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 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 record_loss(n_layers, algo):
u_train = algo.transform_to_u(x_train, lmbd)
u_test = algo.transform_to_u(x_test, lmbd)
if isinstance(algo, ListaTV):
prox_tv_loss_train = compute_prox_tv_errors(algo, x_train, lmbd)
prox_tv_loss_test = compute_prox_tv_errors(algo, x_test, lmbd)
else:
prox_tv_loss_train = prox_tv_loss_test = None
log.append(dict(
key=key, **meta, lmbd=lmbd, extra_args=extra_args,
n_layers=n_layers,
train_loss=analysis_primal_obj(u_train, A, D, x_train, lmbd),
test_loss=analysis_primal_obj(u_test, A, D, x_test, lmbd),
prox_tv_loss_train=prox_tv_loss_train,
prox_tv_loss_test=prox_tv_loss_test
))
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_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_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
_, 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 f(u):
u = u.reshape(n, n_atoms)
# the actual considered loss is not normalized but for
# convenience we want to check the sample-loss average
return analysis_primal_obj(u, A, D, x, lbda=lbda) * n
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 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
