def test_weights():
sparse_X = 1
X, y = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
np.random.seed(0)
weights = np.abs(np.random.randn(X.shape[1]))
tol = 1e-12
params = {'n_alphas': 10, 'tol': tol}
alphas1, coefs1, gaps1 = celer_path(X,
y,
"lasso",
weights=weights,
verbose=1,
**params)
alphas2, coefs2, gaps2 = celer_path(X / weights[None, :], y, "lasso",
**params)
np.testing.assert_allclose(alphas1, alphas2)
np.testing.assert_allclose(coefs1,
coefs2 / weights[:, None],
atol=1e-5,
rtol=1e-3)
np.testing.assert_array_less(gaps1, tol)
np.testing.assert_array_less(gaps2, tol)
def test_weights():
sparse_X = 1
X, y = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
np.random.seed(0)
weights = np.abs(np.random.randn(X.shape[1]))
tol = 1e-14
params = {'n_alphas': 10, 'tol': tol}
alphas1, coefs1, gaps1 = celer_path(X,
y,
"lasso",
weights=weights,
verbose=1,
**params)
alphas2, coefs2, gaps2 = celer_path(X / weights[None, :], y, "lasso",
**params)
assert_allclose(alphas1, alphas2)
assert_allclose(coefs1, coefs2 / weights[:, None], atol=1e-4, rtol=1e-3)
assert_array_less(gaps1, tol * norm(y)**2 / len(y))
assert_array_less(gaps2, tol * norm(y)**2 / len(y))
alpha = 0.001
clf1 = Lasso(alpha=alpha, weights=weights, fit_intercept=False).fit(X, y)
clf2 = Lasso(alpha=alpha, fit_intercept=False).fit(X / weights, y)
assert_allclose(clf1.coef_, clf2.coef_ / weights)
# weights must be > 0
clf1.weights[0] = 0.
np.testing.assert_raises(ValueError, clf1.fit, X=X, y=y)
def test_celer_path(sparse_X, alphas, pb):
"""Test Lasso path convergence."""
X, y = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
tol = 1e-6
if pb == "logreg":
y = np.sign(y)
tol_scaled = tol * len(y) * np.log(2)
else:
tol_scaled = tol * norm(y)**2 / len(y)
n_samples = X.shape[0]
if alphas is not None:
alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
n_alphas = 10
alphas = alpha_max * np.logspace(0, -2, n_alphas)
alphas, _, gaps, _, n_iters = celer_path(X,
y,
pb,
alphas=alphas,
tol=tol,
return_thetas=True,
verbose=1,
return_n_iter=True)
assert_array_less(gaps, tol_scaled)
# hack because array_less wants strict inequality
assert_array_less(0.99, n_iters)
def test_infinite_weights(pb):
n_samples, n_features = 50, 100
X, y = build_dataset(n_samples, n_features)
if pb == "logreg":
y = np.sign(y)
np.random.seed(1)
weights = np.abs(np.random.randn(n_features))
n_inf = n_features // 10
inf_indices = np.random.choice(n_features, size=n_inf, replace=False)
weights[inf_indices] = np.inf
alpha = norm(X.T @ y / weights, ord=np.inf) / n_samples / 100
tol = 1e-8
_, coefs, dual_gaps = celer_path(X,
y,
pb=pb,
alphas=[alpha],
weights=weights,
tol=tol)
if pb == "logreg":
assert_array_less(dual_gaps[0], tol * n_samples * np.log(2))
else:
assert_array_less(dual_gaps[0], tol * norm(y)**2 / 2.)
