This example illustrates the prior and posterior of a GPR with different kernels. Mean, standard deviation, and 10 samples are shown for both prior and posterior.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | print(__doc__)# Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>## License: BSD 3 clauseimport numpy as npfrom matplotlib import pyplot as pltfrom sklearn.gaussian_process import GaussianProcessRegressorfrom sklearn.gaussian_process.kernels import (RBF, Matern, RationalQuadratic, ExpSineSquared, DotProduct, ConstantKernel)kernels = [1.0 * RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0)), 1.0 * RationalQuadratic(length_scale=1.0, alpha=0.1), 1.0 * ExpSineSquared(length_scale=1.0, periodicity=3.0, length_scale_bounds=(0.1, 10.0), periodicity_bounds=(1.0, 10.0)), ConstantKernel(0.1, (0.01, 10.0)) * (DotProduct(sigma_0=1.0, sigma_0_bounds=(0.0, 10.0)) ** 2), 1.0 * Matern(length_scale=1.0, length_scale_bounds=(1e-1, 10.0), nu=1.5)]for fig_index, kernel in enumerate(kernels): # Specify Gaussian Process gp = GaussianProcessRegressor(kernel=kernel) # Plot prior plt.figure(fig_index, figsize=(8, 8)) plt.subplot(2, 1, 1) X_ = np.linspace(0, 5, 100) y_mean, y_std = gp.predict(X_[:, np.newaxis], return_std=True) plt.plot(X_, y_mean, 'k', lw=3, zorder=9) plt.fill_between(X_, y_mean - y_std, y_mean + y_std, alpha=0.5, color='k') y_samples = gp.sample_y(X_[:, np.newaxis], 10) plt.plot(X_, y_samples, lw=1) plt.xlim(0, 5) plt.ylim(-3, 3) plt.title("Prior (kernel: %s)" % kernel, fontsize=12) # Generate data and fit GP rng = np.random.RandomState(4) X = rng.uniform(0, 5, 10)[:, np.newaxis] y = np.sin((X[:, 0] - 2.5) ** 2) gp.fit(X, y) # Plot posterior plt.subplot(2, 1, 2) X_ = np.linspace(0, 5, 100) y_mean, y_std = gp.predict(X_[:, np.newaxis], return_std=True) plt.plot(X_, y_mean, 'k', lw=3, zorder=9) plt.fill_between(X_, y_mean - y_std, y_mean + y_std, alpha=0.5, color='k') y_samples = gp.sample_y(X_[:, np.newaxis], 10) plt.plot(X_, y_samples, lw=1) plt.scatter(X[:, 0], y, c='r', s=50, zorder=10) plt.xlim(0, 5) plt.ylim(-3, 3) plt.title("Posterior (kernel: %s)\n Log-Likelihood: %.3f" % (gp.kernel_, gp.log_marginal_likelihood(gp.kernel_.theta)), fontsize=12) plt.tight_layout()plt.show() |
Total running time of the script: (0 minutes 2.232 seconds)
Download Python source code:
plot_gpr_prior_posterior.py
Download IPython notebook:
plot_gpr_prior_posterior.ipynb
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