Model-based clustering of high dimensional discrete data and compositional data

识别和分析种群的异质性是聚类分析的主要目标。通过聚类，我们可以将数据汇总成同质的观察组或观察群，其中每个群内的观测比群之间的观测更相似。基于模型的聚类利用了混合模型，在过去的二十年里得到了越来越多的应用。有限混合模型假定总体由子总体或成分的有限混合组成，每个子总体或成分都可以用一个参数模型来表示。根据数据的性质，选择适当的分布来对各种数据进行建模。申请者研究计划的长期目标是为生物数据集开发尖端统计算法，以全面了解生物过程。虽然生物信息学中的数据生成已经有了很大的爆炸性，但有效地分析这些复杂的生物数据集仍然是一个挑战。在资助期间，申请者的研究将集中于为高维和纵向离散数据和成分数据开发新的基于模型的聚类算法。这种分析面临的挑战包括组学数据集的大规模性质、数据类型的异质性以及统计模型缺乏可伸缩性，无法捕捉潜在数据生成机制的各种特征。提出的研究重点是开发高效和可扩展的统计模型，用于聚类高维数据和纵向组学数据。除了这些模型的发展，还将探讨基于模型的集群中的几个公开问题。当混合模型中的成分数量未知时，EM算法或其变体必须与模型选择标准结合使用，以便探索每一种可能数量的成分。这在计算上可能很昂贵，对同一数据使用不同的模型选择标准可能会导致选择不同的“最佳”拟合模型。到目前为止，关于模型选择问题的大部分工作都集中在连续数据上。一些工作将侧重于研究离散数据和成分数据的不同模型选择标准。研究一个有效的参数框架也将是一个关键的重点。提出的工作是在基于混合模型的多变量离散数据和成分数据的聚类方面向前迈出的重要一步。虽然拟议的研究将利用生物信息学数据集进行应用，但它们适用于文本分析、运动分析等许多领域中遇到的离散和成分数据。这些算法将作为开放源代码、用户友好的R包公开提供。这项工作的影响将主要集中在计算统计和生物信息学领域。

Identification and analysis of population heterogeneity is the primary goal of cluster analysis. Clustering allows us to summarize data into homogenous groups or clusters of observations where observations within each cluster are more similar than between clusters. Model-based clustering, which utilizes mixture models, has been increasingly used in the last two decades. A finite mixture model assumes that the population consists of a finite mixture of subpopulations or components, each of which can be represented by a parametric model. Depending on the nature of the data, appropriate distributions are chosen to model various kinds of data. The long-term goal of the applicant's research program is to develop cutting edge statistical algorithms for biological datasets to gain a comprehensive understanding of biological processes. While there has been a big explosion in data generation in bioinformatics, efficiently analyzing these complex biological data sets still remains a challenge. During the tenure of the grant, the applicant's research will focus on developing novel model-based clustering algorithms for high dimensional and longitudinal discrete data and compositional data. Challenges with such analyses include the large scale nature of omics datasets, heterogeneity in the data types, and a lack of scalability of statistical models that capture the various characteristics of the underlying data generating mechanisms. The proposed research focuses on developing efficient and scalable statistical models for clustering high dimensional data and longitudinal omics data. In addition to these model developments, several open problems in model-based clustering will be explored. When the number of components in a mixture model is unknown, the EM algorithm or a variant thereof must be used in conjunction with a model-selection criterion so that every possible number of components is explored. This can be computationally expensive and using different model selection criteria on the same data can result in selection of different `best' fitting models. To date, most work on the model selection issue has focused on continuous data. Some work will focus on investigation of different model-selection criteria for discrete data and compositional data in general. Investigation of an efficient parameter framework will also be a key focus. The proposed work presents a major step forward in mixture model-based clustering of multivariate discrete data and compositional data. While the proposed research will utilize bioinformatics datasets for applications, they are applicable to discrete and compositional data encountered in many fields such as text analytics, sport analytics, etc. These algorithms will be made available publicly as open source user-friendly R packages. The impact of this work will be primarily in the computational statistics and bioinformatics communities.