def test_mxne_inverse_sure_synthetic(n_sensors, n_dipoles, n_times, nnz, corr,
n_orient, snr=4):
"""Tests SURE criterion for automatic alpha selection on synthetic data."""
rng = np.random.RandomState(0)
sigma = np.sqrt(1 - corr ** 2)
U = rng.randn(n_sensors)
# generate gain matrix
G = np.empty([n_sensors, n_dipoles], order='F')
G[:, :n_orient] = np.expand_dims(U, axis=-1)
n_dip_per_pos = n_dipoles // n_orient
for j in range(1, n_dip_per_pos):
U *= corr
U += sigma * rng.randn(n_sensors)
G[:, j * n_orient:(j + 1) * n_orient] = np.expand_dims(U, axis=-1)
# generate coefficient matrix
support = rng.choice(n_dip_per_pos, nnz, replace=False)
X = np.zeros((n_dipoles, n_times))
for k in support:
X[k * n_orient:(k + 1) * n_orient, :] = rng.normal(
size=(n_orient, n_times))
# generate measurement matrix
M = G @ X
noise = rng.randn(n_sensors, n_times)
sigma = 1 / np.linalg.norm(noise) * np.linalg.norm(M) / snr
M += sigma * noise
# inverse modeling with sure
alpha_max = norm_l2inf(np.dot(G.T, M), n_orient, copy=False)
alpha_grid = np.geomspace(alpha_max, alpha_max / 10, num=15)
_, active_set, _ = _compute_mxne_sure(M, G, alpha_grid, sigma=sigma,
n_mxne_iter=5, maxit=3000, tol=1e-4,
n_orient=n_orient,
active_set_size=10, debias=True,
solver="auto", dgap_freq=10,
random_state=0, verbose=False)
assert np.count_nonzero(active_set, axis=-1) == n_orient * nnz
def apply_solver(evoked, forward, noise_cov, loose=0.2, depth=0.8, K=2000):
all_ch_names = evoked.ch_names
# put the forward solution in fixed orientation if it's not already
if loose is None and not is_fixed_orient(forward):
forward = deepcopy(forward)
forward = mne.convert_forward_solution(forward, force_fixed=True)
gain, gain_info, whitener, source_weighting, mask = _prepare_gain(
forward,
evoked.info,
noise_cov,
pca=False,
depth=depth,
loose=loose,
weights=None,
weights_min=None)
n_locations = gain.shape[1]
sel = [all_ch_names.index(name) for name in gain_info['ch_names']]
M = evoked.data[sel]
# Whiten data
M = np.dot(whitener, M)
n_orient = 1 if is_fixed_orient(forward) else 3
# The value of lambda for which the solution will be all zero
lambda_max = norm_l2inf(np.dot(gain.T, M), n_orient)
lambda_ref = 0.1 * lambda_max
out = mm_mixed_norm_bayes(M,
gain,
lambda_ref,
n_orient=n_orient,
K=K,
return_lpp=True)
(Xs, active_sets), _, _, _, _ = out
solution_support = np.zeros((K, n_locations))
stcs, obj_fun = [], []
for k in range(K):
X = np.zeros((n_locations, Xs[k].shape[1]))
X[active_sets[k]] = Xs[k]
block_norms_new = compute_block_norms(X, n_orient)
block_norms_new = (block_norms_new > 0.05 * block_norms_new.max())
solution_support[k, :] = block_norms_new
stc = _make_sparse_stc(Xs[k],
active_sets[k],
forward,
tmin=0.,
tstep=1. / evoked.info['sfreq'])
stcs.append(stc)
obj_fun.append(
energy_l2half_reg(M, gain, stc.data, active_sets[k], lambda_ref,
n_orient))
return solution_support, stcs, obj_fun
def test_mm_mixed_norm_bayes():
"""Basic test of the mm_mixed_norm_bayes function"""
# First we define the problem size and the location of the active sources.
n_features = 16
n_samples = 24
n_times = 5
X_true = np.zeros((n_features, n_times))
# Active sources at indices 10 and 30
X_true[5, :] = 2.
X_true[10, :] = 2.
