Lasso on dense and sparse data

We show that linear_model.Lasso provides the same results for dense and sparse data and that in the case of sparse data the speed is improved.

Out:

--- Dense matrices
Sparse Lasso done in 0.099625s
Dense Lasso done in 0.029654s
Distance between coefficients : 1.257580352417723e-13
--- Sparse matrices
Matrix density : 0.6263000000000001 %
Sparse Lasso done in 0.128094s
Dense Lasso done in 0.687114s
Distance between coefficients : 8.64570987628102e-12

from time import time
from scipy import sparse
from scipy import linalg

from sklearn.datasets import make_regression
from sklearn.linear_model import Lasso


# #############################################################################
# The two Lasso implementations on Dense data
print("--- Dense matrices")

X, y = make_regression(n_samples=200, n_features=5000, random_state=0)
X_sp = sparse.coo_matrix(X)

alpha = 1
sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)
dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)

t0 = time()
sparse_lasso.fit(X_sp, 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
print("--- Sparse matrices")

Xs = X.copy()
Xs[Xs < 2.5] = 0.0
Xs = sparse.coo_matrix(Xs)
Xs = Xs.tocsc()

print("Matrix density : %s %%" % (Xs.nnz / float(X.size) * 100))

alpha = 0.1
sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)
dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)

t0 = time()
sparse_lasso.fit(Xs, y)
print("Sparse Lasso done in %fs" % (time() - t0))

t0 = time()
dense_lasso.fit(Xs.toarray(), y)
print("Dense Lasso done in %fs" % (time() - t0))

print(
    "Distance between coefficients : %s"
    % linalg.norm(sparse_lasso.coef_ - dense_lasso.coef_)
)