# Note: the original version of this demo is in sklearn doc: # http://scikit-learn.org/stable/auto_examples/gaussian_process/plot_compare_gpr_krr.html # http://scikit-learn.org/stable/auto_examples/plot_kernel_ridge_regression.html # Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de> # License: BSD 3 clause  import time  import numpy as np import matplotlib matplotlib.use('svg') import matplotlib.pyplot as plt  from sklearn.svm import SVR from sklearn.kernel_ridge import KernelRidge from sklearn.model_selection import GridSearchCV from sklearn.gaussian_process import GaussianProcessRegressor from sklearn.gaussian_process.kernels import WhiteKernel, ExpSineSquared  rng = np.random.RandomState(0)  # Generate sample data X = 15 * rng.rand(100, 1) y = np.sin(X).ravel() y[::2] += rng.normal(scale = 1.0, size = X.shape[0] // 2)  # add noise  # Fit KernelRidge with param selection param_grid_kr = {"alpha": [1e-1, 1e-2, 1e-3],               "kernel": [ExpSineSquared(l, p)                          for l in np.logspace(-2, 2, 10)                          for p in np.logspace(0, 2, 10)]} kr = GridSearchCV(KernelRidge(), cv=5, param_grid=param_grid_kr) stime = time.time() kr.fit(X, y) print("Time for KRR fitting: %.3f" % (time.time() - stime))  # Fit GPR gp_kernel = ExpSineSquared(1.0, 5.0, \              periodicity_bounds=(1e-2, 1e1)) \              + WhiteKernel(1e-1) gpr = GaussianProcessRegressor(kernel=gp_kernel) stime = time.time() gpr.fit(X, y) print("Time for GPR fitting: %.3f" % (time.time() - stime))  # Fit SVR svr = SVR(kernel="rbf", C=1, gamma=1) stime = time.time() svr.fit(X, y) print("Time for SVR fitting: %.3f" % (time.time() - stime))  # Predict using kernel ridge X_plot = np.linspace(0, 20, 10000)[:, None] stime = time.time() y_kr = kr.predict(X_plot) print("Time for KRR prediction: %.3f" % (time.time() - stime))  # Predict using Gaussian process stime = time.time() y_gpr = gpr.predict(X_plot, return_std=False) print("Time for GPR prediction: %.3f" % (time.time() - stime))  stime = time.time() y_gpr, y_std = gpr.predict(X_plot, return_std=True) print("Time for GPR prediction with standard-deviation: %.3f"       % (time.time() - stime))  # Predict using SVR stime = time.time() y_svr = svr.predict(X_plot) print("Time for SVR prediction: %.3f" % (time.time() - stime))  # Plot results plt.figure(figsize=(10, 5)) lw = 2 plt.scatter(X, y, c='k', label='Data') plt.plot(X_plot, np.sin(X_plot), color='navy', lw=lw, label='True') plt.plot(X_plot, y_svr, color='red', lw=lw, label='SVR (kernel=%s, C=%s, gamma=%s)' % (svr.get_params()['kernel'], svr.get_params()['C'], svr.get_params()['gamma'])) plt.plot(X_plot, y_kr, color='turquoise', lw=lw,          label='KRR (%s)' % kr.best_params_) plt.plot(X_plot, y_gpr, color='darkorange', lw=lw,          label='GPR (%s)' % gpr.kernel_) plt.fill_between(X_plot[:, 0], y_gpr - y_std, y_gpr + y_std, color='darkorange',                  alpha=0.2) plt.xlabel('data') plt.ylabel('target') plt.xlim(0, 20) plt.ylim(-3, 5) plt.title('GPR v.s. Kernel Ridge v.s. SVR') plt.legend(loc="best",  scatterpoints=1, prop={'size': 8})  plt.savefig('regressions_sine_demo.svg', format='svg')