using diabetes in lasso/lars examples

Author: agramfort

examples/glm/plot_lar.py

@@ -1,17 +1,21 @@
 #!/usr/bin/env python
 """
-======================
-Least Angle Regression
-======================
+============================
+Least Angle Regression (LAR)
+============================
+
+Compute LAR path on diabetes dataset.
+
+See: http://en.wikipedia.org/wiki/Least-angle_regression
 
 """
+print __doc__
 
 # Author: Fabian Pedregosa <fabian.pedregosa@inria.fr>
 #         Alexandre Gramfort <alexandre.gramfort@inria.fr>
 # License: BSD Style.
 
 from datetime import datetime
-import itertools
 import numpy as np
 import pylab as pl
 
@@ -22,27 +26,21 @@
 X = diabetes.data
 y = diabetes.target
 
+X[:,6] *= -1 # To reproduce wikipedia LAR page
 
 ################################################################################
-# Demo path functions
-################################################################################
+# Compute path functions
 
 print "Computing regularization path using the LARS ..."
 start = datetime.now()
-# should not use a fit predict to get the path
-clf = glm.LeastAngleRegression().fit(X, y, normalize=True)
+alphas_, _, coefs_ = glm.lars_path(X, y, max_iter=9, method="lar")
 print "This took ", datetime.now() - start
 
-alphas = -np.log10(clf.alphas_)
-
-# # Display results
-color_iter = itertools.cycle(['r', 'g', 'b', 'c'])
-
-for coef_, color in zip(clf.coef_path_, color_iter):
-    pl.plot(alphas, coef_.T, color)
-
+###############################################################################
+# Display path
+pl.plot(-np.log10(alphas_), coefs_.T)
 ymin, ymax = pl.ylim()
-pl.vlines(alphas, ymin, ymax, linestyle='dashed')
+pl.vlines(-np.log10(alphas_), ymin, ymax, linestyle='dashed')
 pl.xlabel('-Log(lambda)') # XXX : wrong label
 pl.ylabel('Coefficients')
 pl.title('Least Angle Regression (LAR) Path')

examples/glm/plot_lasso_coordinate_descent_path.py

@@ -6,6 +6,7 @@
 Lasso and elastic net (L1 and L2 penalisation) implemented using a
 coordinate descent.
 """
+print __doc__
 
 # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
 # License: BSD Style.
@@ -15,38 +16,37 @@
 import pylab as pl
 
 from scikits.learn.glm import lasso_path, enet_path
+from scikits.learn import datasets
 
-n_samples, n_features = 100, 10
-np.random.seed(0)
-y = np.random.randn(n_samples)
-X = np.random.randn(n_samples, n_features)
+diabetes = datasets.load_diabetes()
+X = diabetes.data
+y = diabetes.target
 
-################################################################################
-# Fit models
-################################################################################
+X /= X.std(0) # Standardize data (easier to set the rho parameter)
 
 ################################################################################
-# Demo path functions
-################################################################################
+# Compute paths
 
-eps = 1e-2 # the smaller it is the longer is the path
+eps = 5e-3 # the smaller it is the longer is the path
 
 print "Computing regularization path using the lasso..."
 models = lasso_path(X, y, eps=eps)
 alphas_lasso = np.array([model.alpha for model in models])
 coefs_lasso = np.array([model.coef_ for model in models])
 
 print "Computing regularization path using the elastic net..."
-models = enet_path(X, y, eps=eps, rho=0.6)
+models = enet_path(X, y, eps=eps, rho=0.8)
 alphas_enet = np.array([model.alpha for model in models])
 coefs_enet = np.array([model.coef_ for model in models])
 
+################################################################################
 # Display results
+
 color_iter = cycle(['b', 'g', 'r', 'c', 'm', 'y', 'k'])
 for color, coef_lasso, coef_enet in zip(color_iter,
                             coefs_lasso.T, coefs_enet.T):
     pl.plot(-np.log10(alphas_lasso), coef_lasso, color)
-    pl.plot(-np.log10(alphas_enet), coef_enet, color + 'x')
+    pl.plot(-np.log10(alphas_enet), coef_enet, color + '--')
 
 pl.xlabel('-Log(lambda)')
 pl.ylabel('weights')

examples/glm/plot_lasso_lars.py

@@ -5,6 +5,7 @@
 =================================
 
 """
+print __doc__
 
 # Author: Fabian Pedregosa <fabian.pedregosa@inria.fr>
 #         Alexandre Gramfort <alexandre.gramfort@inria.fr>
@@ -24,24 +25,8 @@
 # someting's wrong with our dataset
 X[:, 6] = -X[:, 6]
 
-
-m, n = 200, 200
-np.random.seed(0)
-X = np.random.randn(m, n)
-y = np.random.randn(m)
-
-
-_xmean = X.mean(0)
-_ymean = y.mean(0)
-X = X - _xmean
-y = y - _ymean
-_norms = np.apply_along_axis (np.linalg.norm, 0, X)
-nonzeros = np.flatnonzero(_norms)
-X[:, nonzeros] /= _norms[nonzeros]
-
 ################################################################################
 # Demo path functions
-################################################################################
 
 G = np.dot(X.T, X)
 print "Computing regularization path using the LARS ..."