def test_group_lasso_lasso(sparse_X, fit_intercept, normalize):
# check that group Lasso with groups of size 1 gives Lasso
n_features = 1000
X, y = build_dataset(n_samples=100,
n_features=n_features,
sparse_X=sparse_X)[:2]
alpha_max = norm(X.T @ y, ord=np.inf) / len(y)
alpha = alpha_max / 10
clf = Lasso(alpha,
tol=1e-12,
fit_intercept=fit_intercept,
normalize=normalize,
verbose=0)
clf.fit(X, y)
# take groups of size 1:
clf1 = GroupLasso(alpha=alpha,
groups=1,
tol=1e-12,
fit_intercept=fit_intercept,
normalize=normalize,
verbose=0)
clf1.fit(X, y)
np.testing.assert_allclose(clf1.coef_, clf.coef_, atol=1e-6)
np.testing.assert_allclose(clf1.intercept_, clf.intercept_, rtol=1e-4)
def test_GroupLasso(sparse_X):
n_features = 50
X, y = build_dataset(n_samples=11,
n_features=n_features,
sparse_X=sparse_X,
n_informative_features=n_features)[:2]
tol = 1e-4
clf = GroupLasso(alpha=0.01, groups=10, tol=tol)
clf.fit(X, y)
np.testing.assert_array_less(clf.dual_gap_, tol)
def test_GroupLasso(sparse_X):
n_features = 50
X, y = build_dataset(
n_samples=11, n_features=n_features, sparse_X=sparse_X)
tol = 1e-8
clf = GroupLasso(alpha=0.8, groups=10, tol=tol)
clf.fit(X, y)
np.testing.assert_array_less(clf.dual_gap_, tol)
clf.tol = 1e-6
clf.groups = 1 # unsatisfying but sklearn will fit out of 5 features
check_estimator(clf)
def test_group_lasso_multitask():
"Group Lasso and Multitask Lasso equivalence." ""
n_samples, n_features = 30, 50
X_, Y_ = build_dataset(n_samples,
n_features,
n_informative_features=n_features,
n_targets=3)[:2]
y = Y_.reshape(-1, order='F')
X = np.zeros([3 * n_samples, 3 * n_features], order='F')
# block filling new design
for i in range(3):
X[i * n_samples:(i + 1) * n_samples,
i * n_features:(i + 1) * n_features] = X_
grp_indices = np.arange(3 * n_features).reshape(3, -1).reshape(
-1, order='F').astype(np.int32)
grp_ptr = 3 * np.arange(n_features + 1).astype(np.int32)
alpha_max = np.max(norm(X_.T @ Y_, axis=1)) / len(Y_)
X_data = np.empty([1], dtype=X.dtype)
X_indices = np.empty([1], dtype=np.int32)
X_indptr = np.empty([1], dtype=np.int32)
other = dscal_grp(False, y, grp_ptr, grp_indices, X, X_data, X_indices,
X_indptr, X_data,
len(grp_ptr) - 1, np.zeros(1, dtype=np.int32), False)
np.testing.assert_allclose(alpha_max, other / len(Y_))
alpha = alpha_max / 10
clf = MultiTaskLasso(alpha, fit_intercept=False, tol=1e-8)
clf.fit(X_, Y_)
groups = [grp.tolist() for grp in grp_indices.reshape(50, 3)]
clf1 = GroupLasso(alpha=alpha / 3,
groups=groups,
fit_intercept=False,
tol=1e-8)
clf1.fit(X, y)
np.testing.assert_allclose(clf1.coef_, clf.coef_.reshape(-1), atol=1e-4)
# Create true regression coefficients with 3 groups of 5 non-zero values
w_true = np.zeros(n_features)
w_true[:5] = 1
w_true[20:25] = -2
w_true[40:45] = 1
y = X @ w_true + rng.randn(n_samples)
# Fit an adapted GroupLasso model
groups = 5 # groups are contiguous and of size 5
# irregular groups are also supported,
clf = GroupLasso(groups=groups, alpha=1.1)
clf.fit(X, y)
###############################################################################
# Display results
fig = plt.figure(figsize=(10, 4))
m, s, _ = plt.stem(w_true, label=r"true regression coefficients",
use_line_collection=True)
m, s, _ = plt.stem(clf.coef_, label=r"estimated regression coefficients",
markerfmt='x', use_line_collection=True)
plt.setp([m, s], color='#ff7f0e')
plt.xlabel("feature index")
plt.legend()
plt.show(block=False)