Robust and Missing-Data-Aware Time-Varying Graphical Lasso(RM-TVGL) for High-Dimensional Dynamic Network Estimation

Robust and Missing-Data-Aware Time-Varying Graphical Lasso(RM-TVGL) for High-Dimensional Dynamic Network Estimation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Robust and Missing-Data-Aware Time-Varying Graphical Lasso(RM-TVGL) for High-Dimensional Dynamic Network Estimation lingling zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6875061/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Dec, 2025 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract Time-varying graphical models provide a powerful framework for capturing the evolving conditional dependencies among high-dimensional variables over time. A widely used method in this context is the Time-Varying Graphical Lasso (TVGL), which estimates a sequence of sparse precision matrices while encouraging temporal smoothness. However, standard TVGL assumes Gaussian-distributed, fully observed data, making it vulnerable to outliers and missing values—common challenges in real-world applications. In this work, we introduce RM-TVGL: a Robust and Missing-Data-Aware Time-Varying Graphical Lasso framework that extends TVGL to accommodate noisy and incomplete data. Our method integrates Huber loss to mitigate the influence of outliers and incorporates an Expectation-Maximization (EM) algorithm to handle missing entries in a principled manner. Additionally, RM-TVGL supports flexible regularization schemes, including ℓ1, ℓ2, and Elastic Net, enabling adaptation to diverse network structures. We develop an efficient ADMMbased optimization algorithm and demonstrate the advantages of RM-TVGL through extensive experiments on both synthetic and real gene expression datasets. The results show that RMTVGL consistently improves structural accuracy, temporal stability, and robustness compared to existing methods. Time-varying graphical models robust estimation missing data Huber loss highdimensional networks Elastic Net Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Dec, 2025 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 21 Jul, 2025 Reviews received at journal 18 Jul, 2025 Reviews received at journal 14 Jul, 2025 Reviewers agreed at journal 16 Jun, 2025 Reviewers agreed at journal 13 Jun, 2025 Reviewers invited by journal 13 Jun, 2025 Editor assigned by journal 12 Jun, 2025 Submission checks completed at journal 12 Jun, 2025 First submitted to journal 11 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6875061","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471873515,"identity":"36b3b980-e3c0-4366-a2b6-0465335f30db","order_by":0,"name":"lingling zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYBACPgYeEGUjx8/A3AYVS8CvhQ2iJc1YsoGRNC2HEzccIFoL/9mDnwt+MRsbHz/Y9uDnjsMM/Ow5BgRsOZcsPbOPTc7sTGK7Ye+ZwwySPW8IaGHsMZDm7eExNjuQ2CbB23aYweAGIVuYeYx/8/ZIJG7uf9gm+ReoxZ6gFjYeM2meHwaJGyQS26TBtkgQ0sLDY2bN25BgLHHjYbuxbFs6j8SZZwV4tfDznzG+zfPnvxx/f/Kxh2/brOX425M34NUCBvAYYWBo5iGsHAz+wFl1ROoYBaNgFIyCkQQAKHlEQt7dh8IAAAAASUVORK5CYII=","orcid":"","institution":"University at Albany, State University of New York","correspondingAuthor":true,"prefix":"","firstName":"lingling","middleName":"","lastName":"zhang","suffix":""}],"badges":[],"createdAt":"2025-06-11 22:23:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6875061/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6875061/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-025-10782-9","type":"published","date":"2025-12-02T15:57:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97723769,"identity":"8841e38c-d19a-4f13-8faf-1bb59f47a6db","added_by":"auto","created_at":"2025-12-08 16:05:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":329436,"visible":true,"origin":"","legend":"","description":"","filename":"RMTVGLspringer2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6875061/v1_covered_182c93ab-cc0b-4a4d-ad02-2ee13904057e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Robust and Missing-Data-Aware Time-Varying Graphical Lasso(RM-TVGL) for High-Dimensional Dynamic Network Estimation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Time-varying graphical models, robust estimation, missing data, Huber loss, highdimensional networks, Elastic Net","lastPublishedDoi":"10.21203/rs.3.rs-6875061/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6875061/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTime-varying graphical models provide a powerful framework for capturing the evolving conditional dependencies among high-dimensional variables over time. A widely used method in this context is the Time-Varying Graphical Lasso (TVGL), which estimates a sequence of sparse precision matrices while encouraging temporal smoothness. However, standard TVGL assumes Gaussian-distributed, fully observed data, making it vulnerable to outliers and missing values—common challenges in real-world applications. In this work, we introduce RM-TVGL: a Robust and Missing-Data-Aware Time-Varying Graphical Lasso framework that extends TVGL to accommodate noisy and incomplete data. Our method integrates Huber loss to mitigate the influence of outliers and incorporates an Expectation-Maximization (EM) algorithm to handle missing entries in a principled manner. Additionally, RM-TVGL supports flexible regularization schemes, including ℓ1, ℓ2, and Elastic Net, enabling adaptation to diverse network structures. We develop an efficient ADMMbased optimization algorithm and demonstrate the advantages of RM-TVGL through extensive experiments on both synthetic and real gene expression datasets. 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