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
print("Iteration %s, beta %s" % (i, beta))
def g_prox(x, gamma, pen=beta):
return cp.tv_prox.prox_tv1d_cols(gamma * pen, x, n_rows, n_cols)
def h_prox(x, gamma, pen=beta):
return cp.tv_prox.prox_tv1d_rows(gamma * pen, x, n_rows, n_cols)
cb_adatos = cp.utils.Trace()
x0 = np.zeros(n_features)
adatos = cp.minimize_three_split(
f.f_grad,
x0,
g_prox,
h_prox,
step_size=10 * step_size,
max_iter=max_iter,
tol=1e-14,
verbose=1,
callback=cb_adatos,
h_Lipschitz=beta,
)
trace_ls = [loss(x, beta) for x in cb_adatos.trace_x]
all_trace_ls.append(trace_ls)
all_trace_ls_time.append(cb_adatos.trace_time)
out_img.append(adatos.x.reshape(img.shape))
cb_tos = cp.utils.Trace()
x0 = np.zeros(n_features)
cp.minimize_three_split(
f.f_grad,
x0,
img_np = data.cpu().numpy().squeeze().flatten()
def image_constraint_prox(delta, step_size=None):
"""Projects perturbation delta so that x + delta is in the set of images,
i.e. the (0, 1) range."""
adv_img_np = img_np + delta
delta = adv_img_np.clip(0, 1) - img_np
return delta
callback = copt.utils.Trace(lambda delta: f_grad(delta)[0])
delta0 = np.zeros(data.shape, dtype=float).flatten()
sol = copt.minimize_three_split(f_grad,
delta0,
constraint.prox,
image_constraint_prox,
callback=callback,
max_iter=50)
fig, ax = plt.subplots()
ax.plot([-loss_val for loss_val in callback.trace_fx], lw=3)
ax.set_yscale("log")
ax.set_xlabel("# Iterations")
ax.set_ylabel("Objective value")
ax.grid()
plt.show()
classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse',
'ship', 'truck')
for i, beta in enumerate(all_betas):
print("Iteration %s, beta %s" % (i, beta))
def g_prox(x, gamma, pen=beta):
return cp.tv_prox.prox_tv1d_cols(gamma * pen, x, n_rows, n_cols)
def h_prox(x, gamma, pen=beta):
return cp.tv_prox.prox_tv1d_rows(gamma * pen, x, n_rows, n_cols)
cb_adatos = cp.utils.Trace()
adatos = cp.minimize_three_split(
f.f_grad,
np.zeros(n_features),
g_prox,
h_prox,
step_size=step_size,
max_iter=max_iter,
tol=0,
callback=cb_adatos,
h_Lipschitz=beta,
)
trace_ls = [loss(x, beta) for x in cb_adatos.trace_x]
all_trace_ls.append(trace_ls)
all_trace_ls_time.append(cb_adatos.trace_time)
out_img.append(adatos.x.reshape(img.shape))
cb_tos = cp.utils.Trace()
cp.minimize_three_split(
f.f_grad,
np.zeros(n_features),
g_prox,
for i, beta in enumerate(all_betas):
print("beta = %s" % beta)
G1 = copt.penalty.TraceNorm(beta, Sigma.shape)
G2 = copt.penalty.L1Norm(beta)
def loss(x):
return f(x) + G1(x) + G2(x)
cb_tosls = cp.utils.Trace()
x0 = np.zeros(n_features)
tos_ls = cp.minimize_three_split(
f.f_grad,
x0,
G2.prox,
G1.prox,
step_size=5 * step_size,
max_iter=max_iter,
tol=1e-14,
verbose=1,
callback=cb_tosls,
h_Lipschitz=beta,
)
trace_ls = np.array([loss(x) for x in cb_tosls.trace_x])
all_trace_ls.append(trace_ls)
all_trace_ls_time.append(cb_tosls.trace_time)
cb_tos = cp.utils.Trace()
x0 = np.zeros(n_features)
tos = cp.minimize_three_split(
f.f_grad,
x0,
G1.prox,