Sampling from mixtures with negative weights: application to density approximation by Gaussian processes

Sampling from mixtures with negative weights: application to density approximation by Gaussian processes | 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 Sampling from mixtures with negative weights: application to density approximation by Gaussian processes Luca Martino This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8007555/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 Mixtures of probability densities are widely used in statistics and machine learning. While classical mixtures restrict weights to be non-negative, allowing negative weights enables more flexible density approximation. However, negative weights introduce challenges in handling and sampling such distributions. For this purpose, we propose efficient Monte Carlo (MC) methods (including MC quadratures, rejection sampling and importance sampling schemes)for computing integrals and generating samples from these mixtures. A tailored proposal density ensures accurate and efficient generation of (unweighted) samples. Applications in Gaussian process-based density estimation demonstrate the practical relevance and efficiency of proposed schemes. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Non-convex mixtures mixtures with negative weights Gaussian processes rejection sampling importance sampling 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-8007555","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":562493660,"identity":"8c6f7118-3897-420e-b7dd-cd4d3cbeac42","order_by":0,"name":"Luca Martino","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACPjiLGYg/MDDwgNgH8GlhgzF4gFoYZ4C0AIUO4NOD0AKyiAcmhFeLRPLDD4w5dvn27LwHH9u23ZHhn9/AePgDXi1pxhKM25Ite5j5ko1z257xSBwj5DCJHAagFmYDHmYeM+nctsM8BgT9IpHD/INxWz1EiyWRWtiAthyGaGEkSgvPMzOLxG3HDXgO8xgb9pw7DPRLYsOBM3i08LMnP77xcVu1AXv/GcMHP8oO2/M3Hz78oQKPFjBIQOUyNhDSMApGwSgYBaOAAAAAFRxAU9eLqJwAAAAASUVORK5CYII=","orcid":"","institution":"Università di Catania","correspondingAuthor":true,"prefix":"","firstName":"Luca","middleName":"","lastName":"Martino","suffix":""}],"badges":[],"createdAt":"2025-11-01 19:08:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8007555/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8007555/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98562812,"identity":"dcea5703-510b-4d39-b6df-43254baff7d1","added_by":"auto","created_at":"2025-12-19 03:25:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":529284,"visible":true,"origin":"","legend":"","description":"","filename":"MixNegweightsLucaversionScRep.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8007555/v1/67ccdcbf870540e8a42b3025.pdf"},{"id":98627122,"identity":"63212ffb-a3e6-4b1b-a0ec-54b73079c113","added_by":"auto","created_at":"2025-12-19 17:10:09","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2696,"visible":true,"origin":"","legend":"","description":"","filename":"3c6d14bcfd9e4a9898a058731ca5d64d.json","url":"https://assets-eu.researchsquare.com/files/rs-8007555/v1/6073c71947576a7efabb0138.json"},{"id":104461666,"identity":"f21cf1be-b8a9-492d-a92b-7bf3dcb1db57","added_by":"auto","created_at":"2026-03-12 04:25:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":409645,"visible":true,"origin":"","legend":"","description":"","filename":"MixNegweightsLucaversionScRep.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8007555/v1_covered_8e33b1bc-ba3b-42e3-8551-b543def15966.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sampling from mixtures with negative weights: application to density approximation by Gaussian processes","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":"Non-convex mixtures, mixtures with negative weights, Gaussian processes, rejection sampling, importance sampling","lastPublishedDoi":"10.21203/rs.3.rs-8007555/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8007555/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Mixtures of probability densities are widely used in statistics and machine learning. 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