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New Directions in Bayesian Change-Point Analysis

贝叶斯变点分析的新方向

基本信息

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

项目摘要

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会经历突然而重大的结构变化。这种变化往往是可观察到的数量，例如燃料价格或股票指数或犯罪活动随着不可观察的潜在因素（如经济现象或公共政策变化或疾病爆发）的变化而发生重大变化。这种“变点”在所有科学学科和应用中都是经常观察到的，如经济学、流行病学、社会科学、网络安全和金融。具体的例子可以是当观察到的变量通过随时间变化的平均结构依赖于预测变量时的变化回归，或者具有大规模维度的数据中的变化点，例如高分辨率成像数据或复杂的连接图。虽然有大量的文献提出了在不同的设置中检测变点的详细方法，但对于具有复杂依赖或稀疏结构的分层模型中的变点的贝叶斯方法的考虑有限。这项研究填补了这一空白，新的统计工具的动机是特定的现实生活中的应用，通过开发理论框架，同时保持效率和实用性，在当前的应用程序。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考虑，以创建和促进包容性和多样性的社区。在更高的维度上，由于组合计算的复杂性，检测变点和变化结构的问题往往变得极其困难。通过这项研究，PI概述了一个全面的框架，理论和方法，在变化点估计的背景下，包括可能出现在不同的应用领域的问题。特别是，PI构建了全新的贝叶斯方法，可以1）在具有一致性保证的变化线性回归中执行稀疏信号恢复2）通过高斯图形模型中的变化检测依赖结构中的变点，以及3）通过随机投影构建一种用于处理“超高”维对象的创新方法，以大幅降低计算负担。将开发理论机器，以提供概率的严格性和一致性保证。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。