from scipy import linalg
from sklearn.linear_model.sparse import Lasso as SparseLasso
from sklearn.linear_model import Lasso as DenseLasso
###############################################################################
# The two Lasso implementations on Dense data
print "--- Dense matrices"
n_samples, n_features = 200, 10000
np.random.seed(0)
y = np.random.randn(n_samples)
X = np.random.randn(n_samples, n_features)
alpha = 1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False)
t0 = time()
sparse_lasso.fit(X, y, max_iter=1000)
print "Sparse Lasso done in %fs" % (time() - t0)
t0 = time()
dense_lasso.fit(X, y, max_iter=1000)
print "Dense Lasso done in %fs" % (time() - t0)
print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_ -
dense_lasso.coef_)
###############################################################################
# The two Lasso implementations on Sparse data
from scipy import sparse
from scipy import linalg
from sklearn.datasets.samples_generator import make_regression
from sklearn.linear_model.sparse import Lasso as SparseLasso
from sklearn.linear_model import Lasso as DenseLasso
###############################################################################
# The two Lasso implementations on Dense data
print "--- Dense matrices"
X, y = make_regression(n_samples=200, n_features=5000, random_state=0)
alpha = 1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False, max_iter=1000)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False, max_iter=1000)
t0 = time()
sparse_lasso.fit(X, y)
print "Sparse Lasso done in %fs" % (time() - t0)
t0 = time()
dense_lasso.fit(X, y)
print "Dense Lasso done in %fs" % (time() - t0)
print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_
- dense_lasso.coef_)
###############################################################################
# The two Lasso implementations on Sparse data
from sklearn.linear_model.sparse import Lasso as SparseLasso
from sklearn.linear_model import Lasso as DenseLasso
###############################################################################
# The two Lasso implementations on Dense data
print "--- Dense matrices"
n_samples, n_features = 200, 10000
np.random.seed(0)
y = np.random.randn(n_samples)
X = np.random.randn(n_samples, n_features)
alpha = 1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False)
t0 = time()
sparse_lasso.fit(X, y, max_iter=1000)
print "Sparse Lasso done in %fs" % (time() - t0)
t0 = time()
dense_lasso.fit(X, y, max_iter=1000)
print "Dense Lasso done in %fs" % (time() - t0)
print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_
- dense_lasso.coef_)
###############################################################################
# The two Lasso implementations on Sparse data
from time import time
from scipy import sparse
from scipy import linalg
from sklearn.datasets.samples_generator import make_regression
from sklearn.linear_model.sparse import Lasso as SparseLasso
from sklearn.linear_model import Lasso as DenseLasso
###############################################################################
# The two Lasso implementations on Dense data
print "--- Dense matrices"
X, y = make_regression(n_samples=200, n_features=5000, random_state=0)
alpha = 1
sparse_lasso = SparseLasso(alpha=alpha, fit_intercept=False, max_iter=1000)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False, max_iter=1000)
t0 = time()
sparse_lasso.fit(X, y)
print "Sparse Lasso done in %fs" % (time() - t0)
t0 = time()
dense_lasso.fit(X, y)
print "Dense Lasso done in %fs" % (time() - t0)
print "Distance between coefficients : %s" % linalg.norm(sparse_lasso.coef_ -
dense_lasso.coef_)
###############################################################################
# The two Lasso implementations on Sparse data
# Generate synthetic images, and projections
l = 128
proj_operator = build_projection_operator(l, l / 7.)
data = generate_synthetic_data()
proj = proj_operator * data.ravel()[:, np.newaxis]
proj += 0.15 * np.random.randn(*proj.shape)
# Reconstruction with L2 (Ridge) penalization
rgr_ridge = Ridge(alpha=0.2)
rgr_ridge.fit(proj_operator, proj.ravel())
rec_l2 = rgr_ridge.coef_.reshape(l, l)
# Reconstruction with L1 (Lasso) penalization
# the best value of alpha was determined using cross validation
# with LassoCV
rgr_lasso = Lasso(alpha=0.001)
rgr_lasso.fit(proj_operator, proj.ravel())
rec_l1 = rgr_lasso.coef_.reshape(l, l)
plt.figure(figsize=(8, 3.3))
plt.subplot(131)
plt.imshow(data, cmap=plt.cm.gray, interpolation='nearest')
plt.axis('off')
plt.title('original image')
plt.subplot(132)
plt.imshow(rec_l2, cmap=plt.cm.gray, interpolation='nearest')
plt.title('L2 penalization')
plt.axis('off')
plt.subplot(133)
plt.imshow(rec_l1, cmap=plt.cm.gray, interpolation='nearest')
plt.title('L1 penalization')
