{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T17:07:25Z","timestamp":1771952845368,"version":"3.50.1"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"03","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log"],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory (NIP) and machine learning (PAC-learnability). The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between <jats:italic>stability<\/jats:italic> and learnability in various settings of <jats:italic>online learning.<\/jats:italic> In particular, this gives many new examples of mathematically interesting classes which are learnable in the online setting.<\/jats:p>","DOI":"10.1017\/bsl.2018.71","type":"journal-article","created":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T07:40:02Z","timestamp":1550216402000},"page":"319-332","source":"Crossref","is-referenced-by-count":20,"title":["MODEL THEORY AND MACHINE LEARNING"],"prefix":"10.1017","volume":"25","author":[{"given":"HUNTER","family":"CHASE","sequence":"first","affiliation":[]},{"given":"JAMES","family":"FREITAG","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"S1079898618000719_ref9","first-page":"285","volume":"2","year":"1988","journal-title":"Machine learning"},{"key":"S1079898618000719_ref10","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1009"},{"key":"S1079898618000719_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-009-9201-3"},{"key":"S1079898618000719_ref21","first-page":"93","volume-title":"Proceedings of the 10th Easter Conference on Model Theory","year":"1993"},{"key":"S1079898618000719_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/2273133"},{"key":"S1079898618000719_ref18","volume-title":"Classification Theory and the Number of Nonisomorphic Models","volume":"92","year":"1978"},{"key":"S1079898618000719_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-012-0061-9"},{"key":"S1079898618000719_ref4","volume-title":"Generalized algebraic structures: A model theoretical approach","year":"1968"},{"key":"S1079898618000719_ref16","first-page":"113","volume":"8F","year":"1959","journal-title":"Bulletin of the Research Council of Israel Section F"},{"key":"S1079898618000719_ref15","first-page":"559","volume-title":"Proceedings of the 24th Annual Conference on Learning Theory","year":"2011"},{"key":"S1079898618000719_ref2","volume-title":"Proceedings of the 22nd Annual Conference on Learning Theory COLT","year":"2009"},{"key":"S1079898618000719_ref14","volume-title":"Stable Groups","volume":"87","year":"1987"},{"key":"S1079898618000719_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02756561"},{"key":"S1079898618000719_ref13","first-page":"230","volume":"57","year":"2010","journal-title":"Notices of the AMS"},{"key":"S1079898618000719_ref12","volume-title":"Model Theory of Fields","year":"2005"},{"key":"S1079898618000719_ref11","first-page":"77","year":"2013","journal-title":"Conference on Learning Theory"},{"key":"S1079898618000719_ref8","first-page":"377","volume":"2","year":"1992","journal-title":"Journal of the London Mathematical Society"}],"container-title":["The Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898618000719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T13:35:29Z","timestamp":1571837729000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/product\/identifier\/S1079898618000719\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,15]]},"references-count":17,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["S1079898618000719"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1017\/bsl.2018.71","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,15]]}}}