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.
# Author: Alexandre Gramfort <firstname.lastname@example.org> # License: BSD 3 clause
from sklearn import datasets 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
Compute regularization path¶
import numpy as np from sklearn import linear_model from sklearn.svm import l1_min_c cs = l1_min_c(X, y, loss="log") * np.logspace(0, 7, 16) clf = linear_model.LogisticRegression( penalty="l1", solver="liblinear", tol=1e-6, max_iter=int(1e6), warm_start=True, intercept_scaling=10000.0, ) coefs_ =  for c in cs: clf.set_params(C=c) clf.fit(X, y) coefs_.append(clf.coef_.ravel().copy()) coefs_ = np.array(coefs_)
Plot regularization path¶
Total running time of the script: ( 0 minutes 0.135 seconds)