Finite multivariate density mixtures: applications and new approaches

有限多元密度混合物：应用和新方法

• 批准号: 2311103
• 负责人: Michael Levine
• 金额: $ 16万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311103&HistoricalAwards=false
• 关键词: Finite; multivariate; density; mixtures; applications

Cluster analysis and classification of multivariate datasets are two of the most important tasks in modern statistical and data sciences. By leveraging copula-based density mixtures, this project will introduce new methods for clustering and classification of multivariate data which exhibit sophisticated dependence properties. The proposed methods will provide more reliable clustering solutions that could be in turn used, for example, for development of new therapeutic drugs and more precise quantification of gene interactions. This project will involve students, both at the undergraduate and graduate levels, to work on the computational aspects of this interdisciplinary research. The particular focus of the project will be on bolstering broader participation in statistical sciences and involvement of mentees from the underrepresented groups. Many of the students will be recruited through the National Alliance for Doctoral Studies in the Mathematical Sciences (commonly called simply “Math Alliance”) that is headquartered at Purdue University.Multivariate mixture models are widely applicable in many areas of statistics. They are particularly useful in clustering and classification of multivariate high-dimensional data. The majority of model-based clustering techniques for multivariate data are based on multivariate normal models and their direct generalizations. However, this approach is quite restrictive since, in most cases, it is difficult to model clusters of non-elliptical shapes. Even where it is possible, these models tend to be limited in their capabilities to cluster multivariate data of mixed types that include both continuous and discrete random variables. This project will develop an alternative to the existing model-based clustering methods for multivariate data. This alternative is based on using copula-based density mixtures which will allow for modeling a vast variety of dependence structures. Furthermore, the proposed solution will also allow for the principled clustering of datasets containing both continuous and discrete observations. The immediate outcome of this project will be the development of a family of computationally efficient algorithms. Such algorithms will provide reliable clustering of objects under the minimal assumptions. The proposed methodology will be widely applicable to such areas as clustering of genes and other biological entities in transcriptomics data as well as clustering of text documents, where the number of dimensions may be equal to the size of the vocabulary.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.

多元数据集的聚类分析和分类是现代统计和数据科学中最重要的两个任务。通过利用基于Copula的密度混合物，该项目将引入新的方法，用于聚类和分类多元数据，这些数据暴露了复杂的依赖性属性。所提出的方法将提供更可靠的聚类溶液，例如用于开发新的治疗药物和基因相互作用的更精确的量化。该项目将涉及本科和研究生级别的学生，以研究这项跨学科研究的计算方面。该项目的特定重点将是加强对统计科学的更广泛参与以及代表性不足的群体的月经的参与。许多学生将通过总部位于普渡大学（Purdue University）的数学科学博士研究（通常称为“数学联盟”）中的全国博士研究联盟（通常称为“数学联盟”）。它们在多元高维数据的聚类和分类中特别有用。大多数用于多元数据的基于模型的聚类技术基于多元正常模型及其直接概括。但是，这种方法是非常限制的，因为在大多数情况下，很难对非胸腔形状的簇进行建模。即使在可能的情况下，这些模型的功能也倾向于聚集混合类型的多元数据，包括连续和离散随机变量。该项目将开发用于多元数据的现有基于模型的聚类方法的替代方法。该替代方法基于使用基于副群体的密度混合物，该混合物将允许建模各种依赖性结构。此外，所提出的解决方案还将允许包含连续观察和离散观察的数据集的主要聚类。该项目的直接结果将是开发一个计算有效算法的家族。这种算法将在最小假设下提供对象的可靠聚类。所提出的方法将广泛适用于转录组学数据中基因和其他生物学实体等领域，以及文本文档的聚类，其中维度的数量可能等于词汇的大小。该奖项反映了NSF的法定任务，并通过使用基金会的智力效果和广泛的评估来评估支持，并被认为是珍贵的支持。