Spectral theory of self-adjoint operators in Hilbert space
Spectral theory of self-adjoint operators in Hilbert space
Topics in matrix analysis
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Ten lectures on wavelets
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning Multiple Tasks with Kernel Methods
The Journal of Machine Learning Research
On Learning Vector-Valued Functions
Neural Computation
Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)
Learning Coordinate Covariances via Gradients
The Journal of Machine Learning Research
Estimation of Gradients and Coordinate Covariation in Classification
The Journal of Machine Learning Research
The Journal of Machine Learning Research
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Refinement of Reproducing Kernels
The Journal of Machine Learning Research
Divergence-Free Kernel Methods for Approximating the Stokes Problem
SIAM Journal on Numerical Analysis
Reproducing Kernel Banach Spaces for Machine Learning
The Journal of Machine Learning Research
Vector-valued reproducing kernel Banach spaces with applications to multi-task learning
Journal of Complexity
| Hi-index | 0.00 |
This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given kernel as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occurs. Numerical simulations confirm that the established refinement kernel method is able to meet this need. Various characterizations are provided based on feature maps and vector-valued integral representations of operator-valued reproducing kernels. Concrete examples of refining translation invariant and finite Hilbert-Schmidt operator-valued reproducing kernels are provided. Other examples include refinement of Hessian of scalar-valued translation-invariant kernels and transformation kernels. Existence and properties of operator-valued reproducing kernels preserved during the refinement process are also investigated.