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.

在包括生物工程、流行病学、基因组学和神经科学在内的许多科学研究领域，一项重要任务是对多个分类结果和大量预测变量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，建模患者是否患有 A、B 或 C 亚型癌症以及高或低死亡率风险至关重要。然而，现有的统计方法要么无法应用，要么无法捕捉响应变量之间的复杂关系，要么导致模型难以解释，从而产生很少的科学见解。 PI 通过开发多种新的统计方法来解决这一缺陷。对于每一种新方法，PI 都将提供理论依据和快速计算算法。 PI 还将与研究生和本科生一起创建公开可用的软件，以支持学术界和工业界的应用。该项目旨在解决多元分类数据分析中的一个基本问题：如何对许多变量的联合概率质量函数进行简约建模给定一组通用的高维预测变量的分类随机变量。 PI 将通过使用张量分解、降维以及凸和非凸优化等新兴技术来解决这个问题。该项目重点关注三个研究方向：（1）条件概率张量低秩分解的潜变量方法； (2) 多元广义线性回归框架中用于内在降维的新的重叠凸罚分； (3) 一种基于直接非凸优化的低秩张量回归方法，利用 Tucker 张量分解的显式秩约束。与单独回归预测变量的每个（单变量）分类响应的方法不同，新的模型和方法将允许从业者描述响应之间复杂且通常有趣的依赖关系。该奖项反映了 NSF 的法定使命，并被认为值得通过以下方式获得支持：使用基金会的智力价值和更广泛的影响审查标准进行评估。

项目成果

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: 2023-01
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Zeng, Jing;Zhang, Xin;Mai, Qing
• 通讯作者: Mai, Qing

Envelopes and principal component regression

包络线和主成分回归

• DOI: 10.1214/23-ejs2154
• 发表时间: 2023-01
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Zhang, Xin;Deng, Kai;Mai, Qing
• 通讯作者: Mai, Qing