for https://github.com/scikit-learn/scikit-learn/pull/14378

gpr_log_marginal_likelihood.py

import numpy as np
import matplotlib.pyplot as plt
from sklearn.gaussian_process import kernels as sk_kern
from sklearn.gaussian_process import GaussianProcessRegressor


def objective(x):
    return x + 20 * np.sin(x)


def plot_result(x_test, mean, std):
    plt.plot(x_test[:, 0], mean, color="C0", label="predict mean")
    plt.fill_between(x_test[:, 0], mean + std, mean - std, color="C0", alpha=.3, label="1 sigma confidence")

    xx = np.linspace(-20, 20, 200)
    plt.plot(xx, objective(xx), "--", color="C0", label="true function")
    plt.title("function evaluation")
    plt.legend()
    plt.savefig("gpr_predict.png", dpi=150)


def main():
    kernel = sk_kern.RBF(1.0, (1e-3, 1e3)) + sk_kern.ConstantKernel(1.0, (1e-3, 1e3))
    clf = GaussianProcessRegressor(
        kernel=kernel,
        alpha=1e-10,
        optimizer="fmin_l_bfgs_b",
        n_restarts_optimizer=20,
        normalize_y=True)

    np.random.seed(0)
    x_train = np.random.uniform(-20, 20, 200)
    y_train = objective(x_train) + np.random.normal(loc=0, scale=.1, size=x_train.shape)

    clf.fit(x_train.reshape(-1, 1), y_train)
    np.random.uniform()
    print(clf.log_marginal_likelihood(theta=np.array([0, 0], dtype=np.float64)))
    print(clf.log_marginal_likelihood())  # this line might be changed?


if __name__ == '__main__':
    main()

Before

$ python examples/gpr_profile.py 
-5187014697.037492
-22772.548601943214

After applied the patch

$ python examples/gpr_profile.py 
-5187014697.037492
-22772.548601943214