Numerical Construction of Optimal Estimators Using Machine Learning Tools

最佳的统计程序最大限度地利用了现有数据，使其有可能更准确和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，这些计算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得出最佳程序的新策略。与现有的方法相比，这些策略需要更多的计算方法专业知识和较少的统计理论专业知识。因此，该项目将扩大能够制定最佳统计程序的研究人员队伍。如果初步结果支持新方法的强劲表现，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，研究人员将让本科生从事统计研究，并增进对被指导研究生的理解。调查人员将考虑局部和全球的最优概念。第一种策略将使用有效影响函数(EIF)的新表示法。EIF是构造渐近有效估计量的关键因素，特别是在非参数和半参数模型中。它还为基于去偏机器学习的估计量恢复有效的统计推断提供了一种原则性的方法。不幸的是，推导EIF的传统方法涉及的高级理论往往不在统计课程中教授。此外，在一些问题上，EIF没有封闭的形式，这使得即使是专家也很难使用它。研究人员将推导出适合于计算机化的EIF的新表示，并研究如何使用它来得出新的渐近有效的估计器。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博弈算法，使用计算工具反向学习(全局和局部)极小极大最优统计过程。除了简单的情况外，到目前为止，分析计算只成功地用于导出渐近极小极大最优的估计器。然而，在小样本情况下，渐近最优性通常不能保证最优性。现有的关于数值学习极小极大最优估计器的工作使用了极小极大问题的贝叶斯公式。这种形式导致的学习方案在计算上过于困难，不适用于大多数问题。该项目将开发和研究一种替代方法来构建这些估计器，该方法可以方便地利用大规模并行计算。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.