A new column generation algorithm for Logical Analysis of Data

A new column generation algorithm for Logical Analysis of Data

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Article ID: iaor20117932
Volume: 188
Issue: 1
Start Page Number: 215
End Page Number: 249
Publication Date: Aug 2011
Journal: Annals of Operations Research
Authors: ,
Keywords: column generation, Statistics (classification)
Abstract:

We present a new column generation algorithm for the determination of a classifier in the two classes LAD (Logical Analysis of Data) model. Unlike existing algorithms who seek a classifier that at the same time maximizes the margin of correctly classified observations and minimizes the amount of violations of incorrectly classified observations, we fix the margin to a difficult‐to‐achieve target and minimize a piecewise convex linear function of the violation of incorrectly classified observations. Moreover a part of the training set, called control set, is reserved to select, among all feasible classifiers found by the algorithm, the one with highest performance on that set. One advantage of the proposed algorithm is that it essentially does not require any calibration. Computational results are presented that show the effectiveness of this approach.

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