.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_quantile_regression.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_quantile_regression.py: .. _l-quantile-regression-example: Quantile Regression =================== `scikit-learn `_ does not have a quantile regression. `mlinsights `_ implements a version of it. Simple example -------------- We first generate some dummy data. .. GENERATED FROM PYTHON SOURCE LINES 17-31 .. code-block:: Python import numpy import matplotlib.pyplot as plt from pandas import DataFrame from sklearn.linear_model import LinearRegression from mlinsights.mlmodel import QuantileLinearRegression X = numpy.random.random(1000) eps1 = (numpy.random.random(900) - 0.5) * 0.1 eps2 = (numpy.random.random(100)) * 10 eps = numpy.hstack([eps1, eps2]) X = X.reshape((1000, 1)) Y = X.ravel() * 3.4 + 5.6 + eps .. GENERATED FROM PYTHON SOURCE LINES 33-38 .. code-block:: Python clr = LinearRegression() clr.fit(X, Y) .. raw:: html

LinearRegression()

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.. GENERATED FROM PYTHON SOURCE LINES 40-50 .. code-block:: Python clq = QuantileLinearRegression() clq.fit(X, Y) data = dict(X=X.ravel(), Y=Y, clr=clr.predict(X), clq=clq.predict(X)) df = DataFrame(data) df.head() .. raw:: html

	X	Y	clr	clq
0	0.595399	7.604792	8.122633	7.637637
1	0.474574	7.245636	7.704640	7.225495
2	0.927677	8.749853	9.272139	8.771051
3	0.654316	7.799467	8.326455	7.838605
4	0.960758	8.891691	9.386581	8.883891

.. GENERATED FROM PYTHON SOURCE LINES 52-68 .. code-block:: Python fig, ax = plt.subplots(1, 1, figsize=(10, 4)) choice = numpy.random.choice(X.shape[0] - 1, size=100) xx = X.ravel()[choice] yy = Y[choice] ax.plot(xx, yy, ".", label="data") xx = numpy.array([[0], [1]]) y1 = clr.predict(xx) y2 = clq.predict(xx) ax.plot(xx, y1, "--", label="L2") ax.plot(xx, y2, "--", label="L1") ax.set_title("Quantile (L1) vs Square (L2)") ax.legend() .. image-sg:: /auto_examples/images/sphx_glr_plot_quantile_regression_001.png :alt: Quantile (L1) vs Square (L2) :srcset: /auto_examples/images/sphx_glr_plot_quantile_regression_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 69-74 The L1 is clearly less sensible to extremas. The optimization algorithm is based on `Iteratively reweighted least squares `_. It estimates a linear regression with error L2 then reweights each oberservation with the inverse of the error L1. .. GENERATED FROM PYTHON SOURCE LINES 74-78 .. code-block:: Python clq = QuantileLinearRegression(verbose=True, max_iter=20) clq.fit(X, Y) .. rst-class:: sphx-glr-script-out .. code-block:: none [QuantileLinearRegression.fit] iter=1 error=887.3974799042942 [QuantileLinearRegression.fit] iter=2 error=584.418315445887 [QuantileLinearRegression.fit] iter=3 error=515.6852922462667 [QuantileLinearRegression.fit] iter=4 error=515.2680053173664 [QuantileLinearRegression.fit] iter=5 error=514.9246380365536 [QuantileLinearRegression.fit] iter=6 error=514.5965386047486 [QuantileLinearRegression.fit] iter=7 error=514.3901850422749 [QuantileLinearRegression.fit] iter=8 error=514.2057153574946 [QuantileLinearRegression.fit] iter=9 error=514.0821374889089 [QuantileLinearRegression.fit] iter=10 error=513.9987881952429 [QuantileLinearRegression.fit] iter=11 error=513.9358925448369 [QuantileLinearRegression.fit] iter=12 error=513.890761901876 [QuantileLinearRegression.fit] iter=13 error=513.852366694661 [QuantileLinearRegression.fit] iter=14 error=513.8206482671766 [QuantileLinearRegression.fit] iter=15 error=513.8016564994344 [QuantileLinearRegression.fit] iter=16 error=513.7883817254528 [QuantileLinearRegression.fit] iter=17 error=513.778283428184 [QuantileLinearRegression.fit] iter=18 error=513.7700595409715 [QuantileLinearRegression.fit] iter=19 error=513.7648371043631 [QuantileLinearRegression.fit] iter=20 error=513.7603803736176 .. raw:: html

QuantileLinearRegression(max_iter=20, verbose=True)

.. GENERATED FROM PYTHON SOURCE LINES 80-85 .. code-block:: Python clq.score(X, Y) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.5137603803736176 .. GENERATED FROM PYTHON SOURCE LINES 86-88 Regression with various quantiles --------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 88-96 .. code-block:: Python X = numpy.random.random(1200) eps1 = (numpy.random.random(900) - 0.5) * 0.5 eps2 = (numpy.random.random(300)) * 2 eps = numpy.hstack([eps1, eps2]) X = X.reshape((1200, 1)) Y = X.ravel() * 3.4 + 5.6 + eps + X.ravel() * X.ravel() * 8 .. GENERATED FROM PYTHON SOURCE LINES 98-106 .. code-block:: Python fig, ax = plt.subplots(1, 1, figsize=(10, 4)) choice = numpy.random.choice(X.shape[0] - 1, size=100) xx = X.ravel()[choice] yy = Y[choice] ax.plot(xx, yy, ".", label="data") ax.set_title("Almost linear dataset") .. image-sg:: /auto_examples/images/sphx_glr_plot_quantile_regression_002.png :alt: Almost linear dataset :srcset: /auto_examples/images/sphx_glr_plot_quantile_regression_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'Almost linear dataset') .. GENERATED FROM PYTHON SOURCE LINES 108-115 .. code-block:: Python clqs = {} for qu in [0.1, 0.25, 0.5, 0.75, 0.9]: clq = QuantileLinearRegression(quantile=qu) clq.fit(X, Y) clqs["q=%1.2f" % qu] = clq .. GENERATED FROM PYTHON SOURCE LINES 117-130 .. code-block:: Python fig, ax = plt.subplots(1, 1, figsize=(10, 4)) choice = numpy.random.choice(X.shape[0] - 1, size=100) xx = X.ravel()[choice] yy = Y[choice] ax.plot(xx, yy, ".", label="data") xx = numpy.array([[0], [1]]) for qu in sorted(clqs): y = clqs[qu].predict(xx) ax.plot(xx, y, "--", label=qu) ax.set_title("Various quantiles") ax.legend() .. image-sg:: /auto_examples/images/sphx_glr_plot_quantile_regression_003.png :alt: Various quantiles :srcset: /auto_examples/images/sphx_glr_plot_quantile_regression_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.210 seconds) .. _sphx_glr_download_auto_examples_plot_quantile_regression.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_quantile_regression.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_quantile_regression.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_quantile_regression.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_