def analysis_dual_iter_algo(x_train, x_test, A, D, L, lbda, all_n_layers,
type_, max_iter=300, device=None,
net_kwargs=None, verbose=1):
""" Chambolle solver for analysis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
Psi_A = np.linalg.pinv(A).dot(D)
inv_AtA = np.linalg.pinv(A.dot(A.T))
def _grad(v, x):
return analysis_dual_grad(v, A, D, x, Psi_A=Psi_A)
def _obj(v, x):
v = np.atleast_2d(v)
u = v_to_u(v, x, A=A, D=D, inv_AtA=inv_AtA)
return analysis_primal_obj(u, A, D, x, lbda)
def _prox(v, step_size):
# XXX step_size is here to homogenize API
v = np.atleast_2d(v)
return np.clip(v, -lbda, lbda)
v0_test, _, _ = init_vuz(A, D, x_test)
v0_train, _, _ = init_vuz(A, D, x_train)
max_iter = all_n_layers[-1]
step_size = 1.0 / np.linalg.norm(Psi_A, ord=2) ** 2
momentum = None if type_ == 'ista' else 'fista'
name = 'ISTA' if type_ == 'ista' else 'FISTA'
print("[ISTA iterative] training loss")
params = dict(
grad=lambda v: _grad(v, x_train),
obj=lambda v: _obj(v, x_train), prox=_prox,
x0=v0_train, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose,
)
_, train_loss = fista(**params)
print("[ISTA iterative] testing loss")
params = dict(
grad=lambda v: _grad(v, x_test),
obj=lambda v: _obj(v, x_test), prox=_prox,
x0=v0_test, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose
)
_, test_loss = fista(**params)
train_loss = train_loss[[0] + all_n_layers]
test_loss = test_loss[[0] + all_n_layers]
print(f"\r[{name}] iterations finished train-loss={train_loss[-1]:.6e} "
f"test-loss={test_loss[-1]:.6e}")
return train_loss, test_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 _get_init(self, x, lbda, force_numpy=False):
x0, u0, _ = init_vuz(self.net_solver.A,
self.net_solver.D, x, lbda)
if force_numpy:
return np.array(x0), np.array(u0)
else:
return x0, u0
def forward(self, x, lbda, output_layer=None):
""" Forward pass of the network. """
output_layer = self.check_output_layer(output_layer)
# initialized variables
_, u, _ = init_vuz(self.A,
self.D,
x,
lbda,
inv_A=self.inv_A_,
device=self.device)
for layer_id in range(output_layer):
layer_params = self.parameter_groups[f'layer-{layer_id}']
# retrieve parameters
h = layer_params['h']
hth = layer_params['hth']
mul_lbda = layer_params.get('threshold', 1.0 / self.l_)
mul_lbda = check_tensor(mul_lbda, device=self.device)
# apply one 'iteration'
u = hth_id_u_tensor(hth, u) + htx_tensor(h, x)
u = ProxTV_l1.apply(u, lbda * mul_lbda)
return u
def analysis_primal_dual_iter_algo(x_train, x_test, A, D, L, lbda,
all_n_layers, type_, max_iter=300,
device=None, net_kwargs=None, verbose=1):
""" Condat-Vu solver for analysis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
max_iter = all_n_layers[-1]
rho = 1.0
sigma = 0.5
L_A = np.linalg.norm(A, ord=2) ** 2
L_D = np.linalg.norm(D, ord=2) ** 2
tau = 1.0 / (L_A / 2.0 + sigma * L_D)
v0_test, u0_test, _ = init_vuz(A, D, x_test, force_numpy=True)
v0_train, u0_train, _ = init_vuz(A, D, x_train, force_numpy=True)
if verbose > 0:
print("[Condat-Vu iterative] training loss")
params = dict(
grad=lambda u: analysis_primal_grad(u, A, x_train),
obj=lambda u: analysis_primal_obj(u, A, D, x_train, lbda),
prox=lambda t: _soft_th_numpy(t, lbda / sigma),
psi=lambda u: u.dot(D), adj_psi=lambda v: v.dot(D.T),
v0=v0_train, z0=u0_train, lbda=lbda, sigma=sigma, tau=tau, rho=rho,
