def test_init_parameters(n, lbda, parametrization):
""" Test the gradient of z. """
rng = check_random_state(27)
x, _, _, L, _, A = synthetic_1d_dataset(n=n, s=0.5, snr=0.0, seed=rng)
n_layers = 5
# limit the number of inner layers for origtv to avoid long computations
kwargs = {}
if parametrization == 'origtv':
kwargs['n_inner_layers'] = 5
lista_1 = LearnTVAlgo(algo_type=parametrization, A=A, n_layers=n_layers,
max_iter=10, net_solver_type='one_shot', **kwargs)
lista_1.fit(x, lbda=lbda)
params = lista_1.export_parameters()
loss_lista_1 = []
for n_layer_ in range(n_layers + 1):
z_1 = lista_1.transform(x=x, lbda=lbda, output_layer=n_layer_)
loss_lista_1.append(synthesis_primal_obj(z=z_1, A=A, L=L, x=x,
lbda=lbda))
loss_lista_1 = np.array(loss_lista_1)
lista_2 = LearnTVAlgo(algo_type=parametrization, A=A, n_layers=n_layers,
initial_parameters=params, max_iter=10, **kwargs)
loss_lista_2 = []
for n_layer_ in range(n_layers + 1):
z_2 = lista_2.transform(x=x, lbda=lbda, output_layer=n_layer_)
loss_lista_2.append(synthesis_primal_obj(z=z_2, A=A, L=L, x=x,
lbda=lbda))
loss_lista_2 = np.array(loss_lista_2)
np.testing.assert_allclose(z_1, z_2)
np.testing.assert_allclose(loss_lista_1, loss_lista_2)
def run_experiment(methods, x_train, x_test, A, lbda, n_layers):
""" Experiment launcher. """
print("=" * 80)
l_diff_loss = []
for name, type_, kwargs, _, _, _ in methods:
print(f"[main script] running {name}")
print("-" * 80)
algo_type = 'origtv' if ('untrained' in type_) else type_
network = LearnTVAlgo(algo_type=algo_type,
A=A,
n_layers=n_layers,
max_iter=args.max_iter,
device=device,
verbose=1,
**kwargs)
if 'untrained' not in type_:
network.fit(x_train, lbda=lbda)
diff_loss = compute_prox_tv_errors(network, x_test, lbda)
l_diff_loss.append(diff_loss)
print("=" * 80)
return l_diff_loss
def analysis_learned_taut_string(x_train, x_test, A, D, L, lbda, all_n_layers,
type_=None, max_iter=300, device=None,
net_kwargs=None, verbose=1):
""" NN-algo solver for analysis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
params = None
l_loss = []
def record_loss(l_loss, u_train, u_test):
l_loss.append(dict(
train_loss=analysis_primal_obj(u_train, A, D, x_train, lbda),
test_loss=analysis_primal_obj(u_test, A, D, x_test, lbda),
))
return l_loss
_, u0_train, _ = init_vuz(A, D, x_train)
_, u0_test, _ = init_vuz(A, D, x_test)
record_loss(l_loss, u0_train, u0_test)
for n, n_layers in enumerate(all_n_layers):
# Declare network for the given number of layers. Warm-init the first
# layers with parameters learned with previous networks if any.
algo = LearnTVAlgo(algo_type='lpgd_taut_string', A=A,
n_layers=n_layers, max_iter=max_iter, device=device,
initial_parameters=params, verbose=verbose,
**net_kwargs)
# train
t0_ = time.time()
algo.fit(x_train, lbda=lbda)
delta_ = time.time() - t0_
# save parameters
params = algo.export_parameters()
# get train and test error
u_train = algo.transform(x_train, lbda, output_layer=n_layers)
u_test = algo.transform(x_test, lbda, output_layer=n_layers)
l_loss = record_loss(l_loss, u_train, u_test)
if verbose > 0:
train_loss = l_loss[n]['train_loss']
test_loss = l_loss[n]['test_loss']
print(f"\r[{algo.name}|layers#{n_layers:3d}] model fitted "
f"{delta_:4.1f}s train-loss={train_loss:.4e} "
f"test-loss={test_loss:.4e}")
df = pd.DataFrame(l_loss)
to_return = (df['train_loss'].values, df['test_loss'].values)
return to_return
def analysis_learned_algo(x_train, x_test, A, D, L, lbda, all_n_layers, type_,
max_iter=300, device=None, net_kwargs=None,
verbose=1):
""" NN-algo solver for analysis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
params = None
_, u0_train, _ = init_vuz(A, D, x_train)
_, u0_test, _ = init_vuz(A, D, x_test)
train_loss_init = analysis_primal_obj(u0_train, A, D, x_train, lbda)
test_loss_init = analysis_primal_obj(u0_test, A, D, x_test, lbda)
train_loss, test_loss = [train_loss_init], [test_loss_init]
algo_type = 'origtv' if ('untrained' in type_) else type_
for n_layers in all_n_layers:
# declare network
algo = LearnTVAlgo(algo_type=algo_type, A=A, n_layers=n_layers,
max_iter=max_iter, device=device,
initial_parameters=params, verbose=verbose,
**net_kwargs)
t0_ = time.time()
if 'untrained' not in type_:
algo.fit(x_train, lbda=lbda)
delta_ = time.time() - t0_
