RKHS
A class of function spaces in which every function is uniquely determined by a kernel function and point evaluation is a continuous linear functional. RKHS combines the expressive flexibility of infinite-dimensional function spaces with an inner-product structure, and is widely used in machine learning.
Timeline (last 90 days)
The eigenvalue decay rate directly determines the smoothness of the RKHS and the generalization error bound: the faster the decay, the "smaller" the function space, and the more the model tends to learn smooth functions.
The reproducing kernel Hilbert spaces (RKHS) of integral operators induced by operators on the same group orbit differ only by an orthogonal transformation.
This approximation rate bound holds uniformly over the unit ball of the reproducing kernel Hilbert space (RKHS) with probability at least 1-δ.
An operator-valued kernel must satisfy operator-valued positive definiteness in order to guarantee that the corresponding RKHS exists.
Compared with baseline methods based on RKHS (Reproducing Kernel Hilbert Space), ISBO achieves a significant speedup.
The source condition describes the smoothness of the target function relative to the kernel operator, and the capacity condition characterizes the complexity of the hypothesis space through the decay rate of the kernel operator's eigenvalues.
In Bayesian optimization, the covariance function of a Gaussian process itself defines an RKHS.
In a Reproducing Kernel Hilbert Space, every function can be uniquely determined by a kernel function, and the point evaluation operation is a continuous linear functional.
L0MO searches over a subset of functions with sparse representations in a Reproducing Kernel Hilbert Space (RKHS).
The theoretical foundations of functional gradient descent come from Reproducing Kernel Hilbert Spaces (RKHS) and variational methods in function space.
All Facts (11)
The eigenvalue decay rate directly determines the smoothness of the RKHS and the generalization error bound: the faster the decay, the "smaller" the function space, and the more the model tends to learn smooth functions.
50%UnverifiedThe reproducing kernel Hilbert spaces (RKHS) of integral operators induced by operators on the same group orbit differ only by an orthogonal transformation.
50%UnverifiedThis approximation rate bound holds uniformly over the unit ball of the reproducing kernel Hilbert space (RKHS) with probability at least 1-δ.
50%UnverifiedAn operator-valued kernel must satisfy operator-valued positive definiteness in order to guarantee that the corresponding RKHS exists.
50%UnverifiedCompared with baseline methods based on RKHS (Reproducing Kernel Hilbert Space), ISBO achieves a significant speedup.
50%UnverifiedThe source condition describes the smoothness of the target function relative to the kernel operator, and the capacity condition characterizes the complexity of the hypothesis space through the decay rate of the kernel operator's eigenvalues.
50%UnverifiedIn Bayesian optimization, the covariance function of a Gaussian process itself defines an RKHS.
50%UnverifiedIn a Reproducing Kernel Hilbert Space, every function can be uniquely determined by a kernel function, and the point evaluation operation is a continuous linear functional.
50%UnverifiedL0MO searches over a subset of functions with sparse representations in a Reproducing Kernel Hilbert Space (RKHS).
50%UnverifiedThe theoretical foundations of functional gradient descent come from Reproducing Kernel Hilbert Spaces (RKHS) and variational methods in function space.
50%UnverifiedMMD（Maximum Mean Discrepancy）是基于再生核希尔伯特空间的非参数分布距离度量，相比FID对小样本场景更友好、计算开销更低
50%