{"id":4821,"date":"2025-06-24T07:02:42","date_gmt":"2025-06-24T07:02:42","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/06\/24\/2506-17634\/"},"modified":"2025-06-24T07:02:42","modified_gmt":"2025-06-24T07:02:42","slug":"2506-17634","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/06\/24\/2506-17634\/","title":{"rendered":"Scalable Machine Learning Algorithms using Path Signatures"},"content":{"rendered":"<p>    Scalable Machine Learning Algorithms using Path Signatures<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2506.17634v1 Announce Type: new<br \/>\nAbstract: The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures &#8211; iterated integrals that provide faithful, hierarchical representations of paths &#8211; offering a principled and universal feature map for sequential and structured data. Rooted in rough path theory, path signatures are invariant to reparameterization and well-suited for modelling evolving dynamics, long-range dependencies, and irregular sampling &#8211; common challenges in real-world time series and graph data.<br \/>\n  This thesis investigates how to harness the expressive power of path signatures within scalable machine learning pipelines. It introduces a suite of models that combine theoretical robustness with computational efficiency, bridging rough path theory with probabilistic modelling, deep learning, and kernel methods. Key contributions include: Gaussian processes with signature kernel-based covariance functions for uncertainty-aware time series modelling; the Seq2Tens framework, which employs low-rank tensor structure in the weight space for scalable deep modelling of long-range dependencies; and graph-based models where expected signatures over graphs induce hypo-elliptic diffusion processes, offering expressive yet tractable alternatives to standard graph neural networks. Further developments include Random Fourier Signature Features, a scalable kernel approximation with theoretical guarantees, and Recurrent Sparse Spectrum Signature Gaussian Processes, which combine Gaussian processes, signature kernels, and random features with a principled forgetting mechanism for multi-horizon time series forecasting with adaptive context length.<br \/>\n  We hope this thesis serves as both a methodological toolkit and a conceptual bridge, and provides a useful reference for the current state of the art in scalable, signature-based learning for sequential and structured data.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Csaba T&#8217;oth<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2506.17634\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scalable Machine Learning Algorithms using Path Signatures arXiv:2506.17634v1 Announce Type: new Abstract: The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures &#8211; iterated integrals that provide faithful, hierarchical representations of paths &#8211; offering a principled and universal feature map for sequential and structured data. Rooted in rough path [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,420,112],"tags":[199,2115,3042],"class_list":["post-4821","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-pr","category-stat-ml","tag-learning","tag-path","tag-scalable"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4821"}],"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=4821"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4821\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}