{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T14:18:26Z","timestamp":1772893106528,"version":"3.50.1"},"reference-count":9,"publisher":"MIT Press","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2001,11,1]]},"abstract":"<jats:p>An expectation-maximization algorithm for learning sparse and overcomplete data representations is presented. The proposed algorithm exploits a variational approximation to a range of heavy-tailed distributions whose limit is the Laplacian. A rigorous lower bound on the sparse prior distribution is derived, which enables the analytic marginalization of a lower bound on the data likelihood. This lower bound enables the development of an expectation-maximization algorithm for learning the overcomplete basis vectors and inferring the most probable basis coefficients.<\/jats:p>","DOI":"10.1162\/089976601753196003","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:55:01Z","timestamp":1027770901000},"page":"2517-2532","source":"Crossref","is-referenced-by-count":105,"title":["A Variational Method for Learning Sparse and Overcomplete Representations"],"prefix":"10.1162","volume":"13","author":[{"given":"Mark","family":"Girolami","sequence":"first","affiliation":[{"name":"Laboratory of Computing and Information Science, Helsinki University of Technology, Finland"}]}],"member":"281","reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300016458"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.6.1129"},{"key":"p_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"Dempster A. P.","year":"1977","journal-title":"Journal of the Royal Statistical Society, B"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1109\/34.541406"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1109\/97.752062"},{"issue":"10","key":"p_14","first-page":"1","volume":"22","author":"Lee T. W.","year":"2000","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.16.001587"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015826"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1109\/18.119725"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976601753196003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T23:49:08Z","timestamp":1733701748000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/13\/11\/2517-2532\/6475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,1]]},"references-count":9,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2001,11,1]]}},"alternative-id":["10.1162\/089976601753196003"],"URL":"https:\/\/doi.org\/10.1162\/089976601753196003","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,11,1]]}}}