Latent Gaussian and Hüsler–Reiss graphical models with Golazo penalty

IF 3.2 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Ignacio Echave-Sustaeta Rodríguez, Frank Röttger
{"title":"Latent Gaussian and Hüsler–Reiss graphical models with Golazo penalty","authors":"Ignacio Echave-Sustaeta Rodríguez,&nbsp;Frank Röttger","doi":"10.1016/j.ijar.2025.109468","DOIUrl":null,"url":null,"abstract":"<div><div>The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. This approach has recently been extended successfully to Hüsler–Reiss graphical models, which can be considered as an analogue of Gaussian graphical models in extreme value statistics. In this paper we propose a generalization of structure learning for Gaussian and Hüsler–Reiss graphical models via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop algorithms for both latent graphical models with the Golazo penalty and demonstrate it on simulated and real data.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"185 ","pages":"Article 109468"},"PeriodicalIF":3.2000,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X25001094","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0

Abstract

The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. This approach has recently been extended successfully to Hüsler–Reiss graphical models, which can be considered as an analogue of Gaussian graphical models in extreme value statistics. In this paper we propose a generalization of structure learning for Gaussian and Hüsler–Reiss graphical models via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop algorithms for both latent graphical models with the Golazo penalty and demonstrate it on simulated and real data.
具有Golazo惩罚的潜在高斯和h sler - reiss图形模型
在实际问题中,潜在变量的存在是很常见的,例如当一些变量很难或昂贵的测量,或根本是未知的。当未考虑潜在变量时,由于潜在变量引起的观察变量之间的额外相关性,高斯图形模型的结构学习可能会变得模糊。这个问题的标准方法是图形套索的潜在版本,它将逆协方差矩阵分成一个稀疏部分和一个低秩部分,分别进行惩罚。这种方法最近被成功地扩展到h sler - reiss图形模型中,它可以被认为是极值统计中高斯图形模型的模拟。在本文中,我们通过灵活的Golazo惩罚提出了高斯和h sler - reiss图形模型的结构学习的推广。这允许我们引入潜在版本,例如自适应套索、积极依赖约束或预定稀疏模式,以及它们的组合。我们开发了具有Golazo惩罚的潜在图形模型的算法,并在模拟和实际数据上进行了演示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning 工程技术-计算机:人工智能
CiteScore
6.90
自引率
12.80%
发文量
170
审稿时长
67 days
期刊介绍: The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信