{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T05:20:53Z","timestamp":1769923253360,"version":"3.49.0"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643685489","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T00:00:00Z","timestamp":1729036800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,16]]},"abstract":"<jats:p>Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. Zhou and Feng [51] further propose a deep forest algorithm with multi-layer forests, which outperforms random forests in various tasks. The performance of deep forests is related to three hyperparameters in practice: depth, width, and tree size, but little has been known about its theoretical explanation. This work provides the first upper and lower bounds on the approximation complexity of deep forests concerning the three hyperparameters. Our results confirm the distinctive role of depth, which can exponentially enhance the expressiveness of deep forests compared with width and tree size. Experiments validate these theoretical findings. The detailed proof and code are available in the full version [31].<\/jats:p>","DOI":"10.3233\/faia240721","type":"book-chapter","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T13:13:55Z","timestamp":1729170835000},"source":"Crossref","is-referenced-by-count":1,"title":["The Role of Depth, Width, and Tree Size in Expressiveness of Deep Forest"],"prefix":"10.3233","author":[{"given":"Shen-Huan","family":"Lyu","sequence":"first","affiliation":[{"name":"Key Laboratory of Water Big Data Technology of Ministry of Water Resources, Hohai University, China"},{"name":"College of Computer Science and Software Engineering, Hohai University, China"},{"name":"National Key Laboratory for Novel Software Technology, Nanjing University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin-Hui","family":"Wu","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Novel Software Technology, Nanjing University, China"},{"name":"School of Artificial Intelligence, Nanjing University, China, lvsh@hhu.edu.cn, wujh@lamda.nju.edu.cn, zhengqc@lamda.nju.edu.cn, yebl@nju.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin-Cheng","family":"Zheng","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Novel Software Technology, Nanjing University, China"},{"name":"School of Artificial Intelligence, Nanjing University, China, lvsh@hhu.edu.cn, wujh@lamda.nju.edu.cn, zhengqc@lamda.nju.edu.cn, yebl@nju.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoliu","family":"Ye","sequence":"additional","affiliation":[{"name":"National Key Laboratory for Novel Software Technology, Nanjing University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2024"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA240721","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T13:13:55Z","timestamp":1729170835000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA240721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,16]]},"ISBN":["9781643685489"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia240721","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,16]]}}}