What size net gives valid generalization?
Neural Computation
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
Convergence rates for single hidden layer feedforward networks
Neural Networks
Bounds on the Sample Complexity of Bayesian Learning Using Information Theory and the VC Dimension
Machine Learning - Special issue on computational learning theory
Approximation and Estimation Bounds for Artificial Neural Networks
Machine Learning - Special issue on computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Methods to speed up error back-propagation learning algorithm
ACM Computing Surveys (CSUR)
Stochastic Complexity in Statistical Inquiry Theory
Stochastic Complexity in Statistical Inquiry Theory
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
Concept learning using complexity regularization
IEEE Transactions on Information Theory
Minimum complexity regression estimation with weakly dependent observations
IEEE Transactions on Information Theory - Part 2
The computational intractability of training sigmoidal neural networks
IEEE Transactions on Information Theory
Memory-universal prediction of stationary random processes
IEEE Transactions on Information Theory
Sup-norm approximation bounds for networks through probabilistic methods
IEEE Transactions on Information Theory
Robustness of one-sided cross-validation to autocorrelation
Journal of Multivariate Analysis
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Prequential model selection and delete-onecross-validation are data-driven methodologies for choosing betweenrival models on the basis of their predictive abilities. For a givenset of observations, the predictive ability of a model is measured bythe model‘s accumulated prediction error and by the model‘saverage-out-of-sample prediction error, respectively, for prequentialmodel selection and for cross-validation. In this paper, giveni.i.d. observations, we propose nonparametric regressionestimators—based on neural networks—that select the number of“hidden units” (or “neurons”) using either prequential modelselection or delete-one cross-validation. As our main contributions:(i) we establish rates of convergence for the integrated mean-squarederrors in estimating the regression function using “off-line” or“batch” versions of the proposed estimators and (ii) we establishrates of convergence for the time-averaged expected prediction errorsin using “on-line” versions of the proposed estimators. We alsopresent computer simulations (i) empirically validating the proposedestimators and (ii) empirically comparing the proposed estimatorswith certain novel prequential and cross-validated “mixture”regression estimators.