{"title":"Kernel mean embedding vs kernel density estimation: A quantum perspective","authors":"Yann Berquin","doi":"10.1016/j.physleta.2024.130047","DOIUrl":null,"url":null,"abstract":"<div><div>This short study investigates the link between kernel methods and quantum mechanics. Density operators representing ensembles of pure states of sample wave functions are used in place of probability densities and Kraus operator is used to embed samples. Results show that using density operators associated to different quantum systems along with embedded samples allows to recover kernel density estimation as well as kernel mean embedding equations. Results are illustrated with a simple example using discrete orthogonal wavelet transform.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"528 ","pages":"Article 130047"},"PeriodicalIF":2.3000,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960124007412","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This short study investigates the link between kernel methods and quantum mechanics. Density operators representing ensembles of pure states of sample wave functions are used in place of probability densities and Kraus operator is used to embed samples. Results show that using density operators associated to different quantum systems along with embedded samples allows to recover kernel density estimation as well as kernel mean embedding equations. Results are illustrated with a simple example using discrete orthogonal wavelet transform.
期刊介绍：
Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.
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