Optimal learning of bandlimited functions from localized sampling
Journal of Complexity
Reproducing kernel banach spaces for machine learning
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Reproducing Kernel Banach Spaces for Machine Learning
The Journal of Machine Learning Research
Approximation of high-dimensional kernel matrices by multilevel circulant matrices
Journal of Complexity
Refinement of operator-valued reproducing kernels
The Journal of Machine Learning Research
Regularized learning in Banach spaces as an optimization problem: representer theorems
Journal of Global Optimization
Learning with coefficient-based regularization and ℓ1-penalty
Advances in Computational Mathematics
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Motivated by mathematical learning from training data, we introduce the notion of refinable kernels. Various characterizations of refinable kernels are presented. The concept of refinable kernels leads to the introduction of wavelet-like reproducing kernels. We also investigate a refinable kernel that forms a Riesz basis. In particular, we characterize refinable translation invariant kernels, and refinable kernels defined by refinable functions. This study leads to multiresolution analysis of reproducing kernel Hilbert spaces.