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# EXAMPLE SEE http://scikit-learn.org/stable/auto_examples/plot_isotonic_regression.html#sphx-glr-auto-examples-plot-isotonic-regression-py


    

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print(__doc__)

# Author: Nelle Varoquaux <nelle.varoquaux@gmail.com>
#         Alexandre Gramfort <alexandre.gramfort@inria.fr>
# 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.log(1 + np.arange(n))


    

    




Startup script for IPython kernel.

Installs an import hook to configure the matplotlib backend on the fly.

Originally from @minrk at 
https://github.com/minrk/profile_default/blob/master/startup/mplimporthook.py
Repurposed for docker-stacks to address repeat bugs like
https://github.com/jupyter/docker-stacks/issues/235.

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ir = IsotonicRegression()

y_ = ir.fit_transform(x, y)

lr = LinearRegression()
lr.fit(x[:, np.newaxis], y)  # x needs to be 2d for LinearRegression


    

    
Out[2]:





LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)

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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()


    

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