Note

Click here to download the full example code

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 SAGA 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.

Out:

Computing regularization path ... This took 4.367s

print(__doc__) # Author: Alexandre Gramfort <[email protected]> # 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='saga', tol=1e-6, max_iter=int(1e6), warm_start=True) 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()

**Total running time of the script:** ( 0 minutes 4.392 seconds)

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http://scikit-learn.org/stable/auto_examples/linear_model/plot_logistic_path.html