def test_lasso():
for alpha in np.logspace(-3, 3, 3):
def logloss(x):
return logistic._logistic_loss(x, X, y, 0.)
def fprime_logloss(x):
return logistic._logistic_loss_and_grad(x, X, y, 0.)[1]
def l1_prox(x, step_size):
return np.fmax(x - step_size, 0) - np.fmax(-x - step_size, 0)
L = np.eye(n_features)
opt_proximal = proximal_gradient(
logloss, fprime_logloss, l1_prox, np.zeros(n_features),
tol=1e-24, alpha=alpha)
opt_primal_dual = primal_dual(
logloss, fprime_logloss, l1_prox, None, L, np.zeros(n_features),
alpha=alpha)
assert opt_primal_dual.success
np.testing.assert_allclose(
opt_proximal.x, opt_primal_dual.x, rtol=1e-1)
# same thing but using the other operator
opt_primal_dual2 = primal_dual(
logloss, fprime_logloss, None, l1_prox, L, np.zeros(n_features),
beta=alpha)
np.testing.assert_allclose(
opt_proximal.x, opt_primal_dual2.x, atol=1e-3)
def test_fused():
"""
Test that it can solve a problem with fused lasso regularization
using only the L1-prox and an appropriate L linear operator.
"""
for alpha in np.logspace(-3, 3, 3):
def logloss(x):
return logistic._logistic_loss(x, X, y, 0.)
def fprime_logloss(x):
return logistic._logistic_loss_and_grad(x, X, y, 0.)[1]
def l1_prox(x, step_size):
return np.fmax(x - step_size, 0) - np.fmax(-x - step_size, 0)
L = sparse.diags([1, -1], [0, 1], shape=(n_features - 1, n_features))
# solve the problem using the fused lasso proximal operator
# (only for reference)
opt_proximal = proximal_gradient(
logloss, fprime_logloss, prox_tv1d, np.zeros(n_features),
tol=1e-24, max_iter=10000, alpha=alpha)
opt_primal_dual = primal_dual(
logloss, fprime_logloss, None, l1_prox, L, np.zeros(n_features),
beta=alpha, verbose=True, step_size_y=1)
assert opt_primal_dual.success
np.testing.assert_allclose(
opt_proximal.x, opt_primal_dual.x, atol=1e-1)
def test_optimize():
def logloss(x):
return logistic._logistic_loss(x, X, y, 1.)
def fprime_logloss(x):
return logistic._logistic_loss_and_grad(x, X, y, 1.)[1]
L = np.eye(n_features)
opt = primal_dual(
logloss, fprime_logloss, None, None, L, np.zeros(n_features))
assert opt.success
sol_scipy = optimize.fmin_l_bfgs_b(
logloss, np.zeros(n_features),
fprime=fprime_logloss)[0]
np.testing.assert_allclose(sol_scipy, opt.x, rtol=1e-1)