def test_iterative_reweighted_mxne():
"""Test convergence of irMxNE solver"""
n, p, t, alpha = 30, 40, 20, 1
rng = np.random.RandomState(0)
G = rng.randn(n, p)
G /= np.std(G, axis=0)[None, :]
X = np.zeros((p, t))
X[0] = 3
X[4] = -2
M = np.dot(G, X)
X_hat_l21, _, _ = mixed_norm_solver(
M, G, alpha, maxit=1000, tol=1e-8, verbose=False, n_orient=1,
active_set_size=None, debias=False, solver='bcd')
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='bcd')
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='prox')
assert_allclose(X_hat_bcd, X_hat_l21, rtol=1e-3)
assert_allclose(X_hat_prox, X_hat_l21, rtol=1e-3)
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 4])
assert_array_almost_equal(X_hat_prox, X_hat_cd, 5)
assert_array_almost_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
# suppress a coordinate-descent warning here
with warnings.catch_warnings(record=True):
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2, debias=True,
n_orient=5)
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
with warnings.catch_warnings(record=True): # coordinate-ascent warning
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=5, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
def test_iterative_reweighted_mxne():
"""Test convergence of irMxNE solver"""
n, p, t, alpha = 30, 40, 20, 1
rng = np.random.RandomState(0)
G = rng.randn(n, p)
G /= np.std(G, axis=0)[None, :]
X = np.zeros((p, t))
X[0] = 3
X[4] = -2
M = np.dot(G, X)
X_hat_l21, _, _ = mixed_norm_solver(
M, G, alpha, maxit=1000, tol=1e-8, verbose=False, n_orient=1,
active_set_size=None, debias=False, solver='bcd')
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='bcd')
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 1, maxit=1000, tol=1e-8, active_set_size=None,
debias=False, solver='prox')
assert_allclose(X_hat_bcd, X_hat_l21, rtol=1e-3)
assert_allclose(X_hat_prox, X_hat_l21, rtol=1e-3)
X_hat_prox, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='prox')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 4])
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=None,
debias=True, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 4])
assert_array_almost_equal(X_hat_prox, X_hat_cd, 5)
assert_array_almost_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='bcd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
# suppress a coordinate-descent warning here
with warnings.catch_warnings(record=True):
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=2, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 4, 5])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
X_hat_bcd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2, debias=True,
n_orient=5)
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
with warnings.catch_warnings(record=True): # coordinate-ascent warning
X_hat_cd, active_set, _ = iterative_mixed_norm_solver(
M, G, alpha, 5, maxit=1000, tol=1e-8, active_set_size=2,
debias=True, n_orient=5, solver='cd')
assert_array_equal(np.where(active_set)[0], [0, 1, 2, 3, 4])
assert_array_equal(X_hat_bcd, X_hat_cd, 5)
plt.title("Feature covariance")
###############################################################################
# Simulation of the data with some noise
M = G.dot(X_true)
M += 0.2 * np.max(np.abs(M)) * rng.randn(n_samples, n_times)
###############################################################################
# Define the regularization parameter and run the MM solver
# ---------------------------------------------------------
lambda_max = np.max(np.linalg.norm(np.dot(G.T, M), axis=1))
lambda_ref = lambda_percent / 100. * lambda_max
X_mm, active_set_mm, E = \
iterative_mixed_norm_solver(M, G, lambda_ref, n_mxne_iter=10)
pobj_l2half_X_mm = E[-1]
print("Found support: %s" % np.where(active_set_mm)[0])
###############################################################################
# Run the solver
# --------------
Xs, active_sets, lpp_samples, lpp_Xs, pobj_l2half_Xs = \
mm_mixed_norm_bayes(M, G, lambda_ref, K=K)
# Plot if we found better local minima then the first result found be the
plt.figure()
plt.hist(pobj_l2half_Xs, bins=20, label="Modes obj.")
