CAREER: Maximum likelihood and nonparametric empirical Bayes methods in high dimensions

职业：高维中的最大似然和非参数经验贝叶斯方法

• 批准号: 1454817
• 负责人: Lee Dicker
• 金额: $ 40万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1454817&HistoricalAwards=false
• 关键词: CAREER; Maximum; likelihood; nonparametric; empirical

The investigator is combining classical and elegant ideas from statistics (empirical Bayes, mixture models, and nonparametric maximum likelihood), with important recent breakthroughs in computing to help develop a rigorous, practical framework for many problems in modern data analysis. Applications in genomics and other areas of biology where high-throughput data are generated form an important part of the project. Beyond biology, the methods developed during the course of the project are expected to have applications in finance (e.g. fraud detection), machine learning (e.g. speech, text, and pattern recognition), and other fields where vast high-dimensional datasets are being rapidly generated and require accurate, incisive analysis. Another important aspect of the project addresses questions about reproducibility, which have come to the forefront in many applications involving high-dimensional data analysis. To address these questions, the investigator is studying fundamental properties of statistical risk and risk estimation in high dimensions. Algorithms and methods developed during the course of the project are being implemented in easy-to-use and freely available software packages. Project research is closely integrated with education, via graduate student training and newly developed courses for graduate and undergraduate students.The main objective of the project is to develop new methodologies, computational strategies, and theoretical results for the use of nonparametric maximum likelihood (NPML) techniques and empirical Bayes methods in high-dimensional data analysis. This work is fundamentally related to the analysis of nonparametric mixture models. Empirical Bayes methods have a long and rich history in statistics, and are particularly well-suited to high-dimensional problems. Moreover, recent computational results and convex approximations have greatly simplified the implementation of NPML-based methods. Leveraging these computational breakthroughs, the investigator is developing novel and scalable NPML-based methods for high-dimensional classification, high-dimensional regression, and other statistical problems. New still-faster algorithms for computing NPML estimators, which take advantage of certain types of sparsity in the estimated mixing-measure, are also being developed. The investigator is studying theoretical properties of the proposed methods in high-dimensional settings. Areas of emphasis for theoretical analysis include convergence rates and frequentist risk properties of the proposed empirical Bayes methods.

这位研究人员正在将统计学(经验贝叶斯、混合模型和非参数最大似然)的经典和优雅思想与最近在计算方面的重要突破相结合，以帮助为现代数据分析中的许多问题开发一个严格、实用的框架。产生高通量数据的基因组学和其他生物学领域的应用是该项目的重要组成部分。除了生物学，在项目过程中开发的方法有望应用于金融(例如欺诈检测)、机器学习(例如语音、文本和模式识别)以及其他领域，在这些领域，海量高维数据集正在快速生成，需要准确、深刻的分析。该项目的另一个重要方面涉及可再现性问题，在涉及高维数据分析的许多应用中，这一问题已经走到了前列。为了解决这些问题，研究人员正在研究高维统计风险和风险估计的基本性质。在项目过程中开发的算法和方法正在易于使用和免费提供的软件包中实施。项目研究与教育紧密结合，通过研究生培训和为研究生和本科生新开发的课程。该项目的主要目标是开发新的方法、计算策略和理论结果，以便在高维数据分析中使用非参数最大似然(NPML)技术和经验贝叶斯方法。这项工作从根本上与非参数混合模型的分析有关。经验贝叶斯方法在统计学上有着悠久而丰富的历史，特别适合于高维问题。此外，最近的计算结果和凸近似大大简化了基于NPML的方法的实现。利用这些计算突破，研究人员正在开发基于NPML的新颖且可扩展的方法，用于高维分类、高维回归和其他统计问题。用于计算NPML估计量的新的更快的算法也在开发中，该算法利用了估计的混合测量中的某些类型的稀疏性。研究人员正在研究所提出方法在高维环境下的理论性质。理论分析的重点领域包括所提出的经验贝叶斯方法的收敛速度和频率风险性质。