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Results tagged with kernels
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user 121692
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Monotonicity of kernel matrices with respect to hyperparameters
Some simple examples of which I'm already aware:
Let $K_1$, $K_2$ be two PSD kernels, let $\Phi = \mathbf{R}_+$, and let $K(x, y, \phi) = K_1 (x, y) + \phi \cdot K_2 (x, y)$. … Let $\{ K_i : i \in \mathbf{N} \}$ be a countable collection of PSD kernels, let $\Phi = \mathbf{N}$, and let $K(x, y, \phi) = \sum_{i \leqslant \phi} K_i (x, y)$. …
- 801
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Monotonicity of kernel matrices with respect to hyperparameters
An example which occurred to me is the following: suppose that $K$ indexes a family of stationary kernels (on e.g. $\mathbf{R}^d$) whose Fourier transforms are ordered pointwise. … scalings of Matèrn kernels. …
- 801