New Directions in Bayesian Change-Point Analysis

贝叶斯变点分析的新方向

• 批准号: 2015460
• 负责人: Nilabja Guha
• 金额: $ 14万
• 依托单位: University of Massachusetts Lowell
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-15 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015460&HistoricalAwards=false
• 关键词: New; Directions; Bayesian; Change; Point; New; Directions; Bayesian; Change; Point

Almost all dynamic and random processes in nature go through sudden and significant structural changes. Often the change is in the observable quantity, e.g. fuel prices or stock indices or crime activities changing significantly in response to a change in an unobservable, latent factor such as an economic phenomenon or a public policy change, or a disease outbreak. Such ‘change-points’ are routinely observed across all scientific disciplines and applications, such as economics, epidemiology, social sciences, cybersecurity and finance. Specific examples could be changing regression when the observed variable depends on predictors through a mean structure that changes with time, or change points in data with massive dimensions, such as high-resolution imaging data or complex connected graphs. While there is a substantial literature proposing elaborate methods for detecting change points in different settings, there has been limited consideration of Bayesian methods for change-points in hierarchical models with complex dependence or sparsity structures. This research fills this gap with new statistical tools motivated by specific real-life applications, by developing theoretical framework while retaining efficiency and usefulness in current applications. The project integrates graduate education and training with statistical research, and emphasizes upholding societal and ethical considerations that create and foster an inclusive and diverse community.In higher dimensions, the problem of detecting change-points and the changing structure is often rendered extremely difficult owing to a combinatorial computational complexity. Through this research, the PIs outline a comprehensive framework, both theoretical and methodological, in the context of change point estimation encompassing problems that may arise in different field of applications. In particular, the PIs build fundamentally new Bayesian methods that can 1) perform sparse signal recovery in a changing linear regression with consistency guarantees 2) detect change-points in dependence structure via changes in a Gaussian graphical model, and 3) build an innovative method for handling ‘ultra-high’-dimensional objects via random projections to drastically reduce the computational burden. Theoretical machinery will be developed to provide probabilistic rigor and consistency guarantee. Computationally efficient algorithms will be developed, and user-friendly software tools will be deployed in R for the usage of the developed methods by the scientific community at large.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

自然界中几乎所有的动态和随机过程都经历了突然和重大的结构变化。通常，变化是可观察到的数量，例如燃料价格或股票指数或犯罪活动因响应不可观察的潜在因素（例如经济现象或公共政策变化或疾病爆发）的变化而发生了重大变化。在所有科学学科和应用中，通常会观察到这种“变化点”，例如经济学，流行病学，社会科学，网络安全和金融。当观察到的变量通过随时间变化的平均结构或具有巨大尺寸的数据中的更改点（例如高分辨率成像数据或复杂的连接图）的数据点变化时，特定的示例可能是改变回归。尽管有大量文献提出了用于检测不同设置中变化点的详尽方法，但在具有复杂依赖性或稀疏结构的分层模型中，贝叶斯方法的变化点方法有限。这项研究通过开发理论框架的同时，在当前应用中保留效率和实用性来填补这一空白，以特定的现实生活应用程序促进。该项目将研究生教育和培训与统计研究相结合，并强调维护社会和道德的考虑因素，从而创造和培养一个包容性和潜水员的社区。在更高的维度，检测变化点的问题以及由于组合计算的复杂性而经常变得极其困难。通过这项研究，PI在变化点估计的背景下概述了一个综合框架，包括在不同的应用领域中可能出现的问题。特别是，PI构建了可以从根本上建立新的贝叶斯方法1）在不断变化的线性回归中执行稀疏信号恢复，并保证一致性2）通过高斯图形模型中的更改来检测依赖性结构的变化点； 3）构建一种创新方法来处理“超高dimensional对象通过随机预测，可以通过大量计算型burnen burnentional burnen burnen。将开发理论机制来提供概率严格和一致的保证。将开发出计算高效的算法，并将用户友好的软件工具部署在R中，以通过整个科学界使用开发的方法来使用。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来通过评估来诚实地支持。