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NeuroCOLT
Technical Report NC-TR-96-006
Finite Sample
Size Results for Robust Model Selection; Application to Neural Networks
Joel
Ratsaby
Technion
Israel
Ronny
Meir
Technion
Israel
Abstract
The problem of model selection in the face of finite sample size is
considered within the framework of statistical decision theory.
Focusing on the special case of regression, we introduce a model selection
criterion which is shown to be robust in the sense that, with high
confidence, even for a finite sample size it selects the best model.
Our derivation is based on uniform convergence methods, augmented
by results from the theory of function approximation, which permit
us to make definite probabilistic statements about the finite sample
behavior. These results stand in contrast to classical approaches,
which can only guarantee the asymptotic optimality of the choice.
The criterion is demonstrated for the problem of model selection in
feedforward neural networks.
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