CAREER: Inference with graphs: density skeleton and Markov missing graph

职业：图推理：密度骨架和马尔可夫缺失图

基本信息

批准号：
2141808
负责人：
Yen-Chi Chen
金额：
$ 40万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2027-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2141808&HistoricalAwards=false
关键词：
CAREER Inference graphs density skeleton

项目摘要

This project introduces novel frameworks for using graphs in analyzing complex datasets. These new applications of graphs allow researchers to investigate the intricate relation among quantities of interest. The newly developed methods will offer novel directions for studying the growth and evolution of a galaxy. The PI also plans to develop methodologies to handle complex missing data problems in the National Alzheimer's Coordinating Center's database. The project highlights how abstract mathematical objects like graphs offer a unified treatment on problems arising from different fields such as astronomy and dementia studies. The PI will also initiate several new educational programs and engage both graduate and undergraduate students in research in various ways. The PI plans to investigate two novel research directions of applying graphs to statistical problems. In the first direction, the PI develops a novel graphical approach called density skeleton, an undirected graph summarizing the shape of the covariate distribution. The PI will study how to apply density skeleton to various statistical learning problems, including regression, algorithmic fairness, and topological data analysis. In the second part of the project, the PI develops a new graph-based method called Markov missing graph to handle missing data problems. The Markov missing graph defines an identifying assumption to recover the missing entries' distribution. The PI intends to study how the modeling, computation, and efficiency theory interacts with graph geometry.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.

该项目介绍了用于分析复杂数据集的新颖框架。这些图表的这些新应用使研究人员能够研究关注量之间的复杂关系。新开发的方法将为研究银河系的生长和演变提供新的方向。 PI还计划开发方法，以处理国家阿尔茨海默氏症协调中心的数据库中复杂的缺失数据问题。该项目强调了诸如图形之类的抽象数学对象如何提供有关由天文学和痴呆症研究等不同领域引起的问题的统一处理。 PI还将启动几个新的教育计划，并以各种方式让研究生和本科生参与研究。 PI计划研究将图形应用于统计问题的两个新型研究方向。在第一个方向上，PI开发了一种新型的图形方法，称为密度骨骼，这是一个无方向的图，总结了协变量分布的形状。 PI将研究如何将密度骨骼应用于各种统计学习问题，包括回归，算法公平性和拓扑数据分析。在项目的第二部分中，PI开发了一种基于图形的新方法，称为Markov缺少图形来处理缺失的数据问题。马尔可夫丢失图定义了一个识别假设，以恢复缺失条目的分布。 PI打算研究建模，计算和效率理论如何与图形几何相互作用。该奖项反映了NSF的法定任务，并使用基金会的智力优点和更广泛的影响评估标准，认为值得通过评估来获得支持。