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
• 负责人: Jitendra Tugnait
• 金额: $ 60万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2308473&HistoricalAwards=false
• 关键词: CIF; Small; Learning; Sparse; Vector; CIF; Small; Learning; Sparse; Vector

Graphs are mathematical structures that are frequently used to express dependencies or similarities among data variables. They can capture complex structures inherent in seemingly irregular high-dimensional data, making them an invaluable tool in signal processing, machine learning, and data science. Applications of graphical models include classification and exploratory data analysis in finance, social networks, environmental networks, gene regulatory networks, and functional magnetic resonance imaging (fMRI). However, graphs are not always explicitly available. Therefore, given data, learning the underlying graph structure is central to applications in machine learning and signal processing. In the literature, it is typically assumed that the temporal data consists of multiple independent realizations of a random vector or matrix in the choice of the objective function to be optimized as well as in algorithm design and analysis. This assumption is often violated in practice. This project explicitly considers time-dependent data, without requiring any detailed parametric modeling to capture time dependencies. It is anticipated that better models incorporating short- and long-memory time dependence will yield more accurate graph topology, hence, significant improvements in data analysis and learning tasks. The problem of differential graph estimation is also addressed in this framework where, for example, in a bio-statistical application, one may be interested in the differences in the graphical models of healthy and impaired subjects, or models under different disease states, given gene-expression data or fMRI signals.In this project, three main research thrusts are considered: multivariate dependent time-series graph learning under both short- and long-range dependence, matrix-valued dependent time-series graph learning, and differential graph learning. The focus in all three thrusts is on sparse graphs or sparse differential graphs, under high-dimensional settings wherein the graph size is greater than, or of the order of, the data sample size. Computationally efficient and accurate, general approaches for estimation of undirected weighted graphs from time-dependent multivariate as well as matrix-valued time series will be investigated. Two classes of approaches will be considered: frequency-domain approaches based on the discrete Fourier transform of data which yields approximately independent data in the frequency domain, allowing a broad set of analysis tools based on complex-valued signal processing to be exploited; and time-domain approaches based on time-delay embedding, casting the problem as one of multi-attribute graph estimation wherein a random vector, instead of a scalar, is associated with each graph node. All aspects of the problem will be considered: algorithm design and analysis, optimization under both convex and non-convex regularizing functions for sparse parameter estimation, model selection (choice of penalty parameters), analysis of theoretical properties (such as consistency and model recovery), and application to real data using publicly available data sets.This project is jointly funded by the Communications & Information Foundations (CIF) and the Established Program to Stimulate Competitive Research (EPSCoR) programs.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.

图是数学结构，通常用于表达数据变量之间的依赖性或相似性。他们可以捕获看似不规则的高维数据中固有的复杂结构，从而使它们成为信号处理，机器学习和数据科学的宝贵工具。图形模型的应用包括金融，社交网络，环境网络，基因调节网络和功能磁共振成像（fMRI）中的分类和探索性数据分析。但是，图形并不总是明确可用。因此，给定数据，学习基础图结构对于机器学习和信号处理中的应用至关重要。在文献中，通常假定时间数据是由随机向量或矩阵的多个独立实现，可以在选择要优化的目标函数以及算法设计和分析中。在实践中，通常会违反此假设。该项目明确考虑时间依赖性数据，而无需任何详细的参数建模来捕获时间依赖性。可以预料，结合短期和长期内存时间依赖性的更好模型将产生更准确的图形拓扑，因此，数据分析和学习任务的显着改进。在此框架中还解决了差异图估计问题的问题，例如，在生物统计应用中，一个人可能对健康和受损的受试者的图形模型或不同疾病状态下的模型的差异感兴趣，鉴于基因表达数据或fMRI信号。依赖时间序列图和差分图学习。在高维设置下，所有三个推力中的焦点都在稀疏图或稀疏差分图上，其中图大小大于数据样本尺寸的尺寸或顺序。将研究计算高效且准确的一般方法，用于估算时间依赖性多元和矩阵值时间序列的无向加权图。将考虑两类方法：基于离散的傅立叶数据转换的频域方法，该方法在频域中产生近似独立的数据，从而可以利用基于复杂价值的信号处理的广泛分析工具；以及基于时间延迟嵌入的时间域方法，将问题抛弃为多属性图估计之一，其中，随机向量而不是标量与每个图形节点相关联。该问题的所有方面都将考虑：算法设计和分析，在凸和非凸的正规化功能下进行优化，用于稀疏参数估计，模型选择，模型选择（选择惩罚参数），理论属性的分析（一致性和模型恢复）（例如一致性和模型恢复），以及使用公共可用数据集的真实数据应用程序的应用程序。 （EPSCOR）计划。该奖项反映了NSF的法定任务，并被认为是使用基金会的知识分子优点和更广泛的影响审查标准的评估值得支持的。