Lasso on dense and sparse data

We show that glm.Lasso and glm.sparse.Lasso provide the same results and that in the case of sparse data glm.sparse.Lasso improves the speed.

Python source code: lasso_dense_vs_sparse_data.py

from time import time
import numpy as np
from scipy import sparse
from scipy import linalg

from scikits.learn.glm.sparse import Lasso as SparseLasso
from scikits.learn.glm 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, maxit=1000)
print "Sparse Lasso done in %fs" % (time() - t0)

t0 = time()
dense_lasso.fit(X, y, maxit=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
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 = SparseLasso(alpha=alpha, fit_intercept=False)
dense_lasso = DenseLasso(alpha=alpha, fit_intercept=False)

t0 = time()
sparse_lasso.fit(Xs, y, maxit=1000)
print "Sparse Lasso done in %fs" % (time() - t0)

t0 = time()
dense_lasso.fit(Xs.todense(), y, maxit=1000)
print "Dense Lasso done in %fs" % (time() - t0)

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