Machine Learning Models of Vibrating H2CO: Comparing Reproducing Kernels, FCHL, and PhysNet

Reproducing kernels and regularization methods in machine learning

Frames, Reproducing Kernels, Regularization and Learning

This work deals with a method for building a reproducing kernel Hilbert space (RKHS) from a Hilbert space with frame elements having special properties. Conditions on existence and a method of construction are given. Then, these RKHS are used within the framework of regularization theory for function approximation. Implications on semiparametric estimation are discussed and a multiscale scheme ...

Reproducing kernels , Bergman kernels , Poisson kernels

Refinement of Reproducing Kernels

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 characterization...

Duality by Reproducing Kernels

LetA be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write A( ) for the space of solutions of the system Au= 0 in a domain X. Using reproducing kernels related to various Hilbert structures on subspaces of A( ), we show explicit identifications of the dual spaces. To prove the regularity of reproducing kernels up to the boundary of , we specify t...