Risk Minimization and Minimum Description for Linear Discriminant Functions

Risk Minimization and Minimum Description for Linear Discriminant Functions

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Article ID: iaor200952617
Country: United States
Volume: 20
Issue: 2
Start Page Number: 317
End Page Number: 331
Publication Date: Mar 2008
Journal: INFORMS Journal On Computing
Authors: , ,
Keywords: statistics: multivariate
Abstract:

Statistical learning theory provides a formal criterion for learning a concept from examples. This theory addresses directly the trade–off in empirical fit and generalization. In practice, this leads to the structural risk–minimization principle where one minimizes a bound on the overall risk functional. For learning linear discriminant functions, this bound is impacted by the minimum of two terms—the dimension and the inverse of the margin. A popular and powerful learning mechanism, support vector machines, focuses on maximizing the margin. We compare this to methods that focus on minimizing the dimensionality, which, coincidentally, fulfills another useful criterion—the minimum description length principle.

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