.. 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_logistic_path.py:
==============================================
Regularization path of L1- Logistic Regression
==============================================
Train l1-penalized logistic regression models on a binary classification
problem derived from the Iris dataset.
The models are ordered from strongest regularized to least regularized. The 4
coefficients of the models are collected and plotted as a "regularization
path": on the left-hand side of the figure (strong regularizers), all the
coefficients are exactly 0. When regularization gets progressively looser,
coefficients can get non-zero values one after the other.
Here we choose the liblinear solver because it can efficiently optimize for the
Logistic Regression loss with a non-smooth, sparsity inducing l1 penalty.
Also note that we set a low value for the tolerance to make sure that the model
has converged before collecting the coefficients.
We also use warm_start=True which means that the coefficients of the models are
reused to initialize the next model fit to speed-up the computation of the
full-path.
.. image:: /auto_examples/linear_model/images/sphx_glr_plot_logistic_path_001.png
:alt: Logistic Regression Path
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Computing regularization path ...
This took 0.072s
|
.. code-block:: default
print(__doc__)
# Author: Alexandre Gramfort
# License: BSD 3 clause
from time import time
import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model
from sklearn import datasets
from sklearn.svm import l1_min_c
iris = datasets.load_iris()
X = iris.data
y = iris.target
X = X[y != 2]
y = y[y != 2]
X /= X.max() # Normalize X to speed-up convergence
# #############################################################################
# Demo path functions
cs = l1_min_c(X, y, loss='log') * np.logspace(0, 7, 16)
print("Computing regularization path ...")
start = time()
clf = linear_model.LogisticRegression(penalty='l1', solver='liblinear',
tol=1e-6, max_iter=int(1e6),
warm_start=True,
intercept_scaling=10000.)
coefs_ = []
for c in cs:
clf.set_params(C=c)
clf.fit(X, y)
coefs_.append(clf.coef_.ravel().copy())
print("This took %0.3fs" % (time() - start))
coefs_ = np.array(coefs_)
plt.plot(np.log10(cs), coefs_, marker='o')
ymin, ymax = plt.ylim()
plt.xlabel('log(C)')
plt.ylabel('Coefficients')
plt.title('Logistic Regression Path')
plt.axis('tight')
plt.show()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.164 seconds)
.. _sphx_glr_download_auto_examples_linear_model_plot_logistic_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_logistic_path.ipynb
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_logistic_path.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_logistic_path.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_