File:Regressions sine demo.svg
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Summary
DescriptionRegressions sine demo.svg |
English: Predictions over a perturbed sine curve with various learning models, e.g., GPR, KRR, SVR. The plot was prepared using scikit-learn. |
Date | |
Source |
Own work This W3C-unspecified plot was created with Matplotlib. |
Author | Shiyu Ji |
Python 3 Source Code
# 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')
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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3 July 2017
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Date/Time | Dimensions | User | Comment | |
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current | 12:57, 3 July 2017 | 900 × 450 (582 KB) | Shiyu Ji | User created page with UploadWizard |
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