[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117783-en":3,"doc-seo-117783-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117783,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Signature Methods in Machine Learning - Survey","Signature-based techniques provide mathematical insight into interactions within complex streams of evolving data, supporting numerical methods for analyzing non-stationary and irregular sequences where both dimensionality and sample sizes are moderate. The survey addresses scalable manageability of exponential behavior by focusing on settings with small datasets and small, context-free principled features. It connects intimidating theory to tractable machine-learning examples, including notebooks, while illustrating signature-driven analysis that remains largely agnostic to data type, with applications spanning health, speech emotion, and human action recognition.","arXiv :2206 . 14674v4 [ stat .ML] 26 Jan 2023  \nSignature Methods in Machine Learning  \nTerry Lyons & Andrew D. McLeod  \nJanuary 27, 2023  \nAbstract  \nSignature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps because of their mathematical precision, have proved useful in analysing streamed data in situations where the data is irregular, and not stationary, and the dimension of the data and the sample sizes are both moderate.  \nUnderstanding streamed multi-modal data is exponential: a word in n letters from an alphabet of size d can be any one of dn messages. Signatures remove the exponential amount of noise that arises from sampling irregularity, but an exponential amount of information still remain. This survey aims to stay in the domain where that exponential scaling can be managed directly. Scalability issues are an important challenge in many problems but would require another survey article and further ideas. This survey describes a range of contexts where the data sets are small and the existence of small sets of context free and principled features can be used effectively.  \nThe mathematical nature of the tools can make their use intimidating to non-mathematicians. The examples presented in this article are intended to bridge this communication gap and provide tractable working examples drawn from the machine learning context. Notebooks are available online for several of these examples. This survey builds on the earlier paper of Ilya Chevryev and Andrey Kormilitzin which had broadly similar aims at an earlier point in the development of this machinery.  \nThis article illustrates how the theoretical insights offered by signatures are simply realised in the analysis of application data in a way that is largely agnostic to the data type. Larger and more complex problems would expect to address scalability issues and draw on a wider range of data science techniques.  \nThe article starts with a brief discussion of background material related to machine learning and signatures. This discussion fixes notation and terminology whilst simplifying the dependencies, but these background sections are not a substitute for the extensive literature they draw from.  \nHopefully, by working some of the examples the reader will find access to useful and simple to deploy tools; tools that are moderately effective in analysing longitudinal data that is complex and irregular in contexts where massive machine learning is not a possibility.  \nContents  \n1 Introduction 2  \n2 Background Material 4  \n2.1 Simple Approach to Regression ....................................... 4  \n2.2 Transforming Datasets to Paths ....................................... 6  \n2.3 Signature Involvement ............................................ 12  \n2.4 Tensor Algebra and Signature ........................................ 13  \n3 Signature as a Feature Map 15  \n4 Controlled Differential Equations and the Log-ODE Method 18  \n5 Computing Signatures 20  \n6 Expected Signature 23  \n7 Truncation Order Selection 25  \n8 Signature Kernel 27  \n9 Neural CDEs and Neural RDEs 31  \n10 Speech Emotion Recognition 34  \n11 Health Applications 36  \n11.1 Bipolar and Borderline Personality Disorders ................................ 36  \n11.2 Alzheimer's Disease ............................................. 41  \n11.3 Early Sepsis Detection ............................................ 42  \n11.4 Information Extraction from Medical Prescriptions ............................. 45  \n12 Landmark-based Human Action Recognition 49  \n12.1 Path Disintegration and Transformations .................................. 50  \n12.2 Datasets ................................................... 51  \n12.3 Method Implementation ........................................... 51  \n12.4 Comparison with Specifically-Tailored Methods ................","cbCaipblR7an2fR2","https://ap.wps.com/l/cbCaipblR7an2fR2","pdf",6002786,1,72,"English","en",105,"# Introduction\n# Background Material\n## Simple Approach to Regression\n## Transforming Datasets to Paths\n## Signature Involvement\n## Tensor Algebra and Signature\n# Signature as a Feature Map\n# Controlled Differential Equations and the Log-ODE Method\n# Computing Signatures\n# Expected Signature\n# Truncation Order Selection\n# Signature Kernel\n# Neural CDEs and Neural RDEs\n# Application Sections\n## Speech Emotion Recognition\n## Health Applications\n## Landmark-based Human Action Recognition\n# Distribution Regression via the Expected Signature\n# Anomaly Detection","[{\"question\":\"What problem do signature methods address in machine learning for streamed data?\",\"answer\":\"They provide a mathematically grounded feature representation that captures event order across multiple channels while being insensitive to sampling frequency, helping analyze non-stationary and irregular streams more efficiently than standard time-series approaches.\"},{\"question\":\"How does a path signature behave with respect to sampling and event ordering?\",\"answer\":\"A signature is a forgetful summary that ignores parameterization, so varying how often a path is sampled does not change it, while the order of events across different channels is preserved.\"},{\"question\":\"What application areas does the survey cover?\",\"answer\":\"The survey includes speech emotion recognition, multiple health use cases such as bipolar and borderline personality disorders, Alzheimer’s disease, early sepsis detection, and information extraction from medical prescriptions, plus landmark-based human action recognition and anomaly detection.\"}]","Signature Methods in Machine Learning - Survey | PDF",1785679528,181,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"signature-methods-in-machine-learning-survey","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/signature-methods-in-machine-learning-survey/117783/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem do signature methods address in machine learning for streamed data?","Question",{"text":75,"@type":76},"They provide a mathematically grounded feature representation that captures event order across multiple channels while being insensitive to sampling frequency, helping analyze non-stationary and irregular streams more efficiently than standard time-series approaches.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does a path signature behave with respect to sampling and event ordering?",{"text":80,"@type":76},"A signature is a forgetful summary that ignores parameterization, so varying how often a path is sampled does not change it, while the order of events across different channels is preserved.",{"name":82,"@type":73,"acceptedAnswer":83},"What application areas does the survey cover?",{"text":84,"@type":76},"The survey includes speech emotion recognition, multiple health use cases such as bipolar and borderline personality disorders, Alzheimer’s disease, early sepsis detection, and information extraction from medical prescriptions, plus landmark-based human action recognition and anomaly detection.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]