def get_signals(n_channels=50, n_times_atom=64, n_times_valid=640,
sigma=.01, random_state=None):
"""Generate a signal following the sparse linear model with a rank1
triangle and square atoms and a Bernoulli-uniform distribution."""
n_atoms = 2
rng = np.random.RandomState(random_state)
v0 = get_atoms('triangle', n_times_atom) # temporal atoms
v1 = get_atoms('square', n_times_atom)
u0 = get_atoms('sin', n_channels) # spatial maps
u1 = get_atoms('cos', n_channels)
u0[0] = u1[0] = 1
uv = np.array([np.r_[u0, v0], np.r_[u1, v1]])
uv = prox_uv(uv, 'separate', n_channels)
# add atoms
z = np.array([sparse.random(n_atoms, n_times_valid, density=.05,
random_state=random_state).toarray()
for _ in range(n_trials)])
z = np.swapaxes(z, 0, 1)
X = construct_X_multi(z, uv, n_channels=n_channels)
X = X + sigma * rng.randn(*X.shape)
uv_init = rng.randn(n_atoms, n_channels + n_times_atom)
uv_init = prox_uv(uv_init, uv_constraint='separate', n_channels=n_channels)
return X, uv, uv_init
def test_update_uv(solver_d, uv_constraint):
# Generate synchronous D
n_times_atom, n_times = 10, 100
n_channels = 5
n_atoms = 2
n_trials = 3
rng = np.random.RandomState()
z = rng.normal(size=(n_trials, n_atoms, n_times - n_times_atom + 1))
uv0 = rng.normal(size=(n_atoms, n_channels + n_times_atom))
uv1 = rng.normal(size=(n_atoms, n_channels + n_times_atom))
uv0 = prox_uv(uv0)
uv1 = prox_uv(uv1)
X = construct_X_multi(z, D=uv0, n_channels=n_channels)
def objective(uv):
X_hat = construct_X_multi(z, D=uv, n_channels=n_channels)
return compute_objective(X, X_hat, loss='l2')
# Ensure that the known optimal point is stable
uv = update_uv(X, z, uv0, max_iter=1000, verbose=0)
cost = objective(uv)
assert np.isclose(cost, 0), "optimal point not stable"
assert np.allclose(uv, uv0), "optimal point not stable"
# Ensure that the update is going down from a random initialization
cost0 = objective(uv1)
uv, pobj = update_uv(X,
z,
uv1,
debug=True,
max_iter=5000,
verbose=10,
solver_d=solver_d,
momentum=False,
eps=1e-10,
uv_constraint=uv_constraint)
cost1 = objective(uv)
msg = "Learning is not going down"
try:
assert cost1 < cost0, msg
# assert np.isclose(cost1, 0, atol=1e-7)
except AssertionError:
import matplotlib.pyplot as plt
pobj = np.array(pobj)
plt.semilogy(pobj)
plt.title(msg)
plt.show()
raise
def run_one(reg, sigma, n_atoms, n_times_atom, max_n_channels, n_times_valid,
n_iter, run_n_channels, random_state):
"""Run the benchmark for a given set of parameter."""
X, uv, uv_init = get_signals(max_n_channels, n_times_atom, n_times_valid,
sigma, random_state)
reg_ = reg * get_lambda_max(X, uv_init).max()
# reg_ *= run_n_channels
uv_init_ = prox_uv(np.c_[uv_init[:, :run_n_channels],
uv_init[:, max_n_channels:]])
uv_ = prox_uv(np.c_[uv[:, :run_n_channels], uv[:, max_n_channels:]],
uv_constraint='separate',
n_channels=max_n_channels)
def cb(X, uv_hat, z_hat, pobj):
it = len(pobj) // 2
if it % 10 == 0:
print("[channels{}] iter{} score sig={:.2e}: {:.3e}".format(
run_n_channels, it, sigma, score_uv(uv_, uv_hat,
run_n_channels)))
pobj, times, uv_hat, z_hat, reg = learn_d_z_multi(
X[:, :run_n_channels, :],
n_atoms,
n_times_atom,
random_state=random_state,
# callback=cb,
n_iter=n_iter,
n_jobs=1,
reg=reg_,
uv_constraint='separate',
solver_d='alternate_adaptive',
solver_d_kwargs={'max_iter': 50},
solver_z="lgcd",
solver_z_kwargs=dict(tol=1e-3, maxiter=500),
use_sparse_z=True,
D_init=uv_init_,
verbose=VERBOSE,
)
score = score_uv(uv_, uv_hat, run_n_channels)
print("=" * 79 + "\n" +
"[channels{}-{:.2e}-{}] iter {} score sig={:.2e}: {:.3e}\n".format(
run_n_channels, reg, random_state,
len(pobj) // 2, sigma, score) + "=" * 79)
return random_state, sigma, run_n_channels, score, uv, uv_hat, reg
def test_uv_D():
rng = check_random_state(42)
n_times_atoms = 21
n_atoms = 15
n_channels = 30
uv = rng.randn(n_atoms, n_channels + n_times_atoms)
uv = prox_uv(uv, uv_constraint='separate', n_channels=n_channels)
ds = get_D(uv, n_channels)
uv_hat = get_uv(ds)
assert_allclose(abs(uv / uv_hat), 1)
