File:Regressions sine demo.svg

# 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')