{"id":4151,"date":"2025-05-28T07:02:30","date_gmt":"2025-05-28T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/05\/28\/2505-20465\/"},"modified":"2025-05-28T07:02:30","modified_gmt":"2025-05-28T07:02:30","slug":"2505-20465","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/05\/28\/2505-20465\/","title":{"rendered":"Learning with Expected Signatures: Theory and Applications"},"content":{"rendered":"

Learning with Expected Signatures: Theory and Applications
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arXiv:2505.20465v1 Announce Type: new
\nAbstract: The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This “model-free” embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) algorithms for time series and sequential data. The convergence results proved in this paper bridge the gap between the expected signature’s empirical discrete-time estimator and its theoretical continuous-time value, allowing for a more complete probabilistic interpretation of expected signature-based ML methods. Moreover, when the data generating process is a martingale, we suggest a simple modification of the expected signature estimator with significantly lower mean squared error and empirically demonstrate how it can be effectively applied to improve predictive performance.<\/div>\n

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\n Lorenzo Lucchese, Mikko S. Pakkanen, Almut E. D. Veraart
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Learning with Expected Signatures: Theory and Applications arXiv:2505.20465v1 Announce Type: new Abstract: The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This “model-free” embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,112,191],"tags":[84,2790,2038],"class_list":["post-4151","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-data","tag-expected","tag-signature"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4151"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=4151"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4151\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}