Bartlett, PeterBoucheron, StéphaneLugosi, GáborUniversitat Pompeu Fabra. Departament d'Economia i Empresa2017-07-262017-07-262000-10-01Machine Learning. vol.48, pp. 85-113, 2002http://hdl.handle.net/10230/1148We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPapercomplexity regularizationmodel selectionerror estimationconcentration of measureStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess