Collaborative Research: Novel modeling and Bayesian analysis of high-dimensional time series

合作研究：高维时间序列的新颖建模和贝叶斯分析

• 批准号: 2210282
• 负责人: Anindya Roy
• 金额: $ 11万
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210282&HistoricalAwards=false
• 关键词: Collaborative; Research; Novel; modeling; Bayesian

Every aspect of modern life including economy and finance, communication, and medical records, is associated with large amounts of data on several measurements, often evolving over time. Understanding the progress over time, finding an intrinsic relationship among different variables, and predicting future observations are essential components of decision and policy-making. However, apparent relations between two variables can appear in data caused by their shared association with other components. The principal investigators (PIs) will develop a model to re-express the multi-dimensional time series in independent, one-dimensional, latent time series. The representation will explain the evolution of the data over time and the intrinsic relations present in the component variables. It can also help find a more accurate, efficiently computable prediction formula for future observations by pulling information across different components and time. The approach's simplicity and generality will make it widely applicable and adaptable to diverse fields in economics, finance, social sciences, communications, networks, neuroimaging, and others. The PIs plan to develop free software packages to disseminate the results. They are committed to supporting young researchers and promoting diversity through graduate student training and involvement in the REU program.The developed framework is based on representing an observed multi-dimensional time series as a linear combination of several independent stationary latent processes. The individual latent time series are modeled flexibly with unspecified spectral densities. The PIs will study the conditional independence structure among component time series and the causality of the time series over the temporal domain using a Bayesian approach. They will put independent priors on individual spectral densities through a finite random series prior, and on the matrix of the linear transformation decomposed as a product of a sparse matrix and an orthogonal matrix, the former of which induces a graphical structure for conditional independence among component series. Through this representation, desirable stationarity and causality structures can be imposed. Decoupling through the Whittle likelihood approximation and Hamiltonian Monte-Carlo methods will allow efficient posterior sampling. The causality over nodal time series will be addressed by a Direct Acyclic Graph modeling of the residual process. The formulation seamlessly addresses a mixed frequency sampling situation, difficult to incorporate into competing methods. The developed framework efficiently addresses both temporal and nodal causality respectively by characterization in terms of the Schur-complementation and using a directed acyclic graph, allowing a natural interpretation.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.

现代生活的各个方面，包括经济和金融，沟通和病历，都与大量有关几种测量的数据相关，通常会随着时间的流逝而发展。了解随着时间的推移的进步，在不同变量之间找到内在的关系以及预测未来的观察是决策和决策的重要组成部分。但是，两个变量之间的明显关系可能出现在数据与其他组件共享关联引起的数据中。主要研究人员（PIS）将开发一个模型，以在独立的，一维，潜在的时间序列中重新表达多维时间序列。表示形式将解释数据随时间的演变以及组件变量中存在的固有关系。它还可以帮助找到一个更准确，可有效的可计算预测公式，以通过在不同的组件和时间上拉出信息，以供将来观察。该方法的简单性和普遍性将使其广泛适用并适用于经济学，金融，社会科学，沟通，网络，神经成像等领域的不同领域。 PIS计划开发免费的软件包来传播结果。他们致力于通过研究生培训和参与REU计划来支持年轻的研究人员，并促进多样性。开发的框架基于代表观察到的多维时间序列，作为几种独立的固定潜在过程的线性组合。单个潜在时间序列以未指定的光谱密度灵活地建模。 PI将使用贝叶斯方法研究成分时间序列之间的条件独立性结构和时间序列的因果关系。他们将通过有限的随机序列将独立的先验放在单个光谱密度上，并将线性转化的基质分解为稀疏基质和正交基质的产物，前者在组件系列之间有条件独立性诱导图形结构。通过这种表示，可以施加理想的平稳性和因果关系结构。通过晶状的可能性近似和哈密顿蒙特卡洛方法的脱钩将允许有效的后验采样。淋巴结时间序列的因果关系将通过剩余过程的直接无环形建模来解决。该配方无缝地解决了混合频率采样情况，很难将其纳入竞争方法中。开发的框架有效地通过在SCHUR-COMPELATION中进行表征和使用定向的无环图，分别通过表征分别解决时间和淋巴结，允许自然解释。该奖项反映了NSF的法定任务，并被认为是通过使用该基金会的知识分子和更广泛影响的评估来评估的支持，并被认为是值得的。