.. _sphx_glr_auto_examples_plot_ovk_sparse_quantile_regression.py:


======================================================
Data sparse quantile regression with operator-valued kernels
======================================================

An example to illustrate data sparse quantile regression with operator-valued
kernels.

We compare quantile regression with several levels of data sparsity.




.. image:: /auto_examples/images/sphx_glr_plot_ovk_sparse_quantile_regression_001.png
    :align: center


.. rst-class:: sphx-glr-script-out

 Out::

    Creating dataset...
    Fitting...
    Non-sparse QR
    Non-sparse QR learning time: 5.320 s
    Non-sparse QR score 0.78496
    Non-sparse QR num of support vectors 100
    Sparse QR
    Sparse QR learning time: 10.769 s
    Sparse QR score 0.76306
    Sparse QR num of support vectors 25




|


.. code-block:: python


    # Author: Maxime Sangnier <maxime.sangnier@gmail.com>
    # License: MIT

    # -*- coding: utf-8 -*-
    import time

    import numpy as np
    import matplotlib.pyplot as plt

    from operalib import Quantile, toy_data_quantile


    def main():
        """Example of multiple quantile regression."""

        print("Creating dataset...")
        probs = np.linspace(0.1, 0.9, 5)  # Quantile levels of interest
        x_train, y_train, _ = toy_data_quantile(100, random_state=0)
        x_test, y_test, z_test = toy_data_quantile(1000, probs=probs,
                                                   random_state=1)

        print("Fitting...")
        methods = {'Non-sparse QR':
                   Quantile(probs=probs, kernel='DGauss', lbda=1e-2, gamma=8.,
                            gamma_quantile=1e-2),
                   'Sparse QR':
                   Quantile(probs=probs, kernel='DGauss', lbda=1e-2, gamma=8.,
                            gamma_quantile=1e-2, eps=2.5)}
        # Fit on training data
        for name, reg in sorted(methods.items()):
            print(name)
            start = time.time()
            reg.fit(x_train, y_train)

            coefs = reg.model_["coefs"].reshape(y_train.size, probs.size)
            n_sv = np.sum(np.linalg.norm(coefs, axis=1) *
                          reg.lbda / y_train.size > 1e-5)
            print('%s learning time: %.3f s' % (name, time.time() - start))
            print('%s score %.5f' % (name, reg.score(x_test, y_test)))
            print('%s num of support vectors %d' % (name, n_sv))

        # Plot the estimated conditional quantiles
        plt.figure(figsize=(12, 7))
        for i, method in enumerate(sorted(methods.keys())):
            plt.subplot(2, 2, i + 1)
            plt.plot(x_train, y_train, '.')
            plt.gca().set_prop_cycle(None)
            for quantile in methods[method].predict(x_test):
                plt.plot(x_test, quantile, '-')
            plt.gca().set_prop_cycle(None)
            for prob, quantile in zip(probs, z_test):
                plt.plot(x_test, quantile, '--',
                         label="theoretical {0:0.2f}".format(prob))
            plt.title(method)
            plt.legend(fontsize=8)

            coefs = methods[method].model_["coefs"].reshape(y_train.size,
                                                            probs.size)
            plt.subplot(2, 2, 2 + i + 1)
            plt.plot(np.linalg.norm(coefs, axis=1))
            plt.title("Norm of dual coefs for each point")
        plt.show()


    if __name__ == '__main__':
        main()

**Total running time of the script:** ( 0 minutes  17.301 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_ovk_sparse_quantile_regression.py <plot_ovk_sparse_quantile_regression.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_ovk_sparse_quantile_regression.ipynb <plot_ovk_sparse_quantile_regression.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

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