Description Usage Arguments Details Value Author(s) References Examples
Generate kernels for the kernel library.
1 | generate_kernel(method = "rbf", Sigma = 0, l = 1, p = 2)
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method |
(character) A character string indicating which kernel is to be computed. |
Sigma |
(matrix) The covariance matrix for neural network kernel. |
l |
(numeric) A numeric number indicating the hyperparameter (flexibility) of a specific kernel. |
p |
(integer) For polynomial, p is the power; for matern, v = p + 1 / 2; for rational, alpha = p. |
There are seven kinds of kernel available here. For convenience, we define r=\mid x-x'\mid.
Gaussian RBF Kernels
k_{SE}(r)=exp\Big(-\frac{r^2}{2l^2}\Big)
Matern Kernels
k_{Matern}(r)=\frac{2^{1-ν}}{Γ(ν)}\Big(\frac{√{2ν r}}{l}\Big)^ν K_ν \Big(\frac{√{2ν r}}{l}\Big)
Rational Quadratic Kernels
k_{RQ}(r)=\Big(1+\frac{r^2}{2α l^2}\Big)^{-α}
Polynomial Kernels
k(x, x')=(x \cdot x')^p
We have intercept kernel when p=0, and linear kernel when p=1.
Neural Network Kernels
k_{NN}(x, x')=\frac{2}{π}sin^{-1}\Big(\frac{2\tilde{x}^TΣ \tilde{x}'}{√{(1+2\tilde{x}^TΣ \tilde{x})(1+2\tilde{x}'^TΣ \tilde{x}')}}\Big)
kern |
(function) A function indicating the generated kernel. |
Wenying Deng
The MIT Press. Gaussian Processes for Machine Learning, 2006.
1 2 3 4 5 6 7 | kern_list <- list()
for (d in 1:nrow(kern_par)) {
kern_list[[d]] <- generate_kernel(kern_par[d, ]$method,
kern_par[d, ]$Sigma,
kern_par[d, ]$l,
kern_par[d, ]$p)
}
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