Persistence Landscapes Across Privacy Budgets for Explanation Methods Across Differential Privacy Mechanisms

Persistence Landscapes Across Privacy Budgets for Explanation Methods Across Differential Privacy Mechanisms | 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 Persistence Landscapes Across Privacy Budgets for Explanation Methods Across Differential Privacy Mechanisms Paul Zheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8662668/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Machine-learning credit scoring must be both auditable and privacy-preserving, yet post-hoc explainers may rely on sensitive records or privileged model access that privacy constraints restrict. We study how local explanations for a feed-forward neural-network credit-risk classifier on the Home Equity Line of Credit (HELOC) dataset change when the data or learning pipeline is sanitized with differential privacy (DP) using additive noise, DP-Stochastic gradient descent (SGD), synthetic data generation, and DP-principal component analysis (PCA). While Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), and gradient-based attributions are widely used, their behavior under DP-induced noise remains poorly characterized. Topology-based comparisons using Mapper and persistence summaries can capture explanation structure beyond per-feature averages, but they raise sensitivity and estimation challenges. To close this gap, we treat per-instance attribution vectors as a point cloud, build Mapper graphs using predicted probability as the lens, and convert them to persistence diagrams and persistence landscapes. We introduce a variance-reduced generalized control-variate Monte Carlo (CVMC) estimator for mean landscapes and an adaptive epsilon grid that concentrates computation where stability changes most. Across 49 explainer-mechanism combinations, mean landscapes vary smoothly with privacy budget and exhibit a small set of recurring motifs; in this setting, first-homology landscapes are consistently zero. These results suggest that privatized explanations can remain informative proxies for model behavior, enabling auditing without direct access to raw records and providing a measurable tool for monitoring privacy-interpretability trade-offs and explanation drift in regulated deployments. Explainable artificial intelligence Trustworthy artificial intelligence Artificial neural networks topological data analysis Monte Carlo Methods Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8662668","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":589146586,"identity":"33ab0231-70c5-4254-9a0e-b45db8f2bd78","order_by":0,"name":"Paul Zheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYFACHhBRI8fAzgMVOECclmPGDMwkamFObCBaizn/2YOPC36xpfc38x78XNjGIMd3IwG/FsuGc8nGM/tkcmcc5kuWntnGYCxJSIvBwR4zad4ettyGwzwG0rxtDIkbCGo5zGP+m7eHOV3+MI/xb6CWesJajvGYMfP8YE4A6jUD2ZJgQNAvPTzG0rwNxww3HuZLs+Y5J2E488wD/FrM+c8Yfub5UyMvd7z38G2eMht5vuOEHAYiGNugPEY2CfzK4VoY/sC4f3AqHAWjYBSMghEMAF14QS6P9iwVAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Paul","middleName":"","lastName":"Zheng","suffix":""}],"badges":[],"createdAt":"2026-01-21 18:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8662668/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8662668/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107482275,"identity":"16e7a4d0-1f6a-4fd3-b297-3077a7d72389","added_by":"auto","created_at":"2026-04-22 02:22:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6027431,"visible":true,"origin":"","legend":"","description":"","filename":"PaulZheng.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8662668/v1_covered_4de65d8b-bedc-4391-94bf-2f9e89163ec7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Persistence Landscapes Across Privacy Budgets for Explanation Methods Across Differential Privacy Mechanisms","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Explainable artificial intelligence, Trustworthy artificial intelligence, Artificial neural networks, topological data analysis, Monte Carlo Methods","lastPublishedDoi":"10.21203/rs.3.rs-8662668/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8662668/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMachine-learning credit scoring must be both auditable and privacy-preserving, yet post-hoc explainers may rely on sensitive records or privileged model access that privacy constraints restrict. We study how local explanations for a feed-forward neural-network credit-risk classifier on the Home Equity Line of Credit (HELOC) dataset change when the data or learning pipeline is sanitized with differential privacy (DP) using additive noise, DP-Stochastic gradient descent (SGD), synthetic data generation, and DP-principal component analysis (PCA). While Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), and gradient-based attributions are widely used, their behavior under DP-induced noise remains poorly characterized. Topology-based comparisons using Mapper and persistence summaries can capture explanation structure beyond per-feature averages, but they raise sensitivity and estimation challenges. To close this gap, we treat per-instance attribution vectors as a point cloud, build Mapper graphs using predicted probability as the lens, and convert them to persistence diagrams and persistence landscapes. We introduce a variance-reduced generalized control-variate Monte Carlo (CVMC) estimator for mean landscapes and an adaptive epsilon grid that concentrates computation where stability changes most. Across 49 explainer-mechanism combinations, mean landscapes vary smoothly with privacy budget and exhibit a small set of recurring motifs; in this setting, first-homology landscapes are consistently zero. 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