Estimation, Computation, and Uncertainty Quantification in Structured Regression Models

结构化回归模型中的估计、计算和不确定性量化

基本信息

批准号：
1712822
负责人：
Bodhisattva Sen
金额：
$ 24万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2020-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712822&HistoricalAwards=false
关键词：
Estimation Computation Uncertainty Quantification Structured

项目摘要

In statistical modeling, regression is the primary tool to study the relationship between a response variable and a collection of predictors. In this research project, questions related to estimation, computation, and uncertainty quantification in some structured regression models will be investigated. The imposed "structure" refers to known features (domain knowledge) of a system and helps to reduce the complexity of the fitted statistical model/procedure. Further, imposing such structures yields interpretable (yet flexible) models. Special emphasis is given to methods applicable to multivariate data, an area that has received relatively less attention, though often necessary in performing effective data analysis. Some of the methodological development undertaken in this project will address important scientific questions arising from astronomical data. The investigator also plans to continue the tradition of mentoring undergraduate summer interns and to participate in the NYU GSTEM outreach program, a six-week summer program for high school girls.The three main topics pursued in this project are: (i) incorporating covariate information in multiple hypothesis testing problems; (ii) convexity constrained estimation and inference in regression models; and (iii) statistical methods that are geared towards detecting piecewise constant/affine structure in a (multivariate) regression function. New methodology will be developed to address these topics along with the development of efficient algorithms for computation. Further, a systematic theoretical study of these procedures, focusing on their adaptive (risk) properties, will be undertaken, and the important issues of inference and uncertainty quantification will be addressed. The intended applications of the research are diverse, ranging from estimation of radial velocity distribution of stars in a distant galaxy (astronomy), to developing methodology for detecting interactions between pairs of neurons (neuroscience), to estimating production and utility functions (economics), and to constructing confidence intervals for parameters in a continuous multivariate piecewise affine regression function (engineering).

在统计模型中，回归是研究响应变量与预测因子集合之间关系的主要工具。在该研究项目中，将研究与某些结构化回归模型中的估计，计算和不确定性定量有关的问题。施加的“结构”是指系统的已知特征（域知识），有助于降低拟合统计模型/程序的复杂性。此外，强加此类结构可产生可解释（但灵活的）模型。特别重点是适用于多元数据的方法，该方法受到相对较少的关注，尽管在进行有效的数据分析中通常是必不可少的。该项目中进行的一些方法论发展将解决由天文数据引起的重要科学问题。调查人员还计划继续指导本科暑期实习生并参加NYU GEG STEM STERRY计划，这是一个为期六周的高中女生计划。该项目中提到的三个主要主题是：（i）将协方差信息纳入多个假设测试问题；（ii）在回归模型中的凸度限制估计和推断；（iii）旨在检测（多元）回归函数中的分段常数/仿射结构的统计方法。将开发新的方法来解决这些主题，并开发有效的计算算法。此外，将对这些程序进行系统的理论研究，重点关注其适应性（风险）特性，并将解决推论和不确定性量化的重要问题。该研究的目的应用是多种多样的，从远处星系中恒星（天文学）的恒星的径向速度分布的估计到开发用于检测神经元之间相互作用的方法（神经科学）（神经科学）（神经科学）之间的相互作用，再到估计生产和实用性功能（经济学），以及用于连续性辅助调节的参数构建参数的构建置信区间。