# Construction of a covariance matrix
rng = np.random.RandomState(0)
# Set the correlation of each simulated source
corr = [0.6, 0.95]
cov = []
for c in corr:
this_cov = toeplitz(c**np.arange(0, n_features // len(corr)))
cov.append(this_cov)
cov = np.array(linalg.block_diag(*cov))
# Simulation of the design matrix / forward operator
G = rng.multivariate_normal(np.zeros(n_features), cov, size=n_samples)
# Simulation of the data with some noise
M = G.dot(X_true)
M += 0.1 * np.std(M) * rng.randn(n_samples, n_times)
n_orient = 1
# Define the regularization parameter and run the solver
lambda_max = norm_l2inf(np.dot(G.T, M), n_orient)
lambda_ref = 0.3 * lambda_max
K = 10
random_state = 0 # set random seed to make results replicable
out = mm_mixed_norm_bayes(M,
G,
lambda_ref,
n_orient=n_orient,
K=K,
random_state=random_state)
Xs, active_sets = out[:2]
lpp_samples, lppMAP, pobj_l2half = out[2:]
freq_occ = np.mean(active_sets, axis=0)
assert_equal(np.argsort(freq_occ)[-2:], [9, 5])
assert len(Xs) == K
assert lpp_samples.shape == (K, )
assert pobj_l2half.shape == (K, )
assert lppMAP.shape == (K, )
out = mm_mixed_norm_bayes(M,
G,
lambda_ref,
n_orient=n_orient,
K=K,
return_samples=True,
random_state=random_state)
Xs, active_sets = out[:2]
lpp_samples, lppMAP, pobj_l2half = out[2:-2]
X_samples, gamma_samples = out[-2:]
freq_occ = np.mean(active_sets, axis=0)
assert_equal(np.argsort(freq_occ)[-2:], [9, 5])
assert len(Xs) == K
assert lpp_samples.shape == (K, )
assert pobj_l2half.shape == (K, )
assert lppMAP.shape == (K, )
assert X_samples.shape == (K, n_features, n_times, 2)
assert gamma_samples.shape == (K, n_features, 2)
cov = []
for c in corr:
this_cov = toeplitz(c ** np.arange(0, n_features // len(corr)))
cov.append(this_cov)
cov = np.array(linalg.block_diag(*cov))
# Simulation of the design
G = rng.multivariate_normal(np.zeros(n_features), cov, size=n_samples)
# Simulation of the data
M = G.dot(X_true)
M += 0.3 * np.std(M) * rng.randn(n_samples, n_times)
n_orient = 1
# The value of lambda for which the solution will be all zero
lambda_max = norm_l2inf(np.dot(G.T, M), n_orient)
lambda_ref = 0.1 * lambda_max
K = 2000
out = mm_mixed_norm_bayes(
M, G, lambda_ref, n_orient=n_orient, K=K, return_lpp=True)
(Xs, active_sets), lpp_samples, rel_res_samples, block_norm_samples, lppMAP = \
out
freq_occ = np.mean(active_sets, axis=0)
plt.close('all')
# Plot the covariance to see the correlation of the neighboring
# sources around each simulated one (10 and 30).
def get_STFT_R_solution(evoked_list,X, fwd_list0, G_ind, noise_cov,
label_list, GroupWeight_Param,
active_set_z0,
alpha_seq,beta_seq,gamma_seq,
loose= None, depth=0.0, maxit=500, tol=1e-4,
wsize=16, tstep=4, window=0.02,
L2_option = 0, delta_seq = None,
coef_non_zero_mat = None, Z0_l2 = None,
Maxit_J=10, Incre_Group_Numb=50, dual_tol=0.01,
Flag_backtrack = True, L0 = 1.0, eta = 1.5,
Flag_verbose = False,
Flag_nonROI_L2 = False):
'''
Compute the L21 or L2 inverse solution of the stft regression.
If Flag_trial_by_trial == True, use the "trial-by-trial" model for estiamtion,
otherwise, use the simpler model without trial by trial terms
Input:
evoked_list, a list of evoked objects
X, [n_trials, p] design matrix of the regresison
fwd_list0, a list of n_run forward solution object
run_ind, [n_trials, ] run index, starting from zero
noise_cov, the noise covariance matrix
label_list, a list of labels or ROIs.
it can be None, in that case, each individual dipole is
one group, also, GroupWeight_Param becomes invalid,
penalty alpha is applied to every dipole, Flag_nonROI_L2 is
set to False too.
