Vertical Federated Latent Variable Model Inversion for Collaborative Value Chain Optimization

Vertical Federated Latent Variable Model Inversion for Collaborative Value Chain Optimization | 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 Vertical Federated Latent Variable Model Inversion for Collaborative Value Chain Optimization Du Nguyen Duy, Ramin Nikzad-Langerodi, Josef Scharinger, Michael Affenzeller This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9243934/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 13 You are reading this latest preprint version Abstract In modern manufacturing value chains, achieving optimal product quality and sustainability necessitates collaboration across interconnected stakeholders. Conventional Latent Variable Model Inversion (LVMI) methods, though widely applied in process optimization, face limitations in cross-organizational settings due to data privacy concerns, as they typically require sharing sensitive data. To address this, the present work introduces a novel, two-phase approach for privacy-preserving value chain optimization called Secure LVMI. The approach first utilizes Privacy-Preserving Partial Least Squares (P3LS) to collaboratively build an integrated process model without sharing raw data, followed by the secure estimation of statistical control limits using Secure Multi-Party Computation (MPC). Subsequently, leveraging the established model and limits, a combination of MPC and a Cooperative Coevolution Genetic Algorithm (CCGA) performs secure model inversion to find optimal process settings. The effectiveness of Secure LVMI is demonstrated through experiments on simulated datasets. By providing solutions with quality comparable to centralized methods while maintaining privacy, this framework offers potential for broad application in industries where privacy concerns restrict traditional data sharing and optimization techniques. Cross-organizational Process Optimization Partial Least Squares Cooperative Coevolution Genetic Algorithm Vertical Federated Learning Latent Variable Model Inversion Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 23 Apr, 2026 Reviewers agreed at journal 23 Apr, 2026 Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviews received at journal 15 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers invited by journal 15 Apr, 2026 Editor assigned by journal 28 Mar, 2026 Submission checks completed at journal 28 Mar, 2026 First submitted to journal 27 Mar, 2026 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. 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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-9243934","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627397155,"identity":"f4e1931d-e3e8-4ea5-b0fa-b5bb06fd8c94","order_by":0,"name":"Du Nguyen Duy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVRIiWNgGAWjYDCCAwimAQNDBZCSIE3LGaiWA9gVY9HC2EaEFr4bCWwPv7YdljNnYN4mzTuvTp5/dgPj5w94tEjeSGA3lm07bGzZwFYmzbvtsOGMOweYJfDZYgC0RVqy7XDihgM8ZkAtBxIMJBIYiNJSD9Eypw6khfkHIS2SH9sOJxiAtTQwg7Sw4bVF8szDNmmGc+mGGw6zFVvOOQb0y43ENoszeLTwHU8+JvmjzFre4HjzxhtvaoAhNiP58I0KPFoYGBgbmHkYmhkYmBkYmHigIng1gJX8YKiDMUbBKBgFo2AUYAIAxdVOxdTAphkAAAAASUVORK5CYII=","orcid":"","institution":"Software Competence Center Hagenberg (Austria)","correspondingAuthor":true,"prefix":"","firstName":"Du","middleName":"Nguyen","lastName":"Duy","suffix":""},{"id":627397156,"identity":"8af69e48-b16f-4f7d-b9c3-1ce8773cdc69","order_by":1,"name":"Ramin Nikzad-Langerodi","email":"","orcid":"","institution":"Software Competence Center Hagenberg (Austria)","correspondingAuthor":false,"prefix":"","firstName":"Ramin","middleName":"","lastName":"Nikzad-Langerodi","suffix":""},{"id":627397157,"identity":"35687611-692a-4dd8-9845-4b40cbc6fb8a","order_by":2,"name":"Josef Scharinger","email":"","orcid":"","institution":"Johannes Kepler University of Linz","correspondingAuthor":false,"prefix":"","firstName":"Josef","middleName":"","lastName":"Scharinger","suffix":""},{"id":627397158,"identity":"7bf802d1-a3db-4be2-862a-f9c9248db873","order_by":3,"name":"Michael Affenzeller","email":"","orcid":"","institution":"Johannes Kepler University of Linz","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Affenzeller","suffix":""}],"badges":[],"createdAt":"2026-03-27 11:08:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9243934/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9243934/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107707562,"identity":"73eaebe4-8239-4339-bef8-ac35c16feca4","added_by":"auto","created_at":"2026-04-24 09:20:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":748327,"visible":true,"origin":"","legend":"","description":"","filename":"Sourcefilesupdated.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9243934/v1_covered_b050ac4b-0e51-41db-847d-aad6a46662f2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Vertical Federated Latent Variable Model Inversion for Collaborative Value Chain Optimization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-artificial-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"diai","sideBox":"Learn more about [Discover Artificial Intelligence](https://www.springer.com/44163)","snPcode":"","submissionUrl":"","title":"Discover Artificial Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Cross-organizational Process Optimization, Partial Least Squares, Cooperative Coevolution Genetic Algorithm, Vertical Federated Learning, Latent Variable Model Inversion","lastPublishedDoi":"10.21203/rs.3.rs-9243934/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9243934/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In modern manufacturing value chains, achieving optimal product quality and sustainability necessitates collaboration across interconnected stakeholders. 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