{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T03:14:03Z","timestamp":1752549243767},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:p> \u201cError-Confidence\u201d measures the probability that the proportion of errors made by a classifier will be within \u220a of E<jats:sub>B<\/jats:sub>, the optimal (Bayes) error. Probably Almost Bayes (PAB) theory attempts to quantify how this confidence increases with the number of training samples. We investigate the relationship empirically by comparing average error versus number of training patterns (m) for linear and neural network classifiers. On Gaussian problems, the resulting EC curves demonstrate that the PAB bounds are extremely conservative. Asymptotic statistics predicts a linear relationship between the logarithms of the average error and the number of training patterns. For low Bayes error rates we found excellent agreement between the prediction and the linear discriminant performance. At higher Bayes error rates we still found a linear relationship, but with a shallower slope than the predicted -1. When the underlying true model is a three-layer network, the EC curves show a greater dependence on classifier capacity, and the linear predictions no longer seem to hold. <\/jats:p>","DOI":"10.1142\/s0129065796000245","type":"journal-article","created":{"date-parts":[[2004,10,22]],"date-time":"2004-10-22T11:32:49Z","timestamp":1098444769000},"page":"263-271","source":"Crossref","is-referenced-by-count":1,"title":["EMPIRICAL ERROR-CONFIDENCE CURVES FOR NEURAL NETWORK AND GAUSSIAN CLASSIFIERS"],"prefix":"10.1142","volume":"07","author":[{"given":"GREGORY J.","family":"WOLFF","sequence":"first","affiliation":[{"name":"Machine Learning &amp; Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAVID G.","family":"STORK","sequence":"additional","affiliation":[{"name":"Machine Learning &amp; Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ART","family":"OWEN","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University, Stanford, CA 94305, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["International Journal of Neural Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129065796000245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:49:03Z","timestamp":1565142543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129065796000245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1996,7]]}},"alternative-id":["10.1142\/S0129065796000245"],"URL":"https:\/\/doi.org\/10.1142\/s0129065796000245","relation":{},"ISSN":["0129-0657","1793-6462"],"issn-type":[{"value":"0129-0657","type":"print"},{"value":"1793-6462","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}