max_iter=max_iter, early_stopping=False, debug=True, verbose=verbose,
)
_, _, train_loss = condatvu(**params)
if verbose > 0:
print("[Condat-Vu iterative] testing loss")
params = dict(
grad=lambda u: analysis_primal_grad(u, A, x_test),
obj=lambda u: analysis_primal_obj(u, A, D, x_test, lbda),
prox=lambda t: _soft_th_numpy(t, lbda / sigma),
psi=lambda u: u.dot(D), adj_psi=lambda v: v.dot(D.T),
v0=v0_test, z0=u0_test, lbda=lbda, sigma=sigma, tau=tau, rho=rho,
max_iter=max_iter, early_stopping=False, debug=True, verbose=verbose,
)
_, _, test_loss = condatvu(**params)
train_loss = train_loss[[0] + all_n_layers]
test_loss = test_loss[[0] + all_n_layers]
if verbose > 0:
print(f"\r[Condat-Vu] iterations finished "
f"train-loss={train_loss[-1]:.4e} test-loss={test_loss[-1]:.4e}")
return train_loss, test_loss
def synthesis_iter_algo(x_train, x_test, A, D, L, lbda, all_n_layers, type_,
max_iter=300, device=None, net_kwargs=None,
verbose=1):
""" Iterative-algo solver for synthesis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
name = 'ISTA' if type_ == 'chambolle' else 'FISTA'
max_iter = all_n_layers[-1]
LA = L.dot(A)
step_size = 1.0 / np.linalg.norm(LA, ord=2) ** 2
_, _, z0_test = init_vuz(A, D, x_test)
_, _, z0_train = init_vuz(A, D, x_train)
momentum = None if type_ == 'ista' else type_
if verbose > 0:
print("[ISTA iterative] training loss")
params = dict(
grad=lambda z: synthesis_primal_grad(z, A, L, x_train),
obj=lambda z: synthesis_primal_obj(z, A, L, x_train, lbda),
prox=lambda z, s: pseudo_soft_th_numpy(z, lbda, s),
x0=z0_train, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose,
)
_, train_loss = fista(**params)
if verbose > 0:
print("[ISTA iterative] testing loss")
params = dict(
grad=lambda z: synthesis_primal_grad(z, A, L, x_test),
obj=lambda z: synthesis_primal_obj(z, A, L, x_test, lbda),
prox=lambda z, s: pseudo_soft_th_numpy(z, lbda, s),
x0=z0_test, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose,
)
_, test_loss = fista(**params)
train_loss = train_loss[[0] + all_n_layers]
test_loss = test_loss[[0] + all_n_layers]
if verbose > 0:
print(f"[{name}] iterations finished "
f"train-loss={train_loss[-1]:.4e} test-loss={test_loss[-1]:.4e}")
return train_loss, test_loss
def analysis_primal_iter_algo(x_train, x_test, A, D, L, lbda, all_n_layers,
type_, max_iter=300, device=None,
net_kwargs=None, verbose=1):
""" Iterative-algo solver for synthesis TV problem. """
net_kwargs = dict() if net_kwargs is None else net_kwargs
name = 'ISTA' if type_ == 'ista' else 'FISTA'
max_iter = all_n_layers[-1]
step_size = 1.0 / np.linalg.norm(A, ord=2) ** 2
_, u0_test, _ = init_vuz(A, D, x_test)
_, u0_train, _ = init_vuz(A, D, x_train)
momentum = None if type_ == 'ista' else type_
if verbose > 0:
print(f"[analysis {name} iterative] training loss")
params = dict(
grad=lambda z: analysis_primal_grad(z, A, x_train),
obj=lambda z: analysis_primal_obj(z, A, D, x_train, lbda),
prox=lambda z, s: np.array([tv1_1d(z_, lbda * s) for z_ in z]),
x0=u0_train, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose,
)
_, train_loss = fista(**params)
if verbose > 0:
print(f"[analysis {name} iterative] testing loss")
params = dict(
grad=lambda z: analysis_primal_grad(z, A, x_test),
