def test_vrtos_ogl():
"""Test on overlapping group lasso"""
alpha = 1.0 / n_samples
groups_1 = [np.arange(8)]
groups_2 = [np.arange(5, 10)]
f = cp.utils.LogLoss(A, b, alpha)
for beta in np.logspace(-3, 3, 3):
p_1 = cp.utils.GroupL1(beta, groups_1)
p_2 = cp.utils.GroupL1(beta, groups_2)
L = cp.utils.get_max_lipschitz(A, "logloss") + alpha / density
opt_vrtos = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox_1=p_1.prox_factory(n_features),
prox_2=p_2.prox_factory(n_features),
)
opt_tos = cp.minimize_three_split(
f.f_grad, np.zeros(n_features), prox_1=p_1.prox, prox_2=p_2.prox
)
norm = np.linalg.norm(opt_tos.x)
if norm < 1e-10:
norm = 1
assert np.linalg.norm(opt_vrtos.x - opt_tos.x) / norm < 1e-4
def test_gl(groups):
alpha = 1.0 / n_samples
f = cp.utils.LogLoss(A, b, alpha)
for beta in np.logspace(-3, 3, 3):
p_1 = cp.utils.GroupL1(beta, groups)
L = cp.utils.get_max_lipschitz(A, "logloss") + alpha / density
opt_1 = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox_1=p_1.prox_factory(n_features),
)
opt_2 = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox_2=p_1.prox_factory(n_features),
)
opt_3 = cp.minimize_saga(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox=p_1.prox_factory(n_features),
)
for x in [opt_1.x, opt_2.x, opt_3.x]:
grad = cp.utils.LogLoss(A, b, alpha).f_grad(x)[1]
ss = 1.0 / L
# check that the gradient mapping vanishes
grad_map = (x - p_1.prox(x - ss * grad, ss)) / ss
assert np.linalg.norm(grad_map) < 1e-6
def test_vrtos_l1():
alpha = 1.0 / n_samples
f = cp.utils.LogLoss(A, b, alpha)
for beta in np.logspace(-3, 3, 3):
p_1 = cp.utils.L1Norm(beta)
L = cp.utils.get_max_lipschitz(A, "logloss") + alpha / density
# blocks = np.arange(n_features)
opt_1 = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox_1=p_1.prox_factory(n_features),
)
opt_2 = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
prox_2=p_1.prox_factory(n_features),
)
for x in [opt_1.x, opt_2.x]:
full_prox = cp.utils.L1Norm(beta)
grad = f.f_grad(x)[1]
ss = 1.0 / L
# check that the gradient mapping vanishes
grad_map = (x - full_prox.prox(x - ss * grad, ss)) / ss
assert np.linalg.norm(grad_map) < 1e-6
def test_vrtos():
"""Test VRTOS with no penalty."""
alpha = 1.0 / n_samples
f = cp.utils.LogLoss(A, b)
for beta in np.logspace(-3, 3, 3):
L = cp.utils.get_max_lipschitz(A, "logloss") + alpha / density
opt = cp.minimize_vrtos(
f.partial_deriv,
A,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=200,
)
grad = cp.utils.LogLoss(A, b, alpha).f_grad(opt.x)[1]
assert np.linalg.norm(grad) < 1e-6
def test_vrtos_fl(A_data):
"""Test on overlapping group lasso"""
n_samples, n_features = A_data.shape
alpha = 1.0 / n_samples
f = cp.utils.LogLoss(A_data, b, alpha)
for beta in np.logspace(-3, 3, 3):
pen = cp.utils.FusedLasso(beta)
L = cp.utils.get_max_lipschitz(A_data, "logloss") + alpha / density
opt_vrtos = cp.minimize_vrtos(
f.partial_deriv,
A_data,
b,
np.zeros(n_features),
1 / (3 * L),
alpha=alpha,
max_iter=2000,
prox_1=pen.prox_1_factory(n_features),
prox_2=pen.prox_2_factory(n_features),
tol=0,
)
opt_pgd = cp.minimize_proximal_gradient(
f.f_grad, np.zeros(n_features), prox=pen.prox, max_iter=2000, tol=0
)
norm = np.linalg.norm(opt_pgd.x)
if norm < 1e-10:
norm = 1
assert np.linalg.norm(opt_vrtos.x - opt_pgd.x) / norm < 1e-4
# check also the gradient mapping
ss = 1.0 / L
grad = f.f_grad(opt_vrtos.x)[1]
grad_map = (opt_vrtos.x - pen.prox(opt_vrtos.x - ss * grad, ss)) / ss
assert np.linalg.norm(grad_map) < 1e-6