{"title":"平方根分析估计量的Oracle不等式及其在总变异罚中的应用","authors":"Francesco Ortelli;Sara van de Geer","doi":"10.1093/imaiai/iaaa002","DOIUrl":null,"url":null,"abstract":"Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan et al. (2017, Bernoulli, 23, 552–581). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"483-514"},"PeriodicalIF":1.4000,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa002","citationCount":"6","resultStr":"{\"title\":\"Oracle inequalities for square root analysis estimators with application to total variation penalties\",\"authors\":\"Francesco Ortelli;Sara van de Geer\",\"doi\":\"10.1093/imaiai/iaaa002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan et al. (2017, Bernoulli, 23, 552–581). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.\",\"PeriodicalId\":45437,\"journal\":{\"name\":\"Information and Inference-A Journal of the Ima\",\"volume\":\"10 1\",\"pages\":\"483-514\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2020-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1093/imaiai/iaaa002\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Information and Inference-A Journal of the Ima\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/9514689/\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Inference-A Journal of the Ima","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/9514689/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Oracle inequalities for square root analysis estimators with application to total variation penalties
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan et al. (2017, Bernoulli, 23, 552–581). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.
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