{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T04:25:30Z","timestamp":1773030330383,"version":"3.50.1"},"reference-count":30,"publisher":"MIT Press - Journals","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> The Bradley-Terry model is a statistical representation for one's preference or ranking data by using pairwise comparison results of items. For estimation of the model, several methods based on the sum of weighted Kullback-Leibler divergences have been proposed from various contexts. The purpose of this letter is to interpret an estimation mechanism of the Bradley-Terry model from the viewpoint of flatness, a fundamental notion used in information geometry. Based on this point of view, a new estimation method is proposed on a framework of the em algorithm. The proposed method is different in its objective function from that of conventional methods, especially in treating unobserved comparisons, and it is consistently interpreted in a probability simplex. An estimation method with weight adaptation is also proposed from a viewpoint of the sensitivity. Experimental results show that the proposed method works appropriately, and weight adaptation improves accuracy of the estimate. <\/jats:p>","DOI":"10.1162\/neco_a_00129","type":"journal-article","created":{"date-parts":[[2011,5,7]],"date-time":"2011-05-07T00:12:42Z","timestamp":1304727162000},"page":"1623-1659","source":"Crossref","is-referenced-by-count":5,"title":["An Estimation of Generalized Bradley-Terry Models Based on the <i>em<\/i> Algorithm"],"prefix":"10.1162","volume":"23","author":[{"given":"Yu","family":"Fujimoto","sequence":"first","affiliation":[{"name":"Department of Integrated Information Technology, Aoyama Gakuin University, Chuo, Sagamihara, Kanagawa 252-5258, Japan"}]},{"given":"Hideitsu","family":"Hino","sequence":"additional","affiliation":[{"name":"School of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan"}]},{"given":"Noboru","family":"Murata","sequence":"additional","affiliation":[{"name":"School of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1002\/0471249688"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(95)00003-8"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.10.2780"},{"key":"B4","volume-title":"Methods of information geometry","author":"Amari S.","year":"2000"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.549"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343842"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.2307\/2334029"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90040-7"},{"key":"B9","volume-title":"Elements of information theory","author":"Cover T. 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