Matrix analysis
The nature of statistical learning theory
The nature of statistical learning theory
Model Selection and Error Estimation
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
A new metric-based approach to model selection
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Comparison of model selection for regression
Neural Computation
Extensions to metric based model selection
The Journal of Machine Learning Research
Model Selection for Unsupervised Learning of Visual Context
International Journal of Computer Vision
A Class of Novel Kernel Functions
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Bounds for multistage stochastic programs using supervised learning strategies
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
Auto-WEKA: combined selection and hyperparameter optimization of classification algorithms
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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Model selection is an important ingredient of many machine learning algorithms, in particular when the sample size in small, in order to strike the right trade-off between overfitting and underfitting. Previous classical results for linear regression are based on an asymptotic analysis. We present a new penalization method for performing model selection for regression that is appropriate even for small samples. Our penalization is based on an accurate estimator of the ratio of the expected training error and the expected generalization error, in terms of the expected eigenvalues of the input covariance matrix.