# save parameters
params = algo.export_parameters()
# get train and test error
u_train = algo.transform(x_train, lbda, output_layer=n_layers)
train_loss_ = analysis_primal_obj(u_train, A, D, x_train, lbda)
train_loss.append(train_loss_)
u_test = algo.transform(x_test, lbda, output_layer=n_layers)
test_loss_ = analysis_primal_obj(u_test, A, D, x_test, lbda)
test_loss.append(test_loss_)
if verbose > 0:
print(f"\r[{algo.name}|layers#{n_layers:3d}] model fitted "
f"{delta_:4.1f}s train-loss={train_loss_:.4e} "
f"test-loss={test_loss_:.4e}")
to_return = (np.array(train_loss), np.array(test_loss))
return to_return
def test_coherence_analysis_loss(parametrization, lbda, n):
""" Test coherence regarding the loss function between learnt and fixed
algorithms. """
rng = check_random_state(None)
x, _, _, _, D, A = synthetic_1d_dataset(n=n, s=0.5, snr=0.0, seed=rng)
_, _, z = init_vuz(A, D, x)
z_ = check_tensor(z, device='cpu')
cost = analysis_primal_obj(z, A, D, x, lbda=lbda)
ltv = LearnTVAlgo(algo_type=parametrization,
A=A,
n_layers=10,
device='cpu')
cost_ref = ltv._loss_fn(x, lbda, z_)
np.testing.assert_allclose(cost_ref, cost, atol=1e-30)
def test_untrained_analysis_lista(lbda, parametrization, n):
""" Test the gradient of z. """
rng = check_random_state(None)
x, _, _, _, D, A = synthetic_1d_dataset(n=n, s=0.5, snr=0.0, seed=rng)
v0, u0, _ = init_vuz(A, D, x)
n_layers = 10
rho = 1.0
sigma = 0.5
L_D = np.linalg.norm(D.dot(D.T), ord=2)
L_A = np.linalg.norm(A.dot(A.T), ord=2)
tau = 1.0 / (L_A / 2.0 + sigma * L_D**2)
lista = LearnTVAlgo(algo_type=parametrization,
A=A,
n_layers=n_layers,
device='cpu')
loss_untrained_condat = [analysis_primal_obj(u0, A, D, x, lbda)]
for n_layer_ in range(1, n_layers + 1):
z = lista.transform(x=x, lbda=lbda, output_layer=n_layer_)
loss_untrained_condat.append(analysis_primal_obj(z, A, D, x, lbda))
loss_untrained_condat = np.array(loss_untrained_condat)
v0, u0, _ = init_vuz(A, D, x, force_numpy=True)
params = dict(
grad=lambda u: analysis_primal_grad(u, A, x),
obj=lambda u: analysis_primal_obj(u, A, D, x, lbda),
prox=lambda z: pseudo_soft_th_numpy(z, lbda, 1.0 / sigma),
psi=lambda u: u.dot(D),
adj_psi=lambda v: v.dot(D.T),
v0=v0,
z0=u0,
lbda=lbda,
sigma=sigma,
tau=tau,
rho=rho,
max_iter=n_layers,
early_stopping=False,
debug=True,
verbose=0,
)
_, _, loss_condat = condatvu(**params)
np.testing.assert_allclose(loss_condat, loss_untrained_condat, atol=1e-20)
def test_coherence_training_analysis_loss(parametrization, lbda, n):
""" Test coherence regarding the loss function between learnt and fixed
algorithms. """
rng = check_random_state(None)
x, _, _, _, D, A = synthetic_1d_dataset(n=n, s=0.5, snr=0.0, seed=rng)
_, u0, _ = init_vuz(A, D, x)
train_loss = [analysis_primal_obj(u0, A, D, x, lbda)]
train_loss_ = [analysis_primal_obj(u0, A, D, x, lbda)]
for n_layers in range(1, 10):
lista = LearnTVAlgo(algo_type=parametrization,
A=A,
n_layers=n_layers,
max_iter=10)
lista.fit(x, lbda=lbda)
train_loss_.append(lista.training_loss_[-1])
u = lista.transform(x, lbda, output_layer=n_layers)
train_loss.append(analysis_primal_obj(u, A, D, x, lbda))
np.testing.assert_allclose(train_loss_, train_loss, atol=1e-30)
def test_untrained_synthesis_lista(lbda, parametrization, n):
""" Test the gradient of z. """
rng = check_random_state(None)
x, _, _, L, D, A = synthetic_1d_dataset(n=n, s=0.5, snr=0.0, seed=rng)
_, _, z0 = init_vuz(A, D, x)
n_layers = 10
LA = L.dot(A)
step_size = 1.0 / np.linalg.norm(LA, ord=2)**2
lista = LearnTVAlgo(algo_type=parametrization,
A=A,
n_layers=n_layers,
device='cpu')
loss_untrained_lista = [
synthesis_primal_obj(z=z0, A=A, L=L, x=x, lbda=lbda)
]
for n_layer_ in range(1, n_layers + 1):
z_hat = lista.transform(x=x, lbda=lbda, output_layer=n_layer_)
loss_untrained_lista.append(
synthesis_primal_obj(z=z_hat, A=A, L=L, x=x, lbda=lbda))
loss_untrained_lista = np.array(loss_untrained_lista)
params = dict(
grad=lambda z: synthesis_primal_grad(z, A, L, x),
obj=lambda z: synthesis_primal_obj(z, A, L, x, lbda),
prox=lambda z, s: pseudo_soft_th_numpy(z, lbda, s),
x0=z0,
momentum=None,
restarting=None,
max_iter=n_layers,
step_size=step_size,
early_stopping=False,
debug=True,
verbose=0,
)
_, loss_ista = fista(**params)
np.testing.assert_allclose(loss_ista, loss_untrained_lista, atol=1e-20)