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

研究者正在将统计学中的经典和优雅的思想（经验贝叶斯，混合模型和非参数最大似然）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。在基因组学和其他产生高通量数据的生物学领域的应用是该项目的重要组成部分。除了生物学之外，项目过程中开发的方法预计将在金融（例如欺诈检测），机器学习（例如语音，文本和模式识别）以及其他快速生成大量高维数据集并需要准确，深刻分析的领域中得到应用。该项目的另一个重要方面是解决关于再现性的问题，这在许多涉及高维数据分析的应用中已经成为最前沿。为了解决这些问题，研究者正在研究统计风险和高维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现。通过研究生培训和新开发的研究生和本科生课程，项目研究与教育紧密结合。该项目的主要目标是为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开发新的方法、计算策略和理论结果。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中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极大地简化了基于npml的方法的实现。利用这些计算上的突破，研究者正在为高维分类、高维回归和其他统计问题开发新颖的、可扩展的基于npml的方法。计算NPML估计器的更快的新算法也正在开发中，这些算法利用了估计的混合度量中的某些稀疏性。研究者正在研究在高维环境下提出的方法的理论性质。理论分析的重点领域包括提出的经验贝叶斯方法的收敛率和频率风险特性。

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.