Numerical Construction of Optimal Estimators Using Machine Learning Tools

最佳的统计程序可以最大限度地利用现有数据，从而更精确、更经济地回答紧迫的科学问题。这些程序传统上是通过分析计算得出的，需要经过多年培训获得的专业知识。在这个项目中，研究人员将研究两种新的策略来获得最优程序。与现有的方法相比，这些策略需要更多的计算方法方面的专业知识，而较少的统计理论方面的专业知识。因此，这个项目将扩大能够开发最佳统计程序的研究人员的范围。如果初步结果支持新方法的强大性能，研究人员将把它们纳入疫苗临床试验数据分析。通过这个项目，研究人员将吸引本科生参与统计研究，并促进他们所指导的研究生的理解。研究人员将考虑局部和全局最优的概念。第一种策略将使用有效影响函数（EIF）的新表示。EIF是构造渐近有效估计的关键因素，特别是在非参数和半参数模型中。它还提供了一种有原则的方法来消除基于机器学习的估计器，以恢复有效的统计推断。不幸的是，推导EIF的传统方法涉及高级理论，而这些理论在统计课程中往往没有教授。此外，在一些问题中，EIF没有一个封闭的形式，使得它即使对专家来说也很难使用。研究人员将推导出一种新的EIF表示，使其适合计算机化，并研究如何使用它来推导出新的渐近有效估计量。第二种策略将使用深度强化学习的思想，最近用于构建具有超人性能的自学习游戏算法，并使用计算工具对抗式学习（全局和局部）最小最大最优统计过程。除一些简单的情况外，解析计算迄今为止只成功地用于推导渐近极小极大最优的估计量。然而，渐近最优性通常不能保证小样本的最优性。现有的在数值上学习极大极小最优估计的工作使用极大极小问题的贝叶斯公式。这种表述导致的学习方案在计算上过于繁琐，无法适用于大多数问题。这个项目将开发和研究另一种方法来构建这些可以很容易地利用大规模并行计算的估计器。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Optimal statistical procedures make maximal use of available data, making it possible to answer pressing scientific questions more precisely and cost-effectively. These procedures are traditionally derived via analytic calculations that require expert knowledge achieved over many years of training. In this project, the investigators will study two novel strategies for deriving optimal procedures. Compared to existing approaches, these strategies require more expertise in computational methods and less expertise in statistical theory. As a result, this project will broaden the pool of researchers who can develop optimal statistical procedures. If preliminary results support the strong performance of the new methods, the investigators will incorporate them into vaccine clinical trial data analyses. Through this project, the investigators will engage undergraduates in statistical research and advance the understanding of mentored graduate students.The investigators will consider both local and global notions of optimality. The first strategy will use novel representations of the efficient influence function (EIF). The EIF is a critical ingredient for constructing asymptotically efficient estimators, particularly in nonparametric and semiparametric models. It also provides a principled approach to debias machine learning-based estimators to recover valid statistical inference. Unfortunately, the conventional approach for deriving the EIF involves advanced theory that is often not taught in statistical curricula. Additionally, in some problems, the EIF does not have a closed form, rendering its use difficult even for experts. The investigators will derive a novel representation of the EIF that lends itself to computerization and study how it can be used to derive novel asymptotically efficient estimators. The second strategy will use ideas from deep reinforcement learning, as used recently to build self-learning game playing algorithms with super-human performance, to adversarially learn (globally and locally) minimax optimal statistical procedures with computational tools. Except in simple cases, analytic calculations have thus far only been successfully used to derive estimators that are asymptotically minimax optimal. However, asymptotic optimality does not generally guarantee optimality in small samples. Existing works on numerically learning minimax optimal estimators use a Bayesian formulation of the minimax problem. This formulation results in learning schemes that are too computationally prohibitive to be applicable to most problems. This project will develop and study an alternative means to construct these estimators that can readily leverage massively parallel computing.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.