86 lines
2.1 KiB
Python
86 lines
2.1 KiB
Python
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"""
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==============================================
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Regularization path of L1- Logistic Regression
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==============================================
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Train l1-penalized logistic regression models on a binary classification
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problem derived from the Iris dataset.
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The models are ordered from strongest regularized to least regularized. The 4
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coefficients of the models are collected and plotted as a "regularization
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path": on the left-hand side of the figure (strong regularizers), all the
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coefficients are exactly 0. When regularization gets progressively looser,
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coefficients can get non-zero values one after the other.
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Here we choose the liblinear solver because it can efficiently optimize for the
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Logistic Regression loss with a non-smooth, sparsity inducing l1 penalty.
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Also note that we set a low value for the tolerance to make sure that the model
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has converged before collecting the coefficients.
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We also use warm_start=True which means that the coefficients of the models are
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reused to initialize the next model fit to speed-up the computation of the
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full-path.
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"""
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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# License: BSD 3 clause
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# %%
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# Load data
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# ---------
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from sklearn import datasets
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iris = datasets.load_iris()
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X = iris.data
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y = iris.target
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X = X[y != 2]
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y = y[y != 2]
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X /= X.max() # Normalize X to speed-up convergence
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# %%
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# Compute regularization path
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# ---------------------------
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import numpy as np
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from sklearn import linear_model
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from sklearn.svm import l1_min_c
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cs = l1_min_c(X, y, loss="log") * np.logspace(0, 10, 16)
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clf = linear_model.LogisticRegression(
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penalty="l1",
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solver="liblinear",
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tol=1e-6,
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max_iter=int(1e6),
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warm_start=True,
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intercept_scaling=10000.0,
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)
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coefs_ = []
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for c in cs:
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clf.set_params(C=c)
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clf.fit(X, y)
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coefs_.append(clf.coef_.ravel().copy())
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coefs_ = np.array(coefs_)
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# %%
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# Plot regularization path
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# ------------------------
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import matplotlib.pyplot as plt
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plt.plot(np.log10(cs), coefs_, marker="o")
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ymin, ymax = plt.ylim()
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plt.xlabel("log(C)")
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plt.ylabel("Coefficients")
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plt.title("Logistic Regression Path")
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plt.axis("tight")
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plt.show()
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