Reproducing Kernel Hilbert Space (RKHS)
A function space induced by a kernel function in which the smoothness of functions can be measured by a norm. It serves as the mathematical foundation for kernel methods and Gaussian processes and is widely used in theoretical analysis within machine learning.
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The kernel Stein discrepancy measures the difference between two distributions via the Stein operator and functions in a reproducing kernel Hilbert space, can be computed from samples alone, and is insensitive to the normalization constant.
In the theoretical analysis of GP Bandits, the objective function is usually assumed to belong to the reproducing kernel Hilbert space (RKHS) corresponding to the kernel function, with bounded norm.
Compared with neural networks, kernel methods have more mature theoretical analysis tools (such as the reproducing kernel Hilbert space RKHS framework), and their generalization error bounds are easier to derive.
Kernelized bandits study how to progressively optimize an unknown function with bounded norm in a reproducing kernel Hilbert space (RKHS) under noisy feedback.
All Facts (4)
The kernel Stein discrepancy measures the difference between two distributions via the Stein operator and functions in a reproducing kernel Hilbert space, can be computed from samples alone, and is insensitive to the normalization constant.
50%UnverifiedIn the theoretical analysis of GP Bandits, the objective function is usually assumed to belong to the reproducing kernel Hilbert space (RKHS) corresponding to the kernel function, with bounded norm.
50%UnverifiedCompared with neural networks, kernel methods have more mature theoretical analysis tools (such as the reproducing kernel Hilbert space RKHS framework), and their generalization error bounds are easier to derive.
50%UnverifiedKernelized bandits study how to progressively optimize an unknown function with bounded norm in a reproducing kernel Hilbert space (RKHS) under noisy feedback.
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