Collaborative Research: Generalized Fiducial Inference for Massive Data and High Dimensional Problems

协作研究：海量数据和高维问题的广义基准推理

• 批准号: 1512893
• 负责人: Jan Hannig
• 金额: $ 15万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1512893&HistoricalAwards=false
• 关键词: Collaborative; Research; Generalized; Fiducial; Inference

R. A. Fisher, the father of modern statistics, proposed the idea of Fiducial Inference in the 1930s. While his proposal led to some interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher's approach because it went against the ideas of statistical inference of the time. Beginning around the year 2000, the PIs and collaborators started to re-investigate the ideas of fiducial inference and discovered that Fisher's approach, when properly generalized, would open doors to solve many important and difficult problems of uncertainty quantification. The PIs termed their generalization of Fisher's ideas as generalized fiducial inference. After many years of preliminary investigations, the PIs developed a coherent, well thought out plan for a systematic research program in this area. A large part of this project develops practical solutions for different modeling problems that have natural applications in diverse fields. Finance (volatility estimation) and measurement science (calibration of measurements from different government labs, for example, US NIST) are two primary examples, while others include gene expression data, climate problems, recommender systems, and computer vision.This project is motivated by the success of generalized fiducial inference (GFI) as introduced by the PIs as a generalization of Fisher's fiducial argument. The PIs are now working towards scaling up their GFI methodology to handle big data problems and other difficult problems that have emerged due to our ability to collect massive amounts of data rapidly. In particular the PIs plan to conduct research into the following topics: (i) a thorough investigation of fundamental issues of GFI including connection with Approximate Bayesian Calculations and higher order asymptotics; (ii) sparse covariance estimation using GFI in the "large p small n" context; (iii) development of the idea of Fiducial Selector so that a sparsity of the fiducial distribution is induced as a natural outcome of a minimization problem; (iv) uncertainty quantification for the matrix completion problem using GFI, and (v) applications of GFI to a wide variety of practical problems, such as volatility estimation in finance and international key comparison experiments in measurement science.

现代统计学之父 R. A. Fisher 在 20 世纪 30 年代提出了基准推理的概念。 虽然他的提议带来了一些有趣的量化不确定性的方法，但当时的其他著名统计学家并不接受费舍尔的方法，因为它违背了当时统计推断的思想。 从 2000 年左右开始，PI 和合作者开始重新研究基准推理的想法，并发现费舍尔的方法如果得到适当的推广，将为解决不确定性量化的许多重要且困难的问题打开大门。 PI 将他们对费舍尔思想的概括称为广义基准推理。 经过多年的初步调查，PI 为该领域的系统研究计划制定了连贯的、深思熟虑的计划。 该项目的很大一部分是为不同领域的自然应用的不同建模问题开发实用的解决方案。 金融（波动性估计）和测量科学（不同政府实验室的测量校准，例如美国 NIST）是两个主要例子，其他包括基因表达数据、气候问题、推荐系统和计算机视觉。该项目的动机是广义基准推理 (GFI) 的成功，PI 引入了广义基准推理 (GFI)，作为费舍尔基准论证的概括。 PI 目前正在努力扩展其 GFI 方法，以处理大数据问题以及由于我们快速收集大量数据的能力而出现的其他难题。 特别是，PI 计划对以下主题进行研究：（i）彻底调查 GFI 的基本问题，包括与近似贝叶斯计算和高阶渐近学的联系； (ii) 在“大p小n”背景下使用GFI进行稀疏协方差估计； (iii) 发展基准选择器的思想，以便将基准分布的稀疏性作为最小化问题的自然结果而产生； (iv) 使用 GFI 对矩阵补全问题进行不确定性量化，以及 (v) GFI 在各种实际问题中的应用，例如金融中的波动性估计和测量科学中的国际关键比较实验。