Data reconstruction from machine learning models via inverse estimation and Bayesian inference

Data reconstruction from machine learning models via inverse estimation and Bayesian inference | 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 Article Data reconstruction from machine learning models via inverse estimation and Bayesian inference Agus Hartoyo, Dominika Ciupek, Maciej Malawski, Alessandro Crimi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5220310/v3 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Apr, 2025 Read the published version in Scientific Reports → Version 3 posted 8 You are reading this latest preprint version Show more versions Abstract This study explores the task of data reconstruction from machine learning models via inverse estimation and Bayesian inference, with the goal of recovering the original dataset solely based on the trained model. We introduce a novel theoretical framework that investigates the factors affecting the data reconstruction quality. Specifically, we derive expressions that quantify how variations in key variables influence the divergence between true and estimated posteriors by examining the concurrent behavior of their partial derivatives with respect to independent variables. This derivative-based approach establishes theoretical correlations between the variables, demonstrating that the fidelity of the recovered data is governed by two primary factors: (1) the accuracy of the assumed prior, and (2) the accuracy of the machine learning model. Empirical results across multiple benchmark datasets and machine learning algorithms corroborate these theoretical predictions, reinforcing the validity and robustness of our theoretical framework. Practically, our data reconstruction method enables the creation of synthetic models that closely replicate the performance of the original models. This work contributes to advancing the theoretical understanding and practical techniques for data reconstruction and model introspection within the context of machine learning. Full Text Additional Declarations No competing interests reported. Supplementary Files AppendixAAdditionaldatasetresults.pdf AppendixBFullproofsfortheoremsintheoreticalframework.pdf Cite Share Download PDF Status: Published Journal Publication published 22 Apr, 2025 Read the published version in Scientific Reports → Version 3 posted Editorial decision: Accepted 26 Mar, 2025 Reviews received at journal 26 Mar, 2025 Reviewers agreed at journal 26 Mar, 2025 Reviews received at journal 17 Mar, 2025 Reviewers agreed at journal 17 Mar, 2025 Reviewers invited by journal 17 Mar, 2025 Submission checks completed at journal 16 Mar, 2025 First submitted to journal 13 Mar, 2025 You are reading this latest preprint version Show more versions 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-5220310","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":430754682,"identity":"e41cb7e1-0464-11f0-91e4-06cc9d20a69f","order_by":0,"name":"Agus Hartoyo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCklEQVRIiWNgGAWjYFACHijN3gCh2YjTkgCiD5CsRSKBSGfxN/Ae/Fz5wyaxX/L5w88FFXXyfOy9Bz98YLDJl3fArkXiAF+y5JmEtMSZs3OMpWecOWzYxnMuWXIGQ5rlxgM4rDnAYyDZkHA4ccPtHAZp3rYDCWwSOWbMPAyHDQwbsOuQP8Bj/BOs5ebxx7952+oS2OTfmDH/waPF4ACPGcSWGwxmQFuYgbbwmDEzALXI43CX4WEeM8uGtDTjmT05ZtY8YL/kGEv2GKQZGODQIne8x/hmg42NbD/78ce3eYAhJt9+xvDDjwobA3kcDmNghlCOaPIGIDfj0AIF9phCOG0ZBaNgFIyCkQYAnyxUHCfAPWUAAAAASUVORK5CYII=","orcid":"","institution":"Sano - 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