assert_array_equal(coefs[inf_indices], 0)
def test_celer_path_logreg(solver):
X, y = build_dataset(n_samples=60, n_features=100, sparse_X=True)
y = np.sign(y)
alpha_max = norm(X.T.dot(y), ord=np.inf) / 2
alphas = alpha_max * np.geomspace(1, 1e-2, 10)
tol = 1e-8
coefs, Cs, n_iters = _logistic_regression_path(X,
y,
Cs=1. / alphas,
fit_intercept=False,
penalty='l1',
solver='liblinear',
tol=tol)
_, coefs_c, gaps = celer_path(X,
y,
"logreg",
alphas=alphas,
tol=tol,
verbose=1,
use_PN=(solver == "celer-pn"))
np.testing.assert_array_less(gaps, tol)
np.testing.assert_allclose(coefs != 0, coefs_c.T != 0)
np.testing.assert_allclose(coefs, coefs_c.T, atol=1e-5, rtol=1e-3)
def test_celer_single_alpha(sparse_X, pb):
X, y = build_dataset(n_samples=20, n_features=100, sparse_X=sparse_X)
if pb == "logreg":
y = np.sign(y)
alpha_max = norm(X.T.dot(y), ord=np.inf) / X.shape[0]
tol = 1e-6
_, coefs, gaps = celer_path(X, y, pb, alphas=[alpha_max / 10.], tol=tol)
np.testing.assert_array_less(gaps, tol)
def test_celer_path_sparse():
X, y, _, _ = build_dataset(n_samples=50, n_features=50, n_targets=1)
X = sparse.csc_matrix(X)
alpha_max = np.max(np.abs(X.T.dot(y)))
n_alphas = 10
alphas = alpha_max * np.logspace(0, -2, n_alphas)
tol = 1e-6
betas, thetas, gaps = celer_path(X, y, alphas=alphas, tol=tol, verbose=1)
np.testing.assert_array_less(gaps, tol)
def test_celer_path_vs_lasso_path(sparse_X, prune):
"""Test that celer_path matches sklearn lasso_path."""
X, y, _, _ = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
params = dict(eps=1e-2, n_alphas=10, tol=1e-14)
alphas1, coefs1, gaps1 = celer_path(
X, y, return_thetas=False, verbose=1, prune=prune, **params)
alphas2, coefs2, gaps2 = lasso_path(X, y, verbose=False, **params)
np.testing.assert_allclose(alphas1, alphas2)
np.testing.assert_allclose(coefs1, coefs2, rtol=1e-05, atol=1e-6)
def test_celer_single_alpha(sparse_X, pb):
X, y = build_dataset(n_samples=20, n_features=100, sparse_X=sparse_X)
tol = 1e-6
if pb == "logreg":
y = np.sign(y)
tol_scaled = tol * np.log(2) * len(y)
else:
tol_scaled = tol * norm(y)**2 / len(y)
alpha_max = norm(X.T.dot(y), ord=np.inf) / X.shape[0]
_, _, gaps = celer_path(X, y, pb, alphas=[alpha_max / 10.], tol=tol)
assert_array_less(gaps, tol_scaled)
def test_zero_column(sparse_X):
X, y = build_dataset(n_samples=60, n_features=50, sparse_X=sparse_X)
n_zero_columns = 20
if sparse_X:
X.data[:X.indptr[n_zero_columns]].fill(0.)
else:
X[:, :n_zero_columns].fill(0.)
alpha_max = norm(X.T.dot(y), ord=np.inf) / X.shape[0]
tol = 1e-6
_, coefs, gaps = celer_path(
X, y, "lasso", alphas=[alpha_max / 10.], tol=tol, p0=50, prune=0)
w = coefs.T[0]
np.testing.assert_array_less(gaps, tol)
np.testing.assert_equal(w.shape[0], X.shape[1])
def test_celer_path(sparse_X, alphas, positive):
"""Test Lasso path convergence."""
X, y, _, _ = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
n_samples = X.shape[0]
if alphas is not None:
alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
n_alphas = 10
alphas = alpha_max * np.logspace(0, -2, n_alphas)
tol = 1e-6
alphas, coefs, gaps, thetas, n_iters = celer_path(
X, y, alphas=alphas, tol=tol, return_thetas=True, verbose=False,
verbose_inner=False, positive=positive, return_n_iter=True)
np.testing.assert_array_less(gaps, tol)
# hack because array_less wants strict inequality
np.testing.assert_array_less(0.99, n_iters)
def test_celer_path_vs_lasso_path(sparse_X, prune):
"""Test that celer_path matches sklearn lasso_path."""
X, y = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
tol = 1e-12
params = dict(eps=1e-3, n_alphas=10, tol=tol)
alphas1, coefs1, gaps1 = celer_path(
X, y, "lasso", return_thetas=False, verbose=1, prune=prune,
max_iter=30, **params)
alphas2, coefs2, _ = lasso_path(X, y, verbose=False, **params,
max_iter=10000)
np.testing.assert_allclose(alphas1, alphas2)
np.testing.assert_array_less(gaps1, tol)
np.testing.assert_allclose(coefs1, coefs2, rtol=1e-03, atol=1e-5)
def test_celer_path(sparse_X):
"""Test Lasso path convergence."""
