Topics in unsupervised statistical learning

拟议的研究将开发在响应变量不可用或不完整的情况下进行数据分析的新方法，包括改进在这些情况下测量模型性能的技术。所提出的方法的主要应用之一是在一组数据中找到同质组。这种类型的分析用于科学、民用和工业调查的各种领域：如市场营销、生物信息学、流行病学、教育和运输。研究计划的一个特别重点将与非负面性质的数据有关。有几种情况下，像这样的数据自然出现，包括光谱学和数字图像。主要目标之一将是为这类数据的分析提供统计基础，特别是通过有限混合模型方法。这项研究的影响，实际上是大多数统计研究的影响，将是它在其他领域的应用。从这项研究中获得的统计方法的进步将导致在科学探究的应用领域进行更适当的调查模式。为了确保实现这些成果，所有的研究都将以发布开源软件供公众和其他研究人员使用的明确目标进行。

The proposed research will develop novel methods for data analysis in circumstances where response variables are unavailable or incomplete --- including improvements on techniques for measuring the performance of a model in those circumstances. One of the primary applications of the proposed methodologies is finding homogeneous groups within a set of data. This type of analysis is used in a variety of fields of scientific, civil, and industrial inquiry: such as marketing, bioinformatics, epidemiology, education, and transportation. A particular focus of the research program will be related to data of a non-negative nature. There are several contexts where data like this arises naturally, including spectroscopy and digital imagery. One of the primary goals will be providing a statistical foundation for the analysis of data of this type, specifically via a finite mixture model approach. The impact of this research, and indeed most statistical research, will be its application in other fields. The advancements in statistical methodology gained from this research will lead to more appropriate models for investigations being carried out in applied fields of scientific inquiry. To ensure that these gains are realized, all research will be undertaken with the explicit goal of releasing open-source software for the public and other researchers to utilize.