Matern kernel.
The class of Matern kernels is a generalization of the RBF and the absolute exponential kernel parameterized by an additional parameter nu. The smaller nu, the less smooth the approximated function is. For nu=inf, the kernel becomes equivalent to the RBF kernel and for nu=0.5 to the absolute exponential kernel. Important intermediate values are nu=1.5 (once differentiable functions) and nu=2.5 (twice differentiable functions).
See Rasmussen and Williams 2006, pp84 for details regarding the different variants of the Matern kernel.
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Parameters ---------- length_scale : float or array with shape (n_features,), default: 1.0 The length scale of the kernel. If a float, an isotropic kernel is used. If an array, an anisotropic kernel is used where each dimension of l defines the length-scale of the respective feature dimension.
length_scale_bounds : pair of floats >= 0, default: (1e-5, 1e5) The lower and upper bound on length_scale
nu : float, default: 1.5 The parameter nu controlling the smoothness of the learned function. The smaller nu, the less smooth the approximated function is. For nu=inf, the kernel becomes equivalent to the RBF kernel and for nu=0.5 to the absolute exponential kernel. Important intermediate values are nu=1.5 (once differentiable functions) and nu=2.5 (twice differentiable functions). Note that values of nu not in 0.5, 1.5, 2.5, inf
incur a considerably higher computational cost (appr. 10 times higher) since they require to evaluate the modified Bessel function. Furthermore, in contrast to l, nu is kept fixed to its initial value and not optimized.