TVEG: Model Selection of the Time-Varying Exponential Family Distributions Graphical Models

IF 6.7 2区计算机科学 Q1 ENGINEERING, MULTIDISCIPLINARY

IEEE Transactions on Network Science and Engineering Pub Date : 2025-03-17 DOI:10.1109/TNSE.2025.3551767

Juan Liu;Guofeng Mei;Yuanqing Xia;Xiaoqun Wu;Jinhu Lü

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引用次数: 0

Abstract

The undirected graphical model, a popular class of statistical model, offers a way to describe and explain the relationships among a set of variables. However, it remains a challenge to choose a certain graphical model to explain the relationships of variables adequately, especially when the relationships of variables are rewiring over time. This paper proposes the Time-Varying Exponential Family Distributions Graphical (TVEG) models, with time-varying structures and exponential family node-wise conditional distributions. TVEG models extend the scope of available graph models and can be applied to time-varying and exponential family distribution observation data in reality. We propose the Temporally Smoothed

$L_{1}$

-regularized exponential family graphical estimator (TSLEG), an estimator to infer the structure of TVEG from observations. We derive sufficient conditions for the TSLEG to recover the block partition and sparse pattern with high probability. We derive a message-passing optimization method to solve the TSLEG for time-varying Ising, Gaussian, exponential, and Poisson graphs based on the ADMM. The synthetic network simulations corroborate the theoretical analysis. Analysing of real data of stocks and the US Senate by the time-varying exponential model and Poisson model indicates the effectiveness and practicality of TVEG models.

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时变指数族分布图形模型的模型选择

无向图形模型是一类流行的统计模型，它提供了一种描述和解释一组变量之间关系的方法。然而，选择一个特定的图形模型来充分解释变量之间的关系仍然是一个挑战，特别是当变量之间的关系随着时间的推移而重新布线时。本文提出了具有时变结构和指数族节点条件分布的时变指数族分布图形模型（TVEG）。TVEG模型扩展了现有图模型的范围，可以应用于现实中的时变和指数族分布观测数据。我们提出了时间平滑$L_{1}$-正则化指数族图估计量（TSLEG），这是一种从观测数据推断TVEG结构的估计量。给出了TSLEG高概率恢复块划分和稀疏模式的充分条件。针对时变的伊辛图、高斯图、指数图和泊松图，我们提出了一种基于ADMM的消息传递优化方法来求解TSLEG。综合网络仿真验证了理论分析。用时变指数模型和泊松模型对股票和美国参议院的实际数据进行分析，表明了TVEG模型的有效性和实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Network Science and Engineering Engineering-Control and Systems Engineering

CiteScore

12.60

自引率

9.10%

发文量

393

期刊介绍： The proposed journal, called the IEEE Transactions on Network Science and Engineering (TNSE), is committed to timely publishing of peer-reviewed technical articles that deal with the theory and applications of network science and the interconnections among the elements in a system that form a network. In particular, the IEEE Transactions on Network Science and Engineering publishes articles on understanding, prediction, and control of structures and behaviors of networks at the fundamental level. The types of networks covered include physical or engineered networks, information networks, biological networks, semantic networks, economic networks, social networks, and ecological networks. Aimed at discovering common principles that govern network structures, network functionalities and behaviors of networks, the journal seeks articles on understanding, prediction, and control of structures and behaviors of networks. Another trans-disciplinary focus of the IEEE Transactions on Network Science and Engineering is the interactions between and co-evolution of different genres of networks.