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.

Script output:

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 positve elastic net...

Python source code: plot_lasso_coordinate_descent_path.py

print __doc__

# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# License: BSD Style.

import numpy as np
import pylab as pl

from sklearn.linear_model import lasso_path, enet_path
from sklearn import datasets

diabetes = datasets.load_diabetes()
X = diabetes.data
y = diabetes.target

X /= X.std(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..."
models = lasso_path(X, y, eps=eps)
alphas_lasso = np.array([model.alpha for model in models])
coefs_lasso = np.array([model.coef_ for model in models])

print "Computing regularization path using the positive lasso..."
models = lasso_path(X, y, eps=eps, positive=True)
alphas_positive_lasso = np.array([model.alpha for model in models])
coefs_positive_lasso = np.array([model.coef_ for model in models])

print "Computing regularization path using the elastic net..."
models = enet_path(X, y, eps=eps, l1_ratio=0.8)
alphas_enet = np.array([model.alpha for model in models])
coefs_enet = np.array([model.coef_ for model in models])

print "Computing regularization path using the positve elastic net..."
models = enet_path(X, y, eps=eps, l1_ratio=0.8, positive=True)
alphas_positive_enet = np.array([model.alpha for model in models])
coefs_positive_enet = np.array([model.coef_ for model in models])

###############################################################################
# Display results

pl.figure(1)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(coefs_lasso)
l2 = pl.plot(coefs_enet, linestyle='--')

pl.xlabel('-Log(lambda)')
pl.ylabel('weights')
pl.title('Lasso and Elastic-Net Paths')
pl.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
pl.axis('tight')


pl.figure(2)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(coefs_lasso)
l2 = pl.plot(coefs_positive_lasso, linestyle='--')

pl.xlabel('-Log(lambda)')
pl.ylabel('weights')
pl.title('Lasso and positive Lasso')
pl.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
pl.axis('tight')


pl.figure(3)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(coefs_enet)
l2 = pl.plot(coefs_positive_enet, linestyle='--')

pl.xlabel('-Log(lambda)')
pl.ylabel('weights')
pl.title('Elastic-Net and positive Elastic-Net')
pl.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
          loc='lower left')
pl.axis('tight')
pl.show()

Total running time of the example: 0.40 seconds

Citing

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Lasso and Elastic Net¶