{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T16:46:04Z","timestamp":1784738764571,"version":"3.55.0"},"reference-count":22,"publisher":"MIT Press","issue":"5","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,4,18]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The binary classification problem has a situation where only biased data are observed in one of the classes. In this letter, we propose a new method to approach the positive and biased negative (PbN) classification problem, which is a weakly supervised learning method to learn a binary classifier from positive data and negative data with biased observations. We incorporate a method to correct the negative influence due to a skewed confidence, which is represented by the posterior probability that the observed data are positive. This reduces the distortion of the posterior probability that the data are labeled, which is necessary for the empirical risk minimization of the PbN classification problem. We verified the effectiveness of the proposed method by synthetic and benchmark data experiments.<\/jats:p>","DOI":"10.1162\/neco_a_01580","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T22:26:16Z","timestamp":1679437576000},"page":"977-994","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":2,"title":["Classification From Positive and Biased Negative Data With Skewed Labeled Posterior Probability"],"prefix":"10.1162","volume":"35","author":[{"given":"Shotaro","family":"Watanabe","sequence":"first","affiliation":[{"name":"Graduate School of Data Science, Shiga University, Shiga 522-8522, Japan s6021142@st.shiga-u.ac.jp"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hidetoshi","family":"Matsui","sequence":"additional","affiliation":[{"name":"Faculty of Data Science, Shiga University, Shiga 522-8522, Japan hmatsui@biwako.shiga-u.ac.jp"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"key":"2023041921575045100_B1","first-page":"15773","article-title":"Space and time efficient kernel density estimation in high dimensions","volume-title":"Advances in neural information processing systems","author":"Backurs","year":"2019"},{"key":"2023041921575045100_B2","article-title":"Wireless indoor localization","author":"Bhatt","year":"2017"},{"key":"2023041921575045100_B3","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/9780262033589.001.0001","volume-title":"Semi-supervised learning","author":"Chapelle","year":"2006"},{"key":"2023041921575045100_B4","first-page":"1510","article-title":"Self-PU: Self boosted and calibrated positive-unlabeled training","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Chen","year":"2020"},{"key":"2023041921575045100_B5","first-page":"703","article-title":"Analysis of learning from positive and unlabeled data","volume-title":"Advances in neural information processing systems","author":"du Plessis","year":"2014"},{"key":"2023041921575045100_B6","first-page":"1386","article-title":"Convex formulation for learning from positive and unlabeled data","volume-title":"Proceedings of the Conference on Machine Learning","author":"du Plessis","year":"2015"},{"key":"2023041921575045100_B7","first-page":"221","article-title":"Class-prior estimation for learning from positive and unlabeled data","volume-title":"Proceedings of the Asian Conference on Machine Learning","author":"du Plessis","year":"2016"},{"issue":"5","key":"2023041921575045100_B8","doi-asserted-by":"publisher","first-page":"1358","DOI":"10.1587\/transinf.E97.D.1358","article-title":"Class prior estimation from positive and unlabeled data","volume":"97","author":"du Plessis","year":"2014","journal-title":"IEICE Trans. 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