[MRG] Allow usage of nu=inf in Matern kernel

[sam-dixon]

Reference Issues/PRs

Fixes #12031

What does this implement/fix? Explain your changes.

If the nu parameter is set to inf, the kernel is equivalent to the RBF kernel, as specified in the documentation.

Tests

import numpy as np 
from sklearn.gaussian_process.kernels import Matern, RBF 
a = np.random.randn(3)[:, np.newaxis]
 
mat_kernel = Matern(nu=np.inf) 
mat_k, mat_grad = mat_kernel(a, eval_gradient=True)

rbf_kernel = RBF() 
rbf_k, rbf_grad = rbf_kernel(a, eval_gradient=True)

print(np.all(rbf_k == mat_k), np.all(rbf_grad == mat_grad))

Returns True, True

Any other comments?

[eickenberg]

This contribution looks good to me.

Looking at the referenced issue, it doesn't seem like a decision was reached on whether this should be implemented, so it might be a good idea to ping them to finish the discussion.
(I think this is a great solution.)

[jnothman]

I'm okay with it if it makes the parameter more searchable

[rth]

Thanks @sam-dixon !

Please add unit tests for this feature under sklearn/gaussian_process/tests/test_kernels.py in particular,

• that with nu=inf the output is equal to the RBF kernel
• that for large nu asymptotically this kernel yields approximately the same result as nu=inf

Also please add an entry to the change log at doc/whats_new/v0.22.rst. Like the other entries there, please reference this pull request with :pr: and credit yourself (and other contributors if applicable) with :user:.

[jnothman]

If so you might also want to check that they are not too close!

[jnothman]

Otherwise lgtm

[cmarmo]

@sam-dixon do you think you could find some time to sync to upstream and address the comments? Thanks!