{"paper_id":"357df2df-86c2-433c-9bf4-0ec7bd643bf9","body_text":"Approximation of multivariate Gaussian density by tensor trains | 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 Approximation of multivariate Gaussian density by tensor trains Jiří Ajgl, Ondřej Straka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5895329/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Sep, 2025 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract Tensor train decomposition is a promising tool for dealing with high dimensional arrays. Point mass filters utilise such arrays for representing probability density functions of the state. Proofs of concept of the application of the low rank decomposition have been provided in the literature. However, the application requires to design parameters, such as tensor train ranks. Since the parameters dictating the computational requirements are derived from the data according to more abstract hyper-parameters such as precision, an analysis of benchmark examples is needed for allocating resources. This paper studies the ranks in the case of Gaussian densities. The influence of correlation and the effect of rounding are discussed first. Efficiency of the density representation used by standard point mass filters is considered next. Aspects of series expansion of the Gaussian density evaluated over array are considered for the tensor train format. The growth of the ranks is illustrated on a four-dimensional example. An observation of the growth for a multi-dimensional case is made last. The lessons learned are valuable for designing efficient point mass filters. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Sep, 2025 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 18 Apr, 2025 Reviews received at journal 17 Apr, 2025 Reviews received at journal 26 Mar, 2025 Reviewers agreed at journal 28 Jan, 2025 Reviewers agreed at journal 26 Jan, 2025 Reviewers invited by journal 26 Jan, 2025 Editor assigned by journal 26 Jan, 2025 Submission checks completed at journal 25 Jan, 2025 First submitted to journal 24 Jan, 2025 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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