An illustration of the isotonic regression on generated data. The isotonic regression finds a non-decreasing approximation of a function while minimizing the mean squared error on the training data. The benefit of such a model is that it does not assume any form for the target function such as linearity. For comparison a linear regression is also presented.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | print(__doc__)# Author: Nelle Varoquaux <nelle.varoquaux@gmail.com># Alexandre Gramfort <alexandre.gramfort@inria.fr># License: BSDimport numpy as npimport matplotlib.pyplot as pltfrom matplotlib.collections import LineCollectionfrom sklearn.linear_model import LinearRegressionfrom sklearn.isotonic import IsotonicRegressionfrom sklearn.utils import check_random_staten = 100x = np.arange(n)rs = check_random_state(0)y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n)) |
Fit IsotonicRegression and LinearRegression models
1 2 3 4 5 6 | ir = IsotonicRegression()y_ = ir.fit_transform(x, y)lr = LinearRegression()lr.fit(x[:, np.newaxis], y) # x needs to be 2d for LinearRegression |
plot result
1 2 3 4 5 6 7 8 9 10 11 12 13 | segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)]lc = LineCollection(segments, zorder=0)lc.set_array(np.ones(len(y)))lc.set_linewidths(0.5 * np.ones(n))fig = plt.figure()plt.plot(x, y, 'r.', markersize=12)plt.plot(x, y_, 'g.-', markersize=12)plt.plot(x, lr.predict(x[:, np.newaxis]), 'b-')plt.gca().add_collection(lc)plt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right')plt.title('Isotonic regression')plt.show() |
Total running time of the script: (0 minutes 0.092 seconds)
Download Python source code:
plot_isotonic_regression.py
Download IPython notebook:
plot_isotonic_regression.ipynb
Please login to continue.