EAGER: Learning Graphical Models of High-Dimensional Time Series

EAGER:学习高维时间序列的图形模型

基本信息

  • 批准号:
    2040536
  • 负责人:
  • 金额:
    $ 18万
  • 依托单位:
  • 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

项目摘要

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.
无向图模型已经越来越多地用于探索或利用多变量数据下的不同随机变量之间的依赖结构,表示复杂的系统。图模型是分析多元数据的一个重要而有用的工具。图模型是一种统计模型,其中随机变量和它们之间的条件依赖关系通过图来指定。图形模型最初是为具有多个独立实现(独立同分布时间序列)的随机向量开发的。这种模型已经被广泛研究,并且发现在诸如生物调节网络、功能性脑网络和社交网络的各种应用中是有用的。它们也被证明是有用的聚类,半监督学习和分类任务。时间相关数据(时间序列)的图形建模是最近的。相关数据的时间序列图形模型已被应用于重症监护监测、金融时间序列、空气污染数据和功能磁共振成像数据分析,以提供对不同大脑区域功能连接的见解。几乎所有的相关时间序列的工作都局限于低维序列的变量的数量是远远小于数据样本大小。为了解决变量数量超过或与样本量相当的高维时间序列,对于合成数据和真实的数据,在目标函数的选择以及算法设计和分析中,(几乎总是)假设该序列是独立且同分布的。本项目旨在填补这一空白,专注于高维相关时间序列的图形建模方法。该项目还将为研究生提供培训和研究经验。本研究探讨了高维环境下实值相依多变量时间序列图形建模的新颖、创新、通用统计信号处理方法。一个重点是频域方法,而不需要详细的参数建模的基础时间序列,以捕捉在时域中的任何依赖关系。频域公式导致考虑复值高斯图形模型适当的高斯随机向量,一个话题,很少受到关注。本研究的核心内容是:(1)设计、分析和优化惩罚对数似然函数来拟合图模型。(2)分析所得解的理论性质(如一致性和稀疏性)。(3)应用于合成和真实的数据,以评估所考虑方法的有效性和计算效率。该奖项反映了NSF的法定使命,并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

项目成果

期刊论文数量(19)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Estimation of Differential Graphs via Log-Sum Penalized D-Trace Loss
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:
  • 影响因子:
    0
  • 作者:
    Tugnait, Jitendra K.
  • 通讯作者:
    Tugnait, Jitendra K.
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:
  • 影响因子:
    0
  • 作者:
    Tugnait, Jitendra K.
  • 通讯作者:
    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
Graph Learning from Multi-Attribute Smooth Signals
多属性平滑信号的图学习
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Jitendra Tugnait其他文献

An Edge Exclusion Test for Complex Gaussian Graphical Model Selection
复杂高斯图形模型选择的边缘排除测试
Adaptive estimation and identification for discrete systems with Markov jump parameters
On Multisensor Detection of Improper Signals
Blind equalization and estimation of digital communication FIR channels using cumulant matching
Pilot decontamination under imperfect power control

Jitendra Tugnait的其他文献

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{{ truncateString('Jitendra Tugnait', 18)}}的其他基金

CIF:Small:Learning Sparse Vector and Matrix Graphs from Time-Dependent Data
CIF:小:从瞬态数据中学习稀疏向量和矩阵图
  • 批准号:
    2308473
  • 财政年份:
    2023
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
EAGER: Detection and Mitigation of Pilot Contamination Attacks and Related Issues in Massive MIMO Systems
EAGER:大规模 MIMO 系统中导频污染攻击及相关问题的检测和缓解
  • 批准号:
    1651133
  • 财政年份:
    2016
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
CIF: Small: Complex-Valued Statistical Signal Processing with Dependent Data
CIF:小型:具有相关数据的复值统计信号处理
  • 批准号:
    1617610
  • 财政年份:
    2016
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Using the Channel State Information for Wireless Security Enhancement
使用信道状态信息增强无线安全性
  • 批准号:
    0823987
  • 财政年份:
    2008
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Estimation of MIMO Wireless Communications Channels: Approaches and Applications
MIMO 无线通信信道估计:方法和应用
  • 批准号:
    0424145
  • 财政年份:
    2004
  • 资助金额:
    $ 18万
  • 项目类别:
    Continuing Grant
Frequency-Domain Approaches to Identification of Multiple-Input Multiple-Output Systems Given Time-Domain Data
给定时域数据的多输入多输出系统辨识的频域方法
  • 批准号:
    9912523
  • 财政年份:
    2000
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Spatio-Temporal Statistical Signal Processing For Blind Equalization and Source Separation
用于盲均衡和源分离的时空统计信号处理
  • 批准号:
    9803850
  • 财政年份:
    1998
  • 资助金额:
    $ 18万
  • 项目类别:
    Continuing Grant
Frequency-Domain Approaches To Control-Relevant System Identification
控制相关系统辨识的频域方法
  • 批准号:
    9504878
  • 财政年份:
    1995
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Higher Order Statistical Signal and Image Processing and Analysis
高阶统计信号和图像处理与分析
  • 批准号:
    9312559
  • 财政年份:
    1994
  • 资助金额:
    $ 18万
  • 项目类别:
    Continuing Grant
Blind Equalization and Channel Estimation in Data Communication Systems
数据通信系统中的盲均衡和信道估计
  • 批准号:
    9015587
  • 财政年份:
    1991
  • 资助金额:
    $ 18万
  • 项目类别:
    Continuing Grant

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