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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.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

Load data#

fromsklearnimport datasets
iris = datasets.load_iris ()
X = iris.data
y = iris.target
feature_names = iris.feature_names

Here we remove the third class to make the problem a binary classification

X = X[y != 2]
y = y[y != 2]

Compute regularization path#

importnumpyasnp
fromsklearn.linear_modelimport LogisticRegression
fromsklearn.pipelineimport make_pipeline
fromsklearn.preprocessingimport StandardScaler
fromsklearn.svmimport l1_min_c
cs = l1_min_c (X, y, loss="log") * np.logspace (0, 1, 16)

Create a pipeline with StandardScaler and LogisticRegression, to normalize the data before fitting a linear model, in order to speed-up convergence and make the coefficients comparable. Also, as a side effect, since the data is now centered around 0, we don’t need to fit an intercept.

clf = make_pipeline (
 StandardScaler (),
 LogisticRegression (
 penalty="l1",
 solver="liblinear",
 tol=1e-6,
 max_iter=int(1e6),
 warm_start=True,
 fit_intercept=False,
 ),
)
coefs_ = []
for c in cs:
 clf.set_params(logisticregression__C=c)
 clf.fit(X, y)
 coefs_.append(clf["logisticregression"].coef_.ravel().copy())
coefs_ = np.array (coefs_)

Plot regularization path#

importmatplotlib.pyplotasplt
# Colorblind-friendly palette (IBM Color Blind Safe palette)
colors = ["#648FFF", "#785EF0", "#DC267F", "#FE6100"]
plt.figure (figsize=(10, 6))
for i in range(coefs_.shape[1]):
 plt.semilogx (cs, coefs_[:, i], marker="o", color=colors[i], label=feature_names[i])
ymin, ymax = plt.ylim ()
plt.xlabel ("C")
plt.ylabel ("Coefficients")
plt.title ("Logistic Regression Path")
plt.legend ()
plt.axis ("tight")
plt.show ()