Frames, Reproducing Kernels, Regularization and Learning
The Journal of Machine Learning Research
Elastic-net regularization in learning theory
Journal of Complexity
Scaling kernels: a new least squares support vector machine kernel for approximation
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
Framelet kernels with applications to support vector regression and regularization networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on gait analysis
Adaptive sequential design for regression on multi-resolution bases
Statistics and Computing
Evaluation of a set of new ORF kernel functions of SVM for speech recognition
Engineering Applications of Artificial Intelligence
| Hi-index | 0.00 |
The paper considers regression problems with univariate design points. The design points are irregular and no assumptions on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space (RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical optimization, the problem is replaced by an equivalent quadratic minimization problem with an additional penalty term. The computational algorithm is described in detail and is implemented with both the sets of simulated and real data. Comparison with existing methods showed that the technique suggested in the paper does not oversmooth the function and is superior in terms of the mean squared error. It is also demonstrated that under additional assumptions on design points the method achieves asymptotic optimality in a wide range of Besov spaces.