.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_isotonic_regression.py: =================== Isotonic Regression =================== 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. .. image:: /auto_examples/images/sphx_glr_plot_isotonic_regression_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none | .. code-block:: default print(__doc__) # Author: Nelle Varoquaux # Alexandre Gramfort # License: BSD import numpy as np import matplotlib.pyplot as plt from matplotlib.collections import LineCollection from sklearn.linear_model import LinearRegression from sklearn.isotonic import IsotonicRegression from sklearn.utils import check_random_state n = 100 x = np.arange(n) rs = check_random_state(0) y = rs.randint(-50, 50, size=(n,)) + 50. * np.log1p(np.arange(n)) # ############################################################################# # Fit IsotonicRegression and LinearRegression models 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 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(np.full(n, 0.5)) 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() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.299 seconds) .. _sphx_glr_download_auto_examples_plot_isotonic_regression.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: plot_isotonic_regression.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_isotonic_regression.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_