Note
Click here to download the full example code
This example shows how quantile regression can be used to create prediction intervals.
import numpy as np import matplotlib.pyplot as plt from sklearn.ensemble import GradientBoostingRegressor np.random.seed(1) def f(x): """The function to predict.""" return x * np.sin(x) #---------------------------------------------------------------------- # First the noiseless case X = np.atleast_2d(np.random.uniform(0, 10.0, size=100)).T X = X.astype(np.float32) # Observations y = f(X).ravel() dy = 1.5 + 1.0 * np.random.random(y.shape) noise = np.random.normal(0, dy) y += noise y = y.astype(np.float32) # Mesh the input space for evaluations of the real function, the prediction and # its MSE xx = np.atleast_2d(np.linspace(0, 10, 1000)).T xx = xx.astype(np.float32) alpha = 0.95 clf = GradientBoostingRegressor(loss='quantile', alpha=alpha, n_estimators=250, max_depth=3, learning_rate=.1, min_samples_leaf=9, min_samples_split=9) clf.fit(X, y) # Make the prediction on the meshed x-axis y_upper = clf.predict(xx) clf.set_params(alpha=1.0 - alpha) clf.fit(X, y) # Make the prediction on the meshed x-axis y_lower = clf.predict(xx) clf.set_params(loss='ls') clf.fit(X, y) # Make the prediction on the meshed x-axis y_pred = clf.predict(xx) # Plot the function, the prediction and the 90% confidence interval based on # the MSE fig = plt.figure() plt.plot(xx, f(xx), 'g:', label=u'$f(x) = x\,\sin(x)$') plt.plot(X, y, 'b.', markersize=10, label=u'Observations') plt.plot(xx, y_pred, 'r-', label=u'Prediction') plt.plot(xx, y_upper, 'k-') plt.plot(xx, y_lower, 'k-') plt.fill(np.concatenate([xx, xx[::-1]]), np.concatenate([y_upper, y_lower[::-1]]), alpha=.5, fc='b', ec='None', label='90% prediction interval') plt.xlabel('$x$') plt.ylabel('$f(x)$') plt.ylim(-10, 20) plt.legend(loc='upper left') plt.show()
Total running time of the script: ( 0 minutes 0.564 seconds)
Gallery generated by Sphinx-Gallery
© 2007–2018 The scikit-learn developers
Licensed under the 3-clause BSD License.
http://scikit-learn.org/stable/auto_examples/ensemble/plot_gradient_boosting_quantile.html