Paper #508

Title:

Model selection and error estimation

Authors:

Peter L. Bartlett, Stéphane Boucheron and Gábor Lugosi

Date:

October 2000

Abstract:

We 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.

Keywords:

Complexity regularization, model selection, error estimation, concentration of measure

JEL codes:

C13, C14

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

Machine Learning. vol.48, pp. 85-113, 2002

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