Gaussian Process Log Likelihood Gradient Incorrect

### Describe the bug

The gradient function of in the GaussianProcessRegressor Class is incorrect. This leads to inefficiencies fitting kernel (hyper) parameters.
The root of the issue is in that the gradient of the kernel function is made with respect to the log of the kernel parameter.

See the plot on the right showcasing the incorrect gradient currently being used in the optimization step:

![Image](https://github.com/user-attachments/assets/ec7f5582-b928-4738-9371-02ad1391c7c4)


To fix this apply the chain rule giving:

$\frac{\partial k(x)}{\partial \ln(x)} \frac{\partial \ln(x)}{\partial x} = \frac{\partial k(x)}{\partial x}$
$\frac{\partial k(x)}{\partial \ln(x)} \frac{1}{x} = \frac{\partial k(x)}{\partial x}$

When implementing this the correct gradient is given (middle plot).


TO REPRODUCE THIS BUG - see [my branch](https://github.com/conradstevens/scikit-learn/tree/gpr-log-likelihood-check) 
specifically: [sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py](https://github.com/conradstevens/scikit-learn/blob/gpr-log-likelihood-check/sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py)

I am happy to fix this bug by modifying the `_gpr` class's `log_marginal_likelihood` function. Keeping in mind things may get trickier when kernel functions have multiple hyper parameters (likely resulting in multiple iterations of the chain rule). 

### Steps/Code to Reproduce

TO REPRODUCE THIS BUG - see [my branch](https://github.com/conradstevens/scikit-learn/tree/gpr-log-likelihood-check) 
specifically: [sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py](https://github.com/conradstevens/scikit-learn/blob/gpr-log-likelihood-check/sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py)

### Expected Results

CRRECTION AND GROUND TRUTH TANGENTS CAN BE FOUND IN [my branch](https://github.com/conradstevens/scikit-learn/tree/gpr-log-likelihood-check) 
specifically: [sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py](https://github.com/conradstevens/scikit-learn/blob/gpr-log-likelihood-check/sklearn/gaussian_process/tests/test_gpr_loglikelihood_check.py)

### Actual Results

Logic error giving incorrect results.

### Versions

```shell
System:
    python: 3.12.5 | packaged by conda-forge | (main, Aug  8 2024, 18:31:54) [Clang 16.0.6 ]
executable: /opt/homebrew/Caskroom/miniconda/base/envs/sklearn-dev-5/bin/python
   machine: macOS-14.4.1-x86_64-i386-64bit

Python dependencies:
      sklearn: 1.8.dev0
          pip: 24.2
   setuptools: 72.2.0
        numpy: 2.1.0
        scipy: 1.14.1
       Cython: 3.0.11
       pandas: 2.2.2
   matplotlib: 3.9.2
       joblib: 1.4.2
threadpoolctl: 3.5.0

Built with OpenMP: True

threadpoolctl info:
       user_api: blas
   internal_api: openblas
    num_threads: 10
         prefix: libopenblas
       filepath: /opt/homebrew/Caskroom/miniconda/base/envs/sklearn-dev-5/lib/libopenblasp-r0.3.27.dylib
        version: 0.3.27
threading_layer: openmp
   architecture: Nehalem

       user_api: openmp
   internal_api: openmp
    num_threads: 10
         prefix: libomp
       filepath: /opt/homebrew/Caskroom/miniconda/base/envs/sklearn-dev-5/lib/libomp.dylib
        version: None
```

COMMENT:
Hi, so I investigated more and I think the _BinaryGaussianProcessClassifierLaplace still calculates the gradient wrt to theta in the log-space, it is just that the log-marginal likelihood estimate has extra steps compared to the GPR. Namely, it is calculated using the Laplace approximation of the posterior distribution which estimates the max absolute posteriori (MAP) which in turn is a function of theta. This means that we have to apply the chain rule not only to the kernel but also to the MAP value when calculating the log-marginal likelihood estimate. 

This makes the fix a bit simpler, i.e., we need to factor it in to calculations of s2, and s3 within _BinaryGaussianProcessClassifierLaplace in accordance to RW2006 Algorithm 5.1, alongside the fix to the kernel gradient calculation. @conradstevens what do you think?

Labels: Bug, Needs Investigation