.. note:: :class: sphx-glr-download-link-note Click :ref:here  to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_gaussian_process_plot_gpc_isoprobability.py: ================================================================= Iso-probability lines for Gaussian Processes classification (GPC) ================================================================= A two-dimensional classification example showing iso-probability lines for the predicted probabilities. .. image:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpc_isoprobability_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none Learned kernel: 0.0256**2 * DotProduct(sigma_0=5.72) ** 2 | .. code-block:: default print(__doc__) # Author: Vincent Dubourg # Adapted to GaussianProcessClassifier: # Jan Hendrik Metzen # License: BSD 3 clause import numpy as np from matplotlib import pyplot as plt from matplotlib import cm from sklearn.gaussian_process import GaussianProcessClassifier from sklearn.gaussian_process.kernels import DotProduct, ConstantKernel as C # A few constants lim = 8 def g(x): """The function to predict (classification will then consist in predicting whether g(x) <= 0 or not)""" return 5. - x[:, 1] - .5 * x[:, 0] ** 2. # Design of experiments X = np.array([[-4.61611719, -6.00099547], [4.10469096, 5.32782448], [0.00000000, -0.50000000], [-6.17289014, -4.6984743], [1.3109306, -6.93271427], [-5.03823144, 3.10584743], [-2.87600388, 6.74310541], [5.21301203, 4.26386883]]) # Observations y = np.array(g(X) > 0, dtype=int) # Instantiate and fit Gaussian Process Model kernel = C(0.1, (1e-5, np.inf)) * DotProduct(sigma_0=0.1) ** 2 gp = GaussianProcessClassifier(kernel=kernel) gp.fit(X, y) print("Learned kernel: %s " % gp.kernel_) # Evaluate real function and the predicted probability res = 50 x1, x2 = np.meshgrid(np.linspace(- lim, lim, res), np.linspace(- lim, lim, res)) xx = np.vstack([x1.reshape(x1.size), x2.reshape(x2.size)]).T y_true = g(xx) y_prob = gp.predict_proba(xx)[:, 1] y_true = y_true.reshape((res, res)) y_prob = y_prob.reshape((res, res)) # Plot the probabilistic classification iso-values fig = plt.figure(1) ax = fig.gca() ax.axes.set_aspect('equal') plt.xticks([]) plt.yticks([]) ax.set_xticklabels([]) ax.set_yticklabels([]) plt.xlabel('$x_1$') plt.ylabel('$x_2$') cax = plt.imshow(y_prob, cmap=cm.gray_r, alpha=0.8, extent=(-lim, lim, -lim, lim)) norm = plt.matplotlib.colors.Normalize(vmin=0., vmax=0.9) cb = plt.colorbar(cax, ticks=[0., 0.2, 0.4, 0.6, 0.8, 1.], norm=norm) cb.set_label(r'${\rm \mathbb{P}}\left[\widehat{G}(\mathbf{x}) \leq 0\right]$') plt.clim(0, 1) plt.plot(X[y <= 0, 0], X[y <= 0, 1], 'r.', markersize=12) plt.plot(X[y > 0, 0], X[y > 0, 1], 'b.', markersize=12) plt.contour(x1, x2, y_true, [0.], colors='k', linestyles='dashdot') cs = plt.contour(x1, x2, y_prob, [0.666], colors='b', linestyles='solid') plt.clabel(cs, fontsize=11) cs = plt.contour(x1, x2, y_prob, [0.5], colors='k', linestyles='dashed') plt.clabel(cs, fontsize=11) cs = plt.contour(x1, x2, y_prob, [0.334], colors='r', linestyles='solid') plt.clabel(cs, fontsize=11) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.573 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_auto_examples_gaussian_process_plot_gpc_isoprobability.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: https://mybinder.org/badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.22.X?urlpath=lab/tree/notebooks/auto_examples/gaussian_process/plot_gpc_isoprobability.ipynb :width: 150 px .. container:: sphx-glr-download :download:Download Python source code: plot_gpc_isoprobability.py  .. container:: sphx-glr-download :download:Download Jupyter notebook: plot_gpc_isoprobability.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _