Collaborative Research: New Regression Models and Methods for Studying Multiple Categorical Responses

合作研究：研究多重分类响应的新回归模型和方法

• 批准号: 2113590
• 负责人: Xin Zhang
• 金额: $ 10万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113590&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Regression; Models

In many areas of scientific study including bioengineering, epidemiology, genomics, and neuroscience, an important task is to model the relationship between multiple categorical outcomes and a large number of predictors. In cancer research, for example, it is crucial to model whether a patient has cancer of subtype A, B, or C and high or low mortality risk given the expression of thousands of genes. However, existing statistical methods either cannot be applied, fail to capture the complex relationships between the response variables, or lead to models that are difficult to interpret and thus, yield little scientific insight. The PIs address this deficiency by developing multiple new statistical methods. For each new method, the PIs will provide theoretical justifications and fast computational algorithms. Along with graduate and undergraduate students, the PIs will also create publicly available software that will enable applications across both academia and industry.This project aims to address a fundamental problem in multivariate categorical data analysis: how to parsimoniously model the joint probability mass function of many categorical random variables given a common set of high-dimensional predictors. The PIs will tackle this problem by using emerging technologies on tensor decompositions, dimension reduction, and both convex and non-convex optimization. The project focuses on three research directions: (1) a latent variable approach for the low-rank decomposition of a conditional probability tensor; (2) a new overlapping convex penalty for intrinsic dimension reduction in a multivariate generalized linear regression framework; and (3) a direct non-convex optimization-based approach for low-rank tensor regression utilizing explicit rank constraints on the Tucker tensor decomposition. Unlike the approach of regressing each (univariate) categorical response on the predictors separately, the new models and methods will allow practitioners to characterize the complex and often interesting dependencies between the responses.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.

在许多科学研究领域，包括生物工程，流行病学，基因组学和神经科学，一项重要的任务是对多个分类结果与大量预测因子之间的关系进行建模。例如，在癌症研究中，鉴于数千个基因的表达，对患者是否患有亚型A，B或C的癌症以及高死亡率风险至关重要。但是，现有的统计方法不能应用，无法捕获响应变量之间的复杂关系，或者导致难以解释的模型，因此很少产生科学见解。 PI通过开发多种新的统计方法来解决这种缺陷。对于每种新方法，PI将提供理论上的理由和快速的计算算法。与研究生和本科生一起，PIS还将创建公开可用的软件，该软件将在学术界和行业中都能进行应用程序。本项目旨在解决多变量分类数据分析中的基本问题：如何在高维预测者的常见集合中对许多分类随机变量的共同概率质量函数进行模仿。 PI将通过在张量分解，缩小尺寸以及凸和非凸优化方面使用新兴技术来解决此问题。该项目侧重于三个研究方向：（1）一种潜在的可变量方法，用于将条件概率张量的低级别分解； （2）多变量广义线性回归框架中固有维度降低的新重叠凸额； （3）一种基于直接的非凸优化方法，用于利用Tucker张量分解的显式等级约束，用于低级张量回归。与分别对预测因素的每个（单变量）分类响应进行回归的方法不同，新的模型和方法将使从业人员能够表征响应之间的复杂且经常有趣的依赖关系。该奖项反映了NSF的法定任务，并通过使用该基金会的智力优点和广泛的影响来评估CRITERIA审查CRITERIA。

项目成果

Envelopes and principal component regression

• DOI: 10.1214/23-ejs2154
• 发表时间: 2022-07
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Xin Zhang;Kai Deng;Qing Mai

An Efficient Convex Formulation for Reduced-Rank Linear Discriminant Analysis in High Dimensions

高维降阶线性判别分析的高效凸公式

• DOI: 10.5705/ss.202021.0047
• 发表时间: 2023
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Zeng, Jing;Zhang, Xin;Mai, Qing
• 通讯作者: Mai, Qing