Estimation and Computation for Multivariate Classification and Mixture Problems

多元分类和混合问题的估计和计算

• 批准号: 9802522
• 负责人: Rabindra Bhattacharya
• 金额: $ 6.42万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802522&HistoricalAwards=false
• 关键词: Estimation; Computation; Multivariate; Classification; Mixture

9802522Bernhard FluryThis research focuses on methods of classification in multivariate statistics, studying theoretical, practical, and computational aspects. The investigator explores finite mixture models with an "improper" component, i.e., a component in which each data point has the same density value. This leads to a flexible class of estimators that depend on the setting of a tuning parameter. For the extreme values of the tuning parameter, the resulting methods of estimation correspond to fully parametric maximum likelihood, and to nonparametric likelihood (empirical distribution function), respectively. The estimators are useful for contaminated data, and their performance is compared to traditional robust estimators. The main computational tool is an application of the EM algorithm. In another problem related to finite mixture analysis the investigator studies the question of dimensionality: if interest focuses on a subset of variables measured, should one use only that particular subsetfor the purpose of estimating the parameters of the mixture, or should one use the remaining variables ("covariates") as well? In addition, this research develops the asymptotic distribution theory for maximum likelihood estimators in multivariate models that are usually regarded as untractable by conventional methods (common canonical variates, partial common principal components, the discrimination subspace model, and others), and investigates iterative computational methods needed for estimating their parameters.Methods of classification play an increasingly important role in areas such as remote sensing, pattern and speech recognition, and taxonomy. The investigator studies methods of estimation and computation in multivariate situations, i.e., when many variables are measured on the same objects. In particular, the finite mixture model used in this research allows us to improve statistical methodology in situations where the data is distorted by errors and outliers. Efficient computational methods developed in this research allow us to exploit this powerful methodology, and to make it applicable to problems in many areas, including biotechnoloy and environmental sciences. Further research topics involve models of allometric growth in biology, improved estimation in unsupervised methods of classification, the development of efficient computational algorithms for recentlycreated multivariate methods of data analysis, and the analysis of periodic phenomena in biology.

9802522Bernhard Flury本研究侧重于多元统计中的分类方法，研究理论，实践和计算方面。 研究者探索了具有“不适当”成分的有限混合模型，即，其中每个数据点具有相同密度值的分量。 这导致了一个灵活的类的估计，依赖于调整参数的设置。 对于调整参数的极值，所得到的估计方法对应于完全参数最大似然，和非参数似然（经验分布函数），分别。 估计是有用的污染数据，和他们的性能相比，传统的鲁棒估计。 主要的计算工具是EM算法的应用。 在另一个问题有关的有限混合物分析的调查研究的问题的维度：如果兴趣集中在一个子集的变量测量，应该只使用特定的subsetfor估计参数的混合物的目的，还是应该使用剩余的变量（“协变量”）以及？ 此外，本研究发展了通常被认为是难以处理的多元模型中最大似然估计量的渐近分布理论（共同典型变量、部分共同主成分、判别子空间模型等），分类方法在遥感等领域发挥着越来越重要的作用，传感、模式和语音识别以及分类学。 研究者研究多变量情况下的估计和计算方法，即，当在同一物体上测量许多变量时。特别是，在这项研究中使用的有限混合模型，使我们能够改善统计方法的情况下，数据被扭曲的错误和离群值。 在这项研究中开发的高效计算方法使我们能够利用这种强大的方法，并使其适用于许多领域的问题，包括生物技术和环境科学。 进一步的研究课题涉及生物学中的异速生长模型，改进无监督分类方法的估计，为最近创建的多变量数据分析方法开发有效的计算算法，以及生物学中周期现象的分析。