Differentially Private Lasso: An ISTA Framework with Finite-Iteration Guarantees

Differentially Private Lasso: An ISTA Framework with Finite-Iteration Guarantees | 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 Differentially Private Lasso: An ISTA Framework with Finite-Iteration Guarantees Jiahui Zhang, Chi Seng Pun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9153407/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Differential privacy (DP) offers a principled way to protect individual records, but in high-dimensional sparse regression, it introduces a delicate accuracy-privacy tradeoff. In this paper, we develop an ISTA-based framework for DP estimation in the high-dimensional sparse linear model, instantiated for the Lasso objective. Our main contribution is a set of finite-iteration, high-probability ℓ 2 guarantees for the returned iterates. Across the considered DP mechanisms, the bounds admit an interpretable form: a nonprivate baseline term, a privacy-induced term determined by the effective noise level of the DP mechanism and its accounting , and an optimization residual that vanishes as the iteration budget increases. To enable stable implementations and principled Gaussian calibration, our algorithms incorporate clipping and an ℓ 2 projection step. Simulation studies and real-data experiments under matched privacy budgets support the theoretical predictions and demonstrate competitive accuracy in high-dimensional regimes. High-dimensional Statistics Sparse Linear Regression Differential Privacy Proximal Gradient Iterative Shrinkage-Thresholding Algorithm (ISTA) Finite-Iteration Guarantees Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 11 May, 2026 Reviews received at journal 28 Apr, 2026 Reviewers agreed at journal 25 Mar, 2026 Reviewers agreed at journal 24 Mar, 2026 Reviewers agreed at journal 20 Mar, 2026 Reviewers invited by journal 20 Mar, 2026 Editor assigned by journal 19 Mar, 2026 Submission checks completed at journal 19 Mar, 2026 First submitted to journal 17 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. 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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-9153407","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609222774,"identity":"f430fc2e-fccb-417c-8734-c2aae82da63d","order_by":0,"name":"Jiahui Zhang","email":"","orcid":"","institution":"Nanyang Technological University","correspondingAuthor":false,"prefix":"","firstName":"Jiahui","middleName":"","lastName":"Zhang","suffix":""},{"id":609222775,"identity":"81a32fb3-1fdf-42cc-8c3b-c7d38f3ddd30","order_by":1,"name":"Chi Seng Pun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYNCCCgglQYKWMxDVJGhhbCNFC3//2WPShfPu1BkcYD54m4ehzq6BkBaJG3lp0jO3PZMwOMCWbM3DcDiZoBYDCR4zad5th4FagAwehgPJBB1mwH8GqGUOSAv/N6CWOiK0MOQAtTSAbWEDamG2I6gF6BegF44dlpx5mM3Yco7B4QSCWoAhBgyomsP8fMebH954U1FnT1ALAwMPlGaGuDOxgXgtUECMLaNgFIyCUTDCAACaljMCPTy7ZQAAAABJRU5ErkJggg==","orcid":"","institution":"Nanyang Technological University","correspondingAuthor":true,"prefix":"","firstName":"Chi","middleName":"Seng","lastName":"Pun","suffix":""}],"badges":[],"createdAt":"2026-03-18 01:53:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9153407/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9153407/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105564620,"identity":"28019d93-44d2-4753-aecd-bb989d50f6f9","added_by":"auto","created_at":"2026-03-27 12:50:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":688573,"visible":true,"origin":"","legend":"","description":"","filename":"DPLasso.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9153407/v1_covered_5c995254-1c1e-4d73-a5ea-47ec9dcb3e74.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Differentially Private Lasso: An ISTA Framework with Finite-Iteration Guarantees","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":"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":"High-dimensional Statistics, Sparse Linear Regression, Differential Privacy, Proximal Gradient, Iterative Shrinkage-Thresholding Algorithm (ISTA), Finite-Iteration Guarantees","lastPublishedDoi":"10.21203/rs.3.rs-9153407/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9153407/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Differential privacy (DP) offers a principled way to protect individual records, but in high-dimensional sparse regression, it introduces a delicate accuracy-privacy tradeoff. 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