Pushing the docs for revision for branch: master, commit d3175db3627d739d17ab36bf8752b44fcaf6f638

Author: sklearn-ci

dev/_downloads/plot_ridge_coeffs.py

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+"""
+==============================================================
+Plot Ridge coefficients as a function of the L2 regularization
+==============================================================
+
+.. currentmodule:: sklearn.linear_model
+
+:class:`Ridge` Regression is the estimator used in this example.
+Each color in the left plot represents one different dimension of the
+coefficient vector, and this is displayed as a function of the
+regularization parameter. The right plot shows how exact the solution
+is. This example illustrates how a well defined solution is
+found by Ridge regression and how regularization affects the
+coefficients and their values. The plot on the right shows how
+the difference of the coefficients from the estimator changes
+as a function of regularization.
+
+In this example the dependent variable Y is set as a function
+of the input features: y = X*w + c. The coefficient vector w is
+randomly sampled from a normal distribution, whereas the bias term c is
+set to a constant.
+
+As alpha tends toward zero the coefficients found by Ridge
+regression stabilize towards the randomly sampled vector w.
+For big alpha (strong regularisation) the coefficients
+are smaller (eventually converging at 0) leading to a
+simpler and biased solution.
+These dependencies can be observed on the left plot.
+
+The right plot shows the mean squared error between the
+coefficients found by the model and the chosen vector w.
+Less regularised models retrieve the exact
+coefficients (error is equal to 0), stronger regularised
+models increase the error.
+
+Please note that in this example the data is non-noisy, hence
+it is possible to extract the exact coefficients.
+"""
+
+# Author: Kornel Kielczewski -- <[email protected]>
+
+print(__doc__)
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from sklearn.datasets import make_regression
+from sklearn.linear_model import Ridge
+from sklearn.metrics import mean_squared_error
+
+clf = Ridge()
+
+X, y, w = make_regression(n_samples=10, n_features=10, coef=True,
+                          random_state=1, bias=3.5)
+
+coefs = []
+errors = []
+
+alphas = np.logspace(-6, 6, 200)
+
+# Train the model with different regularisation strengths
+for a in alphas:
+    clf.set_params(alpha=a)
+    clf.fit(X, y)
+    coefs.append(clf.coef_)
+    errors.append(mean_squared_error(clf.coef_, w))
+
+# Display results
+plt.figure(figsize=(20, 6))
+
+plt.subplot(121)
+ax = plt.gca()
+ax.plot(alphas, coefs)
+ax.set_xscale('log')
+plt.xlabel('alpha')
+plt.ylabel('weights')
+plt.title('Ridge coefficients as a function of the regularization')
+plt.axis('tight')
+
+plt.subplot(122)
+ax = plt.gca()
+ax.plot(alphas, errors)
+ax.set_xscale('log')
+plt.xlabel('alpha')
+plt.ylabel('error')
+plt.title('Coefficient error as a function of the regularization')
+plt.axis('tight')
+
+plt.show()