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In the rendered docs this PR raises a ConvergenceWarning whereas in my local machine this PR raises no warnings. My guess is that something changed in the fmin_l_bfgs_b optimizer with respect to the scipy version we use for building the doc (v.1.6) and my local version (v.1.14).

Maybe @glemaitre (who bumped the last version in #27910) knows better?

Merging main to see if #29388 fixes the issue.

The good news is that merging main did solve the UserWarning.
The bad news is that it created a RuntimeWarning somewhere else in the same example.

In any case, we can consider the original intention of #29055 to be solved. So thanks again for your contribution, @ovenpickled. Merging!

Example from commit before merging main had some ConvergenceWarning in the Dot-product kernel section:

/home/circleci/project/sklearn/gaussian_process/kernels.py:452: ConvergenceWarning:

The optimal value found for dimension 0 of parameter k1__constant_value is close to the specified upper bound 10.0. Increasing the bound and calling fit again may find a better value.

/home/circleci/project/sklearn/gaussian_process/kernels.py:452: ConvergenceWarning:

The optimal value found for dimension 0 of parameter k2__kernel__sigma_0 is close to the specified upper bound 10.0. Increasing the bound and calling fit again may find a better value.

/home/circleci/project/sklearn/gaussian_process/_gpr.py:476: UserWarning:

Predicted variances smaller than 0. Setting those variances to 0.

Example from last commit doesn't have these warning any more but now there is a warning later in the example in the "Rational Quadradtic kernel" section

/home/circleci/project/sklearn/gaussian_process/_gpr.py:521: RuntimeWarning:

covariance is not symmetric positive-semidefinite.

By the way there is a typo "Quadractic" (additonal d) should be "Quadratic", maybe worth fixing in this PR?

I just pushed a commit fixing the typo, if you can double-check c891815 @ArturoAmorQ that would be great.

I just pushed a commit fixing the typo

Thanks! Nice catch.