.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_linear_model_plot_lasso_coordinate_descent_path.py:
=====================
Lasso and Elastic Net
=====================
Lasso and elastic net (L1 and L2 penalisation) implemented using a
coordinate descent.
The coefficients can be forced to be positive.
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_001.png
:alt: Lasso and Elastic-Net Paths
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_002.png
:alt: Lasso and positive Lasso
:class: sphx-glr-multi-img
*
.. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_003.png
:alt: Elastic-Net and positive Elastic-Net
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Computing regularization path using the lasso...
Computing regularization path using the positive lasso...
Computing regularization path using the elastic net...
Computing regularization path using the positive elastic net...
|
.. code-block:: default
print(__doc__)
# Author: Alexandre Gramfort
# License: BSD 3 clause
from itertools import cycle
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import lasso_path, enet_path
from sklearn import datasets
X, y = datasets.load_diabetes(return_X_y=True)
X /= X.std(axis=0) # Standardize data (easier to set the l1_ratio parameter)
# Compute paths
eps = 5e-3 # the smaller it is the longer is the path
print("Computing regularization path using the lasso...")
alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps=eps, fit_intercept=False)
print("Computing regularization path using the positive lasso...")
alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
X, y, eps=eps, positive=True, fit_intercept=False)
print("Computing regularization path using the elastic net...")
alphas_enet, coefs_enet, _ = enet_path(
X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)
print("Computing regularization path using the positive elastic net...")
alphas_positive_enet, coefs_positive_enet, _ = enet_path(
X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)
# Display results
plt.figure(1)
colors = cycle(['b', 'r', 'g', 'c', 'k'])
neg_log_alphas_lasso = -np.log10(alphas_lasso)
neg_log_alphas_enet = -np.log10(alphas_enet)
for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):
l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
l2 = plt.plot(neg_log_alphas_enet, coef_e, linestyle='--', c=c)
plt.xlabel('-Log(alpha)')
plt.ylabel('coefficients')
plt.title('Lasso and Elastic-Net Paths')
plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
plt.axis('tight')
plt.figure(2)
neg_log_alphas_positive_lasso = -np.log10(alphas_positive_lasso)
for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):
l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
l2 = plt.plot(neg_log_alphas_positive_lasso, coef_pl, linestyle='--', c=c)
plt.xlabel('-Log(alpha)')
plt.ylabel('coefficients')
plt.title('Lasso and positive Lasso')
plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
plt.axis('tight')
plt.figure(3)
neg_log_alphas_positive_enet = -np.log10(alphas_positive_enet)
for (coef_e, coef_pe, c) in zip(coefs_enet, coefs_positive_enet, colors):
l1 = plt.plot(neg_log_alphas_enet, coef_e, c=c)
l2 = plt.plot(neg_log_alphas_positive_enet, coef_pe, linestyle='--', c=c)
plt.xlabel('-Log(alpha)')
plt.ylabel('coefficients')
plt.title('Elastic-Net and positive Elastic-Net')
plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
loc='lower left')
plt.axis('tight')
plt.show()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.292 seconds)
.. _sphx_glr_download_auto_examples_linear_model_plot_lasso_coordinate_descent_path.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: binder-badge
.. image:: https://mybinder.org/badge_logo.svg
:target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.23.X?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_lasso_coordinate_descent_path.ipynb
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_lasso_coordinate_descent_path.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_lasso_coordinate_descent_path.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_