EAGER: Learning Graphical Models of High-Dimensional Time Series

EAGER：学习高维时间序列的图形模型

• 批准号: 2040536
• 负责人: Jitendra Tugnait
• 金额: $ 18万
• 依托单位: Auburn University
• 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: 2020-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2040536&HistoricalAwards=false
• 关键词: EAGER; Learning; Graphical; Models; Dimensional

Undirected graphical models have been increasingly used for exploring or exploiting dependency structures among different random variables underlying multivariate data, representing complex systems. Graphical models are an important and useful tool for analyzing multivariate data. A graphical model is a statistical model where random variables and the conditional dependencies between them are specified via a graph. Graphical models were originally developed for random vectors with multiple independent realizations (independent and identically distributed time series). Such models have been extensively studied, and found to be useful in a wide variety of applications such as biological regulatory networks, functional brain networks, and social networks. They have also proved to be useful for clustering, semi-supervised learning and classification tasks. Graphical modeling of time-dependent data (time series) is more recent. Time series graphical models of dependent data have been applied to intensive care monitoring, financial time series, air pollution data, and analysis of functional magnetic resonance imaging data to provide insights into the functional connectivity of different brain regions. Almost all existing works on dependent time series are limited to low-dimensional series where number of variables is much smaller than the data sample size. To address high-dimensional time series where number of variables exceed, or are comparable to, the sample size, it is (almost always) assumed that the series is independent and identically distributed in choice of objective function, and algorithm design and analysis, for both synthetic and real data. This project aims to fill this gap by focusing on methods for graphical modeling of high-dimensional dependent time series. The project will also provide training and research experiences for graduate students.Novel, innovative, general statistical signal processing approaches to graphical modeling of real-valued dependent multivariate time series in high-dimensional settings are investigated in this research. An emphasis is on frequency-domain approaches without requiring detailed parametric modeling of the underlying time series to capture any dependencies in the time domain. Frequency-domain formulation leads to consideration of complex-valued Gaussian graphical models for proper Gaussian random vectors, a topic that has received scant attention. The following thrusts form the core of this research: (1) Design, analysis and optimization of penalized log-likelihood functions to fit graphical models. (2) Analysis of theoretical properties (such as consistency and sparsistency) of the obtained solutions. (3) Application to synthetic and real data to evaluate the efficacy and computational efficiency of the considered approaches.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.

无向图形模型越来越多地用于探索或利用多元数据基础不同随机变量之间的依赖性结构，代表复杂的系统。图形模型是用于分析多元数据的重要且有用的工具。图形模型是一个统计模型，其中随机变量和它们之间的条件依赖性是通过图指定的。图形模型最初是针对具有多个独立实现（独立且相同分布的时间序列）的随机向量开发的。此类模型已经进行了广泛的研究，并发现在各种应用程序中很有用，例如生物监管网络，功能性脑网络和社交网络。事实证明，它们对于聚类，半监督的学习和分类任务很有用。时间依赖性数据（时间序列）的图形建模是更新的。依赖数据的时间序列图形模型已应用于重症监护，财务时间序列，空气污染数据以及功能磁共振成像数据的分析，以提供有关不同大脑区域功能连接性的见解。几乎所有关于依赖时间序列的现有作品都限于低维度序列，其中变量数量远小于数据样本量。为了解决高维时间序列，其中变量数量超过或与样本量相当，（几乎总是）假定该系列是独立的，并且在选择目标函数以及算法设计和分析方面是独立的，用于合成和真实数据。该项目旨在通过重点介绍用于高维依赖时间序列的图形建模的方法来填补这一空白。该项目还将为研究生提供培训和研究经验。在这项研究中研究了新的，创新的，一般的统计信号处理方法，用于在高维环境中对实价依赖依赖的多元时间序列的图形建模。重点是频域方法，而无需对基础时间序列的详细参数建模来捕获时间域中的任何依赖项。频域的配方导致考虑适当的高斯随机向量的复杂值高斯图形模型，这一主题受到了很少的关注。以下推力构成了这项研究的核心：（1）惩罚对数类样函数的设计，分析和优化以适合图形模型。 （2）分析获得的解决方案的理论特性（例如一致性和稀疏性）。 （3）应用于合成和真实数据，以评估所考虑方法的功效和计算效率。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。

项目成果

Consistency of Sparse-Group Lasso Graphical Model Selection for Time Series

时间序列稀疏组Lasso图形模型选择的一致性

• DOI: 10.1109/ieeeconf51394.2020.9443298
• 发表时间: 2020
• 期刊: and Computers
• 作者: Tugnait, Jitendra K.

Estimation of Differential Graphs via Log-Sum Penalized D-Trace Loss

• DOI: 10.1109/ssp53291.2023.10208014
• 发表时间: 2023-07
• 期刊: 2023 IEEE Statistical Signal Processing Workshop (SSP)
• 作者: Jitendra Tugnait

Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series

时间序列的稀疏组对数和惩罚图形模型学习

• DOI: 10.1109/icassp43922.2022.9747446
• 发表时间: 2022
• 期刊: Speech and Signal Processing (ICASSP
• 作者: Tugnait, Jitendra K.

Corrections to “Sparse-Group Lasso for Graph Learning From Multi-Attribute Data”

对“从多属性数据进行图学习的稀疏组套索”的更正

• DOI: 10.1109/tsp.2021.3104727
• 发表时间: 2021
• 期刊: IEEE Transactions on Signal Processing
• 影响因子: 5.4
• 作者: Tugnait, Jitendra

Sparse High-Dimensional Matrix-Valued Graphical Model Learning from Dependent Data

• DOI: 10.1109/ssp53291.2023.10208070
• 发表时间: 2023-07
• 期刊: 2023 IEEE Statistical Signal Processing Workshop (SSP)
• 作者: Jitendra Tugnait