obj=lambda z: analysis_primal_obj(z, A, D, x_test, lbda),
prox=lambda z, s: np.array([tv1_1d(z_, lbda * s) for z_ in z]),
x0=u0_test, momentum=momentum, restarting=None,
max_iter=max_iter, step_size=step_size, early_stopping=False,
debug=True, verbose=verbose,
)
_, test_loss = fista(**params)
train_loss = train_loss[[0] + all_n_layers]
test_loss = test_loss[[0] + all_n_layers]
if verbose > 0:
print(f"\r[{name}] iterations finished "
f"train-loss={train_loss[-1]:.6e} test-loss={test_loss[-1]:.6e}")
return train_loss, test_loss
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_init(lbda, seed):
rng = check_random_state(seed)
x, _, _, L, D, A = synthetic_1d_dataset()
v0 = None
v0, u0, z0 = init_vuz(A, D, x, v0=v0)
cost_1 = synthesis_primal_obj(z0, A, L, x, lbda)
cost_2 = analysis_primal_obj(u0, A, D, x, lbda)
cost_3 = analysis_primal_obj(v_to_u(v0, x, A, D), A, D, x, lbda)
np.testing.assert_allclose(cost_1, cost_2)
np.testing.assert_allclose(cost_1, cost_3)
v0 = rng.randn(*v0.shape)
v0, u0, z0 = init_vuz(A, D, x, v0=v0)
synthesis_primal_obj(z0, A, L, x, lbda)
cost_1 = synthesis_primal_obj(z0, A, L, x, lbda)
cost_2 = analysis_primal_obj(u0, A, D, x, lbda)
cost_3 = analysis_primal_obj(v_to_u(v0, x, A, D), A, D, x, lbda)
np.testing.assert_allclose(cost_1, cost_2)
np.testing.assert_allclose(cost_1, cost_3)
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 transform(self, x, lbda, output_layer=None):
if output_layer is None:
output_layer = self.n_layers
_, _, z0 = init_vuz(self.A, self.D, x)
params = dict(
grad=lambda z: synthesis_primal_grad(z, self.A, self.L, x),
obj=lambda z: synthesis_primal_obj(z, self.A, self.L, x, lbda),
prox=lambda z, mu: pseudo_soft_th_numpy(z, lbda, mu),
x0=z0,
momentum=self.momentum,
step_size=self.step_size,
restarting=None,
max_iter=output_layer,
early_stopping=False,
debug=True,
verbose=self.verbose)
return fista(**params)[0]
def transform(self, x, lbda, output_layer=None):
if output_layer is None:
output_layer = self.n_layers
_, u0, _ = init_vuz(self.A, self.D, x)
params = dict(
grad=lambda z: analysis_primal_grad(z, self.A, x),
obj=lambda z: analysis_primal_obj(z, self.A, self.D, x, lbda),
prox=lambda z, s: np.array([tv1_1d(z_, lbda * s) for z_ in z]),
x0=u0,
momentum=self.momentum,
step_size=self.step_size,
restarting=None,
max_iter=output_layer,
early_stopping=False,
debug=True,
verbose=self.verbose,
)
return fista(**params)[0]
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)
h=h,
n_times_valid=n_times_valid,
name='Iterative-z',
max_iter_z=int(args.iter_mult * args.max_iter_z),
solver_type='fista-z-step',
verbose=1)
ta_iter = TA(**params)
t0 = time.time()
_, _, _ = ta_iter.prox_t(y_test, args.temp_reg)
print(f"ta_iterative.prox_t finished : {time.time() - t0:.2f}s")
loss_ta_iter = ta_iter.l_loss_prox_t
n_samples = nx * ny * nz
y_test_ravel = y_test.reshape(n_samples, args.n_time_frames)
_, u0, _ = init_vuz(H, D, y_test_ravel, args.temp_reg)
loss_ta_learn = [_obj_t_analysis(u0, y_test_ravel, h, args.temp_reg)]
init_net_params = None
params = dict(t_r=t_r,
h=h,
n_times_valid=n_times_valid,
net_solver_training_type='recursive',
name='Learned-z',
solver_type='learn-z-step',
verbose=1,
max_iter_training_net=args.max_training_iter)
for i, n_layers in enumerate(all_layers):
params['max_iter_z'] = n_layers