DOC add ucurve example

examples/plot_ucurve.py

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+"""
+==============================
+Show U-curve of regularization
+==============================
+Illustrate the sweet spot of regularization: not too much, not too little.
+"""
+
+import numpy as np
+from numpy.linalg import norm
+import matplotlib.pyplot as plt
+from libsvmdata import fetch_libsvm
+from sklearn.model_selection import train_test_split
+
+from skglm import Lasso
+
+
+X, y = fetch_libsvm("rcv1.binary")
+# we keep only 2000 features and samples
+X = X[:, :2000]
+X_train, X_test, y_train, y_test = train_test_split(X, y)
+X_train, y_train = X_train[:2000], y_train[:2000]
+
+alpha_max = norm(X_train.T @ y_train, ord=np.inf) / len(y_train)
+alphas = np.geomspace(1, 1e-4) * alpha_max
+mse = []
+mse_test = []
+
+clf = Lasso(fit_intercept=False, tol=1e-8, warm_start=True)
+for idx, alpha in enumerate(alphas):
+    clf.alpha = alpha
+    clf.fit(X_train, y_train)
+    mse.append(np.mean((y_train - clf.predict(X_train)) **2))
+    mse_test.append(np.mean((y_test - clf.predict(X_test)) **2))
+
+plt.close('all')
+plt.semilogx(alphas, mse, label='train MSE')
+plt.semilogx(alphas, mse_test, label='test MSE')
+plt.legend()
+plt.title("Mean squared error")
+plt.xlabel(r"Lasso regularization strength $\lambda$")
+plt.show(block=False)