A Subsampling Based Neural Network for Spatial Data

A Subsampling Based Neural Network for Spatial Data | 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PDF Research Article A Subsampling Based Neural Network for Spatial Data Debjoy Thakur This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5376863/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 The application of deep neural networks in geospatial data has become a trending research problem in the present day. A significant amount of statistical research has already been introduced, such as generalized least square optimization by incorporating spatial variance-covariance matrix, considering basis functions in the input nodes of the neural networks, and so on. However, for lattice data, there is no available literature about the utilization of asymptotic analysis of neural networks in regression for spatial data. This article proposes a consistent localized two-layer deep neural network-based regression for spatial data. We have proved the consistency of this deep neural network for bounded and unbounded spatial domains under a fixed sampling design of mixed-increasing spatial regions. We have proved that its asymptotic convergence rate is faster than that of [1]'s neural network and an improved generalization of [2]'s neural network structure. We empirically observe the rate of convergence of discrepancy measures between the empirical probability distribution of observed and predicted data, which will become faster for a less smooth spatial surface. We have applied our asymptotic analysis of deep neural networks to the estimation of the monthly average temperature of major cities in the USA from its satellite image. This application is an effective showcase of non-linear spatial regression. We demonstrate our methodology with simulated lattice data in various scenarios. Applied Statistics Spatial Subsampling Deep Neural Network Lattice Data Convergence Full Text Additional Declarations The authors declare no competing interests. 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. 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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-5376863","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":373206443,"identity":"7b0e7bc2-416e-418a-8bfb-32d23d9d43c2","order_by":0,"name":"Debjoy Thakur","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYDCCAzwMBkAqgYEHSH78YwMkGRsPEKHFAKyFcWZDGkhLA0EtDDAtzLwNhyGC+HTwHe89UPCx7U8ef88Zs8+8O87brW0/DLSlxiYalxbJM+cSDGe2GRRLnO0xnjn3zO3kbWcSgVqOpeU24NBicCPHwJi3zSCx4TyPMcMbttvJZgeAWhgbDuPWcv8NRMt8kBYetnPJZucfEtBygweiZQPQYYy8bQfszG4QsEXyTF6C4YxzxokbzxwrZpxxJjnB7AbQlgQ8fuE7fvaYwYcyucR5Z5I3M3yosLM3O5/+8MGHGhucWoCAzYCRDcFLBKtMwK0cBJgfMPxB8OzxKx4Fo2AUjIKRCACdEWwkg2rS4QAAAABJRU5ErkJggg==","orcid":"","institution":"Washington University in St. Louis","correspondingAuthor":true,"prefix":"","firstName":"Debjoy","middleName":"","lastName":"Thakur","suffix":""}],"badges":[],"createdAt":"2024-11-02 07:18:55","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5376863/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5376863/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68226848,"identity":"d8bd9362-1b6f-4664-b9b4-6c42003a8229","added_by":"auto","created_at":"2024-11-05 03:54:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2485949,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscriptmainbody.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5376863/v1_covered_1c9f02a3-1a69-4b39-b28f-4c3d28dab8a2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Subsampling Based Neural Network for Spatial Data\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Spatial Subsampling, Deep Neural Network, Lattice Data, Convergence","lastPublishedDoi":"10.21203/rs.3.rs-5376863/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5376863/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe application of deep neural networks in geospatial data has become a trending research problem in the present day. 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