[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126538-en":3,"doc-seo-126538-105":31,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126538,962085662650,"Jiven","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","The Shape of Explanations - A Topological Account of Rule-Based Explanations in Machine Learning","Rule-based explanations provide simple reasons that describe how machine learning classifiers behave at specific feature-space points. Recent approaches such as Anchors and LORE generate rule-based explanations for arbitrary or black-box classifiers, but their general effectiveness remains unclear. This work introduces a topological framework that characterizes explainability via the definability of a classifier relative to an explanation scheme. It analyzes multiple scheme choices and argues the best option depends on user domain knowledge and the probability measure over the feature space.","The AAAI 2023 Workshop on Representation Learning for Responsible Human-Centric AI (R2 HCAI)  \nThe Shape of Explanations: A Topological Account of Rule-Based Explanations in  \nMachine Learning  \nBrett Mullins 1  \n1 University of Massachusetts Amherst  \n[bmullins@umass.edu](bmullins@umass.edu)  \narXiv :2301 .09042v1 [ cs .LG] 22 Jan 2023  \nAbstract  \nRule-based explanations provide simple reasons explaining the behavior of machine learning classi􀀂ers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for arbitrary or black-box classi􀀂ers. But what makes these methods work in general? We introduce a topological framework for rulebased explanation methods and provide a characterization of explainability in terms of the de􀀂nability of a classi􀀂er relative to an explanation scheme. We employ this framework to consider various explanation schemes and argue that the preferred scheme depends on how much the user knows about the domain and the probability measure over the feature space.  \n1 Introduction  \nExplanations for predictions of machine learning models act as reasons for a predictive model’s behavior and are desirable for trustworthy and transparent machine learning (Molnar 2022) . With this being said, there is not much agreement in the machine learning community on exactly what counts as an explanation (Doshi-Velez and Kim 2017; Burkart and Huber 2021). Machine learning practitioners have developed a large set of domain-speci􀀂c explanation methods in recent years. These methods are tailored either to the speci􀀂c task the model is seeking to perform, e.g. regression, classi􀀂cation, object detection, etc., or to the type of inputs and outputs of the model, e.g., tabular features, images, sentences, etc. (Islam et al. 2022) .  \nA promising technique for explaining the predictions of structured or tabular classi􀀂ers is rule-based explanations. A rule-based explanation is a predicate de􀀂ning a simple region in the feature space that is suf􀀂cient for classifying a given point. In this paper, we take advantage of the connection between the inherent de􀀂nability of rule-based explanations and de􀀂nability in topology to develop a general framework to represent varieties of explanations based on existing explanation algorithms.  \nTo summarize this paper, we make the following contributions:  \n• We present a novel framework of explainability for rulebased classi􀀂ers based on existing explanation algorithms.  \n• We characterize explainability as a topological property relative to an explanation scheme i.e. relative to a choice of explanation shape and a measure of explanation size. We conjecture that all classi􀀂ers “in the wild” satisfy this notion of explainability.  \n• Employing our framework, we identify two principles for explanation algorithms that apply both theoretically and in practice. The 􀀂rst is that rule-based explanations can take nearly any desired shape. The second holds that if no probability measure is known over the feature space and at least one feature is not bounded, then explanations should be bounded, i.e. include all unbounded features.  \nThis paper proceeds as follows. In Section 2, we discuss various existing explanation algorithms and provide a brief introduction to topology. We introduce explanation schemes as a framework for explainability and characterize explainability as a topological property in Sections 3, 4, respectively. In Section 5, we derive principles for both formal and practical explanation algorithms. In Sections 6, 7, we conclude by discussing limitations and open problems and surveying related work.  \n2 Background  \nRule-Based Explanations  \nIn this section, we introduce rule-based explanation algorithms and consider their representative properties. Given a classi􀀂er and a point in the feature space, a rule-based explanation algorithm generates a rule de􀀂ned in terms of the features of the classi􀀂er that both covers the","cbCaiiL0YiDf8nLx","https://ap.wps.com/l/cbCaiiL0YiDf8nLx","pdf",113084,3,1,6,"English","en",105,"# Abstract\n# Introduction\n# Background\n## Rule-Based Explanations\n## Topology\n## Rule-based Explanation Algorithms","[{\"question\":\"What does the paper study about rule-based explanations?\",\"answer\":\"It studies when and why rule-based explanation methods work in general. The paper connects rule-based explainability to topological definability relative to an explanation scheme.\"},{\"question\":\"How does the proposed topological framework characterize explainability?\",\"answer\":\"Explainability is characterized as a topological property tied to a chosen explanation shape and a measure that determines explanation size. It is expressed through the definability of the classifier relative to that scheme.\"},{\"question\":\"What factors influence which explanation scheme is preferred?\",\"answer\":\"The paper argues preference depends on how much the user knows about the domain and on the probability measure over the feature space.\"}]","The Shape of Explanations - A Topological Account of Rule-Based Explanations in Machine Learning | PDF",1785933208,15,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"the-shape-of-explanations-a-topological-account-of-rule-based-explanations-in-machine-learning","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":20},"https://docshare.wps.com/document/research-report/",{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/the-shape-of-explanations-a-topological-account-of-rule-based-explanations-in-machine-learning/126538/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-24","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What does the paper study about rule-based explanations?","Question",{"text":76,"@type":77},"It studies when and why rule-based explanation methods work in general. The paper connects rule-based explainability to topological definability relative to an explanation scheme.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the proposed topological framework characterize explainability?",{"text":81,"@type":77},"Explainability is characterized as a topological property tied to a chosen explanation shape and a measure that determines explanation size. It is expressed through the definability of the classifier relative to that scheme.",{"name":83,"@type":74,"acceptedAnswer":84},"What factors influence which explanation scheme is preferred?",{"text":85,"@type":77},"The paper argues preference depends on how much the user knows about the domain and on the probability measure over the feature space.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":22,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":113,"slug":114},"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":47,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":47,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":47,"category_name":137,"show_sort_weight":107,"slug":138},19,"General","general"]