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 occu...

By re-defining the inner product of a reproducing kernel space, the reproducing kernel functions of that space can be represented by form of polynomials without changing any other conditions, and the higher order of the derivatives, the simpler of the reproducing kernel function expressions. Such expressions of reproducing kernel functions are the simplest from the computational point of view, ...