X, y, _, _ = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
n_samples = X.shape[0]
alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
n_alphas = 10
alphas = alpha_max * np.logspace(0, -2, n_alphas)
tol = 1e-6
alphas, coefs, gaps, thetas = celer_path(X,
y,
alphas=alphas,
tol=tol,
return_thetas=True,
verbose=False,
verbose_inner=False)
np.testing.assert_array_less(gaps, tol)
n_alphas = 11
alphas = alpha_max * np.geomspace(1, 0.1, n_alphas)
###############################################################################
# Run Celer on a grid of regularization parameters, for various tolerances:
tols = [1e-2, 1e-4, 1e-6]
results = np.zeros([1, len(tols)])
gaps = np.zeros((len(tols), len(alphas)))
print("Starting path computation...")
for tol_ix, tol in enumerate(tols):
t0 = time.time()
res = celer_path(X,
y,
'lasso',
alphas=alphas,
tol=tol,
prune=True,
verbose=1)
results[0, tol_ix] = time.time() - t0
_, coefs, gaps[tol_ix] = res
labels = [r"\sc{Celer}"]
figsize = (4, 3.5)
df = pd.DataFrame(results.T, columns=["Celer"])
df.index = [str(tol) for tol in tols]
df.plot.bar(rot=0, figsize=figsize)
plt.xlabel("stopping tolerance")
plt.ylabel("path computation time (s)")
plt.tight_layout()
alphas = alpha_max * np.logspace(0, -2, n_alphas)
gap_freq = 10
prune = 1
verbose = 0
verbose_inner = 0
tols = [1e-2, 1e-4, 1e-6]
results = np.zeros([1, len(tols)])
for tol_ix, tol in enumerate(tols):
t0 = time.time()
res = celer_path(X,
y,
alphas=alphas,
max_iter=100,
gap_freq=gap_freq,
p0=100,
verbose=verbose,
verbose_inner=verbose_inner,
tol=tol,
prune=prune,
return_thetas=True)
results[0, tol_ix] = time.time() - t0
_, coefs, gaps, thetas = res
betas = coefs.T
labels = [r"\sc{Celer}"]
figsize = (7, 4)
fig = plot_path_hist(results, labels, tols, figsize, ylim=None)
plt.show()
alphas = alpha_max * np.logspace(0, -2, n_alphas)
gap_freq = 10
prune = 1
verbose = 0
verbose_inner = 0
tols = [1e-2, 1e-4, 1e-6, 1e-8]
results = np.zeros([2, len(tols)])
for tol_ix, tol in enumerate(tols):
t0 = time.time()
res = celer_path(X,
y,
alphas,
max_iter=100,
gap_freq=gap_freq,
max_epochs_inner=50000,
p0=100,
verbose=verbose,
verbose_inner=verbose_inner,
tol=tol,
prune=prune)
results[0, tol_ix] = time.time() - t0
print('Celer time: %.2f s' % results[0, tol_ix])
betas, thetas, gaps = res
t0 = time.time()
_, coefs, dual_gaps = lasso_path(X, y, tol=tol, alphas=alphas / n_samples)
results[1, tol_ix] = time.time() - t0
coefs = coefs.T
labels = [r"\sc{CELER}", "scikit-learn"]
y -= np.mean(y)
y /= np.std(y)
print("Starting path computation...")
alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
n_alphas = 100
alphas = alpha_max * np.geomspace(1, 0.01, n_alphas)
tols = [1e-2, 1e-4, 1e-6, 1e-8]
results = np.zeros([2, len(tols)])
for tol_ix, tol in enumerate(tols):
t0 = time.time()
_, coefs, gaps = celer_path(X,
y,
pb='lasso',
alphas=alphas,
tol=tol,
prune=True)
results[0, tol_ix] = time.time() - t0
print('Celer time: %.2f s' % results[0, tol_ix])
t0 = time.time()
_, coefs, dual_gaps = lasso_path(X, y, tol=tol, alphas=alphas)
results[1, tol_ix] = time.time() - t0
labels = [r"\sc{Celer}", "scikit-learn"]
figsize = (7.1, 4.3)
fig = plot_path_hist(results, labels, tols, figsize, ylim=None)
plt.show()