。研究人员将把研究成果发布给广大学术界和专业人士，并通过研究生和本科生课程将其纳入教学课程。本项目研究的框架由一个隐藏的随机变量（或随机向量）组成，可以通过选择几种测量机制（称为臂）之一来间接采样。在选择其中一个臂时，观察到隐藏随机变量的实现的任意函数，而不是直接样本。在这个框架内，研究人员追求的问题包括：i）最大化通过在相关的多臂强盗设置中对不同的武器进行采样而获得的奖励;以及ii）使用最少数量的样本来估计隐藏随机变量的概率分布。这些研究重点将通过三个主要目标进行研究：1）通过累积遗憾的界限和估计分布的误差来了解问题的基本限制; 2）设计满足基本限制的高效采样算法;和3）在现实世界的数据集上验证所提出的算法。由于武器之间的相关性，该项目偏离了经典的多臂强盗框架，由于数据生成的顺序性和多保真度性，该项目也偏离了经典的统计推断。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The modern world is rich with diverse sources of data that provide invaluable insights into underlying random phenomena. The data, however, generally provide only indirect or imprecise information about the latent phenomena due to measurement limitations or privacy protections. This project develops efficient algorithms to use sequential samples to infer a hidden random phenomenon and use this knowledge to make decisions. Outcomes of the project will improve the efficiency and accuracy of data-driven decision-making and inference in a wide range of applications such as marketing and recommendation systems, cloud computing, manufacturing, and health care. The investigators will publish the research outcomes to broad academic and professional audiences and incorporate them into teaching curricula via graduate and undergraduate courses.The framework studied in this project consists of a hidden random variable (or, a random vector) that can be indirectly sampled by choosing one of several measurement mechanisms (referred to as arms). Upon choosing one of the arms, an arbitrary function of a realization of the hidden random variable is observed, instead of a direct sample. Within this framework, the investigators pursue problems including i) maximizing the reward obtained by sampling different arms in a correlated multi-armed bandit setting; and ii) estimating the probability distribution of the hidden random variable using minimum number of samples. These research thrusts will be studied with three main goals: 1) understanding the fundamental limits of the problem via bounds on the cumulative regret, and the error in the estimated distribution; 2) designing efficient sampling algorithms that meet the fundamental limits; and 3) validating the proposed algorithms on real-world datasets. The project deviates from the classic multi-armed bandit framework due to the correlation between arms and from the classic statistical inference due to the sequential and multi-fidelity nature of the data generation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.