[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122537-en":3,"doc-seo-122537-105":30,"detail-sidebar-cat-0-en-105":96},{"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":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},122537,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Non-asymptotic performance of social machine learning under limited data","This paper studies the probability of error associated with the social machine learning framework, where agents perform an independent training phase and then cooperative decision-making over a graph. The focus is on classification using limited observations during the decision-making phase, requiring a non-asymptotic performance analysis. A condition for consistent training is established, together with an upper bound on the classification error probability. The results characterize how data statistics and graph combination policies affect performance, and show exponential decay of error with the number of unlabeled samples.","Signal Processing 230 (2025) 109849  \n| Non-asymptotic performance of social machine learning under limited data ✩ Ping Hu ∗, Virginia Bordignon, Mert Kayaalp, Ali H. Sayed\u003Cbr>School of Engineering, EPFL, CH-1015, Lausanne, Switzerland |  |  |\n| --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |\n| Keywords:\u003Cbr>Social machine learning\u003Cbr>Probability of error\u003Cbr>Classification\u003Cbr>Non-asymptotic analysis |  | This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. In this work, we examine the classification task with limited observations during the decision-making phase, which requires a non-asymptotic performance analysis. We establish a condition for consistent training and derive an upper bound on the probability of error for classification. The results clarify the dependence on the statistical properties of the data and the combination policy used over the graph. They also establish the exponential decay of the probability of error with respect to the number of unlabeled samples. |\n\n1. Introduction  \nSocial learning is a useful paradigm for addressing decision-making tasks involving a group of agents. Practical applications arise in various scenarios, such as detection and object recognition using autonomous robots, as well as statistical inference and learning across multiple processors [1,2]. In this paper, we focus on the social machine learning (SML) framework introduced in [3], which is a data-driven cooperative decision-making paradigm. The main motivation for the introduction of this framework is to address a critical limitation of traditional social learning solutions [4–11]. These solutions allow a group of agents to interact over a graph to arrive at consensus decisions about a hypothesis of interest. However, a limiting assumption in all these studies is the requirement that the likelihood models for data generation are known beforehand. The SML strategy removes this requirement, thus opening up the door for solving classification tasks in a distributed manner with performance guarantees by relying solely on a data-driven implementation.  \nThe SML strategy consists of two learning phases, as depicted in Fig. 1. In the training phase on the left, each agent trains a classifier independently using a finite set of labeled samples within a supervised learning framework (such as logistic regression, neural networks, or other convenient frameworks). The purpose of this phase is to learn some discriminative information that allows agents to distinguish different hypotheses. The output of the trained classifier is used to forma local decision statistic for inference in the form of a log-likelihood ratio [12,13]. In the prediction phase shown on the right of Fig. 1, agents receive streaming unlabeled samples and implement a social learning  \nprotocol based on the trained classifiers to infer the true state. With the well-established performance guarantees for both supervised learning and more recent social learning solutions, it is expected that the SML strategy, which combines the benefits of both approaches, should be able to deliver correct learning with high probability for a sufficient number of training samples.  \nTo support this claim, the work [3] has provided a rigorous theoretical analysis on the probability of consistent training concerning the asymptotic truth learning in the prediction phase, and also illustrated the excellent classification performance of the SML strategy through extensive supporting simulations. As we will show in the main body of this paper, the probability of consistent training derived in [3] providesan upper bound for the probability of error in the infinite-sample case, namely, the probability of wrong decisions when the num","cbCaiu0QolJEXP9m","https://ap.wps.com/l/cbCaiu0QolJEXP9m","pdf",1499251,1,12,"English","en",105,"# Introduction\n## Problem motivation and social learning background\n## Social machine learning framework and two-phase strategy\n## Finite-sample motivation for non-asymptotic analysis","[{\"question\":\"What are the two phases in the social machine learning framework studied here?\",\"answer\":\"Agents first perform an independent training phase using labeled samples, learning discriminative information. They then enter a prediction phase where they cooperate over a graph to infer the true state from streaming unlabeled data.\"},{\"question\":\"What is analyzed in the paper regarding classification performance?\",\"answer\":\"The paper derives a non-asymptotic performance analysis for the probability of error when the number of observations during decision-making is limited. It provides a consistency condition for training and an upper bound on classification error.\"},{\"question\":\"How do graph combination policies and data statistics influence the results?\",\"answer\":\"The derived error bounds clarify the dependence on both statistical properties of the data and the combination policy used across the graph during cooperative inference.\"},{\"question\":\"What convergence behavior does the paper establish for the probability of error?\",\"answer\":\"It shows exponential decay of the probability of error as the number of unlabeled samples increases.\"}]","Non-asymptotic performance of social machine learning under limited data | PDF",1785811142,30,{"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":91,"head_meta":93,"extra_data":95,"updated_unix":28},"non-asymptotic-performance-of-social-machine-learning-under-limited-data","",{"@graph":36,"@context":90},[37,54,69],{"@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/non-asymptotic-performance-of-social-machine-learning-under-limited-data/122537/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82,86],{"name":73,"@type":74,"acceptedAnswer":75},"What are the two phases in the social machine learning framework studied here?","Question",{"text":76,"@type":77},"Agents first perform an independent training phase using labeled samples, learning discriminative information. They then enter a prediction phase where they cooperate over a graph to infer the true state from streaming unlabeled data.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What is analyzed in the paper regarding classification performance?",{"text":81,"@type":77},"The paper derives a non-asymptotic performance analysis for the probability of error when the number of observations during decision-making is limited. It provides a consistency condition for training and an upper bound on classification error.",{"name":83,"@type":74,"acceptedAnswer":84},"How do graph combination policies and data statistics influence the results?",{"text":85,"@type":77},"The derived error bounds clarify the dependence on both statistical properties of the data and the combination policy used across the graph during cooperative inference.",{"name":87,"@type":74,"acceptedAnswer":88},"What convergence behavior does the paper establish for the probability of error?",{"text":89,"@type":77},"It shows exponential decay of the probability of error as the number of unlabeled samples increases.","https://schema.org",{"og:url":52,"og:type":92,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":94,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":97},[98,102,106,110,115,120,125,127,132,135,139],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Exam",70,"exam",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":29,"slug":126},"research-report",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":130,"slug":131},9,"Religion & Spirituality",20,"religion-spirituality",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":130,"slug":134},"World Cup","world-cup",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":136,"slug":138},10,"Lifestyle","lifestyle",{"id":140,"doc_module":4,"doc_module_name":46,"category_name":141,"show_sort_weight":111,"slug":142},19,"General","general"]