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
Vector-valued reproducing kernel Banach spaces with applications to multi-task learning
Journal of Complexity
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We continue our recent study on constructing a refinement kernel for a given kernel so that the reproducing kernel Hilbert space associated with the refinement kernel contains that with the original kernel as a subspace. To motivate this study, we first develop a refinement kernel method for learning, which gives an efficient algorithm for updating a learning predictor. Several characterizations of refinement kernels are then presented. It is shown that a nontrivial refinement kernel for a given kernel always exists if the input space has an infinite cardinal number. Refinement kernels for translation invariant kernels and Hilbert-Schmidt kernels are investigated. Various concrete examples are provided.