[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119319-en":3,"doc-seo-119319-105":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},119319,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Signature Methods in Machine Learning - A Survey","Signature-based techniques provide mathematical insight into interactions between evolving data streams, turning these insights into numerical methods for analyzing sequential data. Such approaches work particularly well when data is irregular, non-stationary, and where dimensionality and sample sizes are moderate. Truncated signatures yield a compact, lossy compression by filtering parameterisation noise, while preserving an exponential dependence on channel structure. This survey focuses on manageable regimes using principled context-free features with small datasets, supported by tractable examples and available notebooks, bridging communication gaps.","Signature Methods in Machine Learning  \nTerry Lyons & Andrew D. McLeod  \nFebruary 20, 2025  \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 sized can be any one of dn messages. Signatures provide a “lossy compression” of the information contained within such a stream by filtering out the parameterisation noise. More concretely, suppose we have a time series with 3 channels and N samples. There are 1+3N+ 3N(3N2+1) = 1+ ~~9~~2N (N+1) linearly independent quadratic polynomials defined on the time series. But the signature of this time series truncated to depth 2 only consists of 1 + 3 + 32 = 13 components which is, in particular, independent of the number of samples  \nN. However, whilst the independence of the number of samples N has removed an exponential amount of noise, the dependence on the number of channels to the power of the depth ensures that an exponential amount of information remains.  \nThis 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 5  \n2.1 Illustrative Toy Regression Problem ............................... 5  \n2.2 Incremental Streamed Data .................................... 6  \n2.3 Mathematical Framework ..................................... 9  \n2.4 Simple Regression Approach ................................... 11  \n2.5 Streams of Increments as Paths .................................. 13  \n2.6 Signature Involvement ...................................... 15  \n2.7 Tensor Algebra and Signature .................................. 17  \n2.8 Signature of Paths with Finite p-Variation ............................ 20  \n2.9 Rough Paths ............................................ 24  \n3 Signature as a Feature Map 28  \n4 Controlled Differential Equations and the Log-ODE Method 32  \n5 Comp","cbCaic7NzzRI8IxA","https://ap.wps.com/l/cbCaic7NzzRI8IxA","pdf",3997664,1,104,"English","en",105,"# Introduction\n# Background Material\n## Illustrative Toy Regression Problem\n## Incremental Streamed Data\n## Mathematical Framework\n## Simple Regression Approach\n## Streams of Increments as Paths\n## Signature Involvement\n## Tensor Algebra and Signature\n## Signature of Paths with Finite p-Variation\n## Rough Paths\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# Speech Emotion Recognition\n# Health Applications\n## Bipolar and Borderline Personality Disorders\n## Alzheimer’s Disease\n## Early Sepsis Detection\n## Information Extraction from Medical Prescriptions\n# Landmark-based Human Action Recognition\n## Path Disintegration and Transformations\n## Datasets\n## Method Implementation\n## Comparison with Specifically-Tailored Methods\n## Demo Notebook\n# Distribution Regression via the Expected Signature\n# Conformance and SigMahaKNN Method for Anomaly Detection\n# Randomised Signature","[{\"question\":\"What problem do signature-based methods address in machine learning?\",\"answer\":\"They analyze evolving data streams by extracting mathematical structure from irregular, non-stationary sequential data, and converting it into numerical approaches suited to moderate sample sizes and dimensions.\"},{\"question\":\"How do truncated signatures compress information from a data stream?\",\"answer\":\"Truncated signatures act as a lossy compression by filtering out parameterisation noise, reducing dependence on the number of samples while retaining significant dependence on channel interactions through the chosen depth.\"},{\"question\":\"What kinds of applications does the survey cover?\",\"answer\":\"It presents contexts including speech emotion recognition, multiple health applications such as Alzheimer’s disease and early sepsis detection, and landmark-based human action recognition, along with methods for distribution regression and anomaly detection.\"}]","Signature Methods in Machine Learning - A Survey | PDF",1785723701,262,{"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-a-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-a-survey/119319/",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","2026-08-03",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-based methods address in machine learning?","Question",{"text":75,"@type":76},"They analyze evolving data streams by extracting mathematical structure from irregular, non-stationary sequential data, and converting it into numerical approaches suited to moderate sample sizes and dimensions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do truncated signatures compress information from a data stream?",{"text":80,"@type":76},"Truncated signatures act as a lossy compression by filtering out parameterisation noise, reducing dependence on the number of samples while retaining significant dependence on channel interactions through the chosen depth.",{"name":82,"@type":73,"acceptedAnswer":83},"What kinds of applications does the survey cover?",{"text":84,"@type":76},"It presents contexts including speech emotion recognition, multiple health applications such as Alzheimer’s disease and early sepsis detection, and landmark-based human action recognition, along with methods for distribution regression 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"]