Matrix analysis
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Ridge Regression Learning Algorithm in Dual Variables
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Everything old is new again: a fresh look at historical approaches in machine learning
Everything old is new again: a fresh look at historical approaches in machine learning
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
A Unifying View of Sparse Approximate Gaussian Process Regression
The Journal of Machine Learning Research
An efficient algorithm for learning to rank from preference graphs
Machine Learning
On Learning and Cross-Validation with Decomposed Nyström Approximation of Kernel Matrix
Neural Processing Letters
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Hold-out and cross-validation are among the most useful methods for model selection and performance assessment of machine learning algorithms. In this paper, we present a computationally efficient algorithm for calculating the hold-out performance for sparse regularized least-squares (RLS) in case the method is already trained with the whole training set. The computational complexity of performing the holdout is O(|H|3 + |H|2n), where |H| is the size of the hold-out set and n is the number of basis vectors. The algorithm can thus be used to calculate various types of cross-validation estimates effectively. For example, when m is the number of training examples, the complexities of N-fold and leave-one-out cross-validations are O(m3/N2 + (m2n)/N) and O(mn), respectively. Further, since sparse RLS can be trained in O(mn2) time for several regularization parameter values in parallel, the fast holdout algorithm enables efficient selection of the optimal parameter value.