GroupWeight_param, a ratio of weights within ROIs / outside ROIs
Group weights = 1/ n_dipoles in the group, times ratio,
then normalized
active_set_z0, the initial active_set
alpha_seq, tuning sequence for alpha, (the group penalty)
beta_seq, tuning sequence for beta, ( penalty for a single STFT basis function )
loose, depth, the loose and depth paramter for the source space
maxit, the maximum number of iteration
tol, numerical tolerance of the optimizaiton
wsize, window size of the STFT
tstep, time steps of the STFT
window, windowing of the data, just to remove edge effects
L2_option, 0, only compute the L21 solution
1, after computing the L21 solution,
use them as the active set and get an L2 solution.
If delta_seq is provided, run cross validation
to get the best tuning parameter.
2, only compute the L2 solution,
coef_non_zero_mat must not be None for this option,
active_set_z0, active_t_ind must correspond to the active set
delta_seq, the tuning sequence for the L2 solution
if None, a default value will be used.
coef_non_zero_mat, [active_set.sum(), n_coefs*p], boolean matrix, active set
e.g. coef_non_zero_mat = np.abs(Z)>0
Z0_l2, the same size as coef_non_zero_mat, the initial value for L2 problems
verbose, mne-python parameter, level of verbose
Flag_nonROI_L2 = False, if true, all dipoles outside the ROIs are one large group.
Maxit_J, when solving the L21 problem, maximum number of greedy steps to take in the active-set gready method
Incre_Group_Numb: when solving the L21 problem, in the greedy step, each time include this number of first-level groups
dual_tol: when solving the L21 problem,, if the violation of KKT for the greedy method is smaller than this value, stop
depth, 0 to 1, the depth prior defined in the MNE algorithm, it normalizes the forward matrix,
by dividing each column with (np.sum(G**2, axis = 0))**depth, such that deeper source points can
larger influence.
To make it valid, the input forward objects must not have fixed orientation!
Flag_verbose, whether to print the optimization details of solving L21.
Flag_backtrack = True, L0 = 1.0, eta = 1.5, parameters for backtracking
Output:
Z_full, [n_dipoles, n_coefs*p], complex matrix, the regression results
active_set, [n_dipoles,] boolean array, dipole active set
active_t_ind, [n_step,], boolean array, temporal active set, should be a full True vector
stc_list, a list of stc objects, the source solutions
alpha_star, the best alpha
beta_star, the best beta
gamma_star, the best gamma
delta_star, the best delta
'''
# =========================================================================
# some parameters to prepare the forward solution
weights, weights_min, pca=None, None, True
all_ch_names = evoked_list[0].ch_names
info = evoked_list[0].info
n_trials = len(evoked_list)
# put the forward solution in fixed orientation if it's not already
n_runs = len(np.unique(G_ind))
G_list = list()
whitener_list = list()
fwd_list = deepcopy(fwd_list0)
for run_id in range(n_runs):
if loose is None and not is_fixed_orient(fwd_list[run_id]):
# follow the tf_mixed_norm
_to_fixed_ori(fwd_list[run_id])
# mask should be None
gain, gain_info, whitener, source_weighting, mask = _prepare_gain(
fwd_list[run_id], info, noise_cov, pca, depth, loose, weights, weights_min)
G_list.append(gain)
whitener_list.append(whitener)
# to debug
# print np.linalg.norm(G_list[0]-G_list[1])/np.linalg.norm(G_list[0])
# print np.linalg.norm(whitener_list[0]-whitener_list[1])
# the whitener is the same across runs
# apply the window to the data
if window is not None:
for r in range(n_trials):
evoked_list[r] = _window_evoked(evoked_list[r], window)
# prepare the sensor data
sel = [all_ch_names.index(name) for name in gain_info["ch_names"]]
_, n_times = evoked_list[0].data[sel].shape
n_sensors = G_list[0].shape[0]
M = np.zeros([n_sensors, n_times, n_trials], dtype = np.float)
# Whiten data
logger.info('Accessing and Whitening data matrix.')
# deal with SSP
# the projector information should be applied to Y
info = evoked_list[0].info
# all forward solutions must hav ethe same channels,
# if there are bad channels, make sure to remove them for all trials before using this function
fwd_ch_names = [c['ch_name'] for c in fwd_list[0]['info']['chs']]
ch_names = [c['ch_name'] for c in info['chs']
if (c['ch_name'] not in info['bads']
and c['ch_name'] not in noise_cov['bads'])
and (c['ch_name'] in fwd_ch_names
and c['ch_name'] in noise_cov.ch_names)]
# ?? There is no projection in the 0.11 version, should I remove this too
# proj should be None, since the projection should be applied after epoching
proj, _, _ = mne.io.proj.make_projector(info['projs'], ch_names)
for r in range(n_trials):
M[:,:,r] = reduce(np.dot,[whitener,proj, evoked_list[r].data[sel]])
#=========================================================================
# Create group information
src = fwd_list[0]['src']
n_dip_per_pos = 1 if is_fixed_orient(fwd_list[0]) else 3
# number of actual nodes, each node can be associated with 3 dipoles
n_dipoles = G_list[0].shape[1]//n_dip_per_pos
## this function is only for n_dip_per_pos == 1
#if n_dip_per_pos != 1:
# raise ValueError("n_orientation must be 1 for now!")
##
if label_list is None:
nROI = 0
Flag_nonROI_L2 = False
else:
label_ind = list()
for label in label_list:
# get the column index corresponding to the ROI
_, tmp_sel = label_src_vertno_sel(label,src)
label_ind.append(tmp_sel)
nROI = len(label_ind)
DipoleGroup = list()
isinROI = np.zeros(n_dipoles, dtype = np.bool)
if n_dip_per_pos == 1:
for i in range(nROI):
DipoleGroup.append((np.array(label_ind[i])).astype(np.int))
isinROI[label_ind[i]] = True
# dipoles outside the ROIs
notinROI_ind = np.nonzero(isinROI==0)[0]
if Flag_nonROI_L2:
DipoleGroup.append(notinROI_ind.astype(np.int))
else:
for i in range(len(notinROI_ind)):
DipoleGroup.append(np.array([notinROI_ind[i]]))
else:
for i in range(nROI):
tmp_ind = np.array(label_ind[i])
tmp_ind = np.hstack([tmp_ind*3,
tmp_ind*3+1,
tmp_ind*3+2])
DipoleGroup.append(tmp_ind.astype(np.int))
isinROI[tmp_ind] = True
# dipoles outside the ROIs
notinROI_ind = np.nonzero(isinROI==0)[0]
if Flag_nonROI_L2:
DipoleGroup.append(notinROI_ind.astype(np.int))
else:
for i in range(len(notinROI_ind)):
DipoleGroup.append(np.array([3*notinROI_ind[i],
3*notinROI_ind[i]+1,
3*notinROI_ind[i]+2]).astype(np.int))
# Group weights, weighted by number of dipoles in the group
DipoleGroupWeight = 1.0/np.array([len(x) for x in DipoleGroup ])
DipoleGroupWeight[0:nROI] *= GroupWeight_Param
DipoleGroupWeight /= DipoleGroupWeight.sum()
# =========================================================================
# STFT constants
n_step = int(np.ceil(n_times/float(tstep)))
n_freq = wsize// 2+1
n_coefs = n_step*n_freq
p = X.shape[1]
# =========================================================================
# Scaling to make setting of alpha easy, modified from tf_mixed_norm in v0.11
alpha_max = norm_l2inf(np.dot(G_list[0].T, M[:,:,0]),
n_dip_per_pos, copy=False)
alpha_max *= 0.01
for run_id in range(n_runs):
G_list[run_id] /= alpha_max
# mne v0.11 tf_mixed_norm, "gain /= alpha_max source_weighting /= alpha_max"
# so maybe the physcial meaning of source_weighting changed to its inverse
# i.e. G_tilde = G*source_weighting
# for MNE0.8, I used
#source_weighting *= alpha_max
source_weighting /= alpha_max
cv_partition_ind = np.zeros(n_trials)
cv_partition_ind[1::2] = 1
cv_MSE_lasso, cv_MSE_L2 = 0,0
# =========================================================================
if L2_option == 0 or L2_option == 1:
# compute the L21 solution
# setting the initial values, make sure ROIs are in the initial active set
isinROI_ind = np.nonzero(isinROI)[0]
if n_dip_per_pos == 1:
active_set_z0[isinROI_ind] = True
else:
active_set_z0[3*isinROI_ind ] = True
active_set_z0[3*isinROI_ind+1] = True
active_set_z0[3*isinROI_ind+2] = True
active_set_J_ini = np.zeros(len(DipoleGroup), dtype = np.bool)
for l in range(len(DipoleGroup)):
if np.sum(active_set_z0[DipoleGroup[l]]) > 0:
active_set_J_ini[l] = True
# if alpha and beta are sequences, use cross validation to select the best
if len(alpha_seq) > 1 or len(beