Bayesian Global-Local Shrinkage in High Dimensions

高维贝叶斯全局局部收缩

• 批准号: 1613063
• 负责人: Anindya Bhadra
• 金额: $ 10万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613063&HistoricalAwards=false
• 关键词: Bayesian; Global; Local; Shrinkage; Dimensions

High-dimensional data are ubiquitous in many modern applications such as genomics, finance, and image analysis. Developing approaches that are computationally scalable to the size of these data sets while retaining strong theoretical justifications remains a challenge. The goal of the project is to develop new methodology to enable tractable analysis of modern high-dimensional data sets. Software developed from this research will be made publicly available.Bayesian methodology for high-dimensional data traditionally relies on point mass mixture priors that have attractive theoretical properties but often scale poorly due to the computational difficulties associated with searching a high-dimensional discrete space. The goal of the project is to explore the use of global-local alternatives to high-dimensional problems. Many recent investigations using global-local priors, while showing signs of promise, have been restricted to studying the simple normal means model. The PIs will employ the techniques of global-local shrinkage to problems of fundamental interest in statistics, such as regression, nonlinear function estimation and covariance estimation. More specifically, the PIs aim to show in regression problems that using global-local shrinkage instead of purely global shrinkage methods such as ridge regression or principal components regression can result in improved prediction. They aim to show global-local shrinkage priors are good candidates for non-informative analysis of low-dimensional functions of high-dimensional parameters. The PIs also propose to use global-local shrinkage in covariance estimation and joint mean-covariance estimation problems and apply the developed methodology in suitable applications arising from genomics or finance.

高维数据在许多现代应用中无处不在，例如基因组学，金融和图像分析。开发在计算上可扩展到这些数据集的大小同时保留强大理论依据的方法仍然是一个挑战。该项目的目的是开发新的方法，以实现对现代高维数据集的可进行分析。从这项研究开发的软件将被公开使用。用于高维数据的Bayesian方法传统上依赖于具有吸引人理论属性的点质量混合先验，但由于与搜索高维离散空间相关的计算困难，因此通常会缩放较差。该项目的目的是探索全球本地替代方案的高维问题。许多使用全球本地先验的调查虽然表现出诺言，但仍仅限于研究简单的正常手段模型。 PI将利用全球本地收缩的技术来解决统计学的基本兴趣问题，例如回归，非线性功能估计和协方差估计。更具体地说，PI的目的是显示回归问题，这些问题使用全球本地收缩而不是纯粹的全球收缩方法，例如脊回归或主要成分回归可以改善预测。他们的目的是显示全部本地收缩率是对高维参数低维功能的非信息分析的良好候选者。 PI还建议在协方差估计和联合均值协方差估计问题中使用全球本地收缩率，并将开发的方法应用于基因组学或金融的适当应用中。

项目成果

Joint mean–covariance estimation via the horseshoe

通过马蹄形进行联合均值协方差估计

• DOI: 10.1016/j.jmva.2020.104716
• 发表时间: 2021
• 期刊: Journal of Multivariate Analysis
• 影响因子: 1.6
• 作者: Li, Yunfan;Datta, Jyotishka;Craig, Bruce A.;Bhadra, Anindya
• 通讯作者: Bhadra, Anindya