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

基本信息

批准号：
1512945
负责人：
Thomas Chun Man Lee
金额：
$ 15万
依托单位：
University of California-Davis
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=1512945&HistoricalAwards=false
关键词：
Collaborative Research Generalized Fiducial Inference

项目摘要

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.

现代统计的父亲R. A. Fisher提出了1930年代基准推论的想法。尽管他的提议导致了一些有趣的方法来量化不确定性，但当时的其他杰出统计学家并不接受费舍尔的方法，因为这违背了当时的统计推断。从2000年左右开始，PIS和合作者开始重新调查信托推断的想法，并发现Fisher的方法在正确概括后将打开大门，以解决许多不确定性量化的重要和困难的问题。 PIS称他们对Fisher的思想的概括是普遍的信托推断。经过多年的初步研究，PIS制定了一项连贯，经过深思熟虑的计划，该计划在该领域进行了系统的研究计划。该项目的很大一部分为在不同领域具有自然应用的不同建模问题开发了实用解决方案。金融（波动率估计）和测量科学（例如，来自不同政府实验室的测量值的校准）是两个主要示例，而其他示例包括基因表达数据，气候问题，推荐系统和计算机视觉。 PIS引入了普遍的基准推断（GFI）的成功，这是因为Fisher的基准论证的概括。 PI现在正在努力扩大其GFI方法，以处理大数据问题和其他困难问题，这些问题由于我们能够快速收集大量数据而出现。特别是PIS计划对以下主题进行研究：（i）对GFI的基本问题进行彻底调查，包括与近似贝叶斯计算和高阶渐近学的联系；（ii）使用GFI在“大P小N”上下文中使用GFI的稀疏协方差估计；（iii）发展基准选择者的思想，以使基准分布的稀疏性被诱导为最小化问题的自然结果；（iv）使用GFI的矩阵完成问题的不确定性量化，以及（v）GFI在各种实际问题上的应用，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。