{"title":"Optimal clustering from noisy binary feedback","authors":"","doi":"10.1007/s10994-024-06532-z","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent reCAPTCHA systems, users clicks (binary answers) can be used to efficiently label images. In our inference problem, items are grouped into initially unknown non-overlapping clusters. To recover these clusters, the learner sequentially presents to users a finite list of items together with a question with a binary answer selected from a fixed finite set. For each of these items, the user provides a noisy answer whose expectation is determined by the item cluster and the question and by an item-specific parameter characterizing the <em>hardness</em> of classifying the item. The objective is to devise an algorithm with a minimal cluster recovery error rate. We derive problem-specific information-theoretical lower bounds on the error rate satisfied by any algorithm, for both uniform and adaptive (list, question) selection strategies. For uniform selection, we present a simple algorithm built upon the K-means algorithm and whose performance almost matches the fundamental limits. For adaptive selection, we develop an adaptive algorithm that is inspired by the derivation of the information-theoretical error lower bounds, and in turn allocates the budget in an efficient way. The algorithm learns to select items hard to cluster and relevant questions more often. We compare the performance of our algorithms with or without the adaptive selection strategy numerically and illustrate the gain achieved by being adaptive.</p>","PeriodicalId":49900,"journal":{"name":"Machine Learning","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Machine Learning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10994-024-06532-z","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent reCAPTCHA systems, users clicks (binary answers) can be used to efficiently label images. In our inference problem, items are grouped into initially unknown non-overlapping clusters. To recover these clusters, the learner sequentially presents to users a finite list of items together with a question with a binary answer selected from a fixed finite set. For each of these items, the user provides a noisy answer whose expectation is determined by the item cluster and the question and by an item-specific parameter characterizing the hardness of classifying the item. The objective is to devise an algorithm with a minimal cluster recovery error rate. We derive problem-specific information-theoretical lower bounds on the error rate satisfied by any algorithm, for both uniform and adaptive (list, question) selection strategies. For uniform selection, we present a simple algorithm built upon the K-means algorithm and whose performance almost matches the fundamental limits. For adaptive selection, we develop an adaptive algorithm that is inspired by the derivation of the information-theoretical error lower bounds, and in turn allocates the budget in an efficient way. The algorithm learns to select items hard to cluster and relevant questions more often. We compare the performance of our algorithms with or without the adaptive selection strategy numerically and illustrate the gain achieved by being adaptive.
期刊介绍：
Machine Learning serves as a global platform dedicated to computational approaches in learning. The journal reports substantial findings on diverse learning methods applied to various problems, offering support through empirical studies, theoretical analysis, or connections to psychological phenomena. It demonstrates the application of learning methods to solve significant problems and aims to enhance the conduct of machine learning research with a focus on verifiable and replicable evidence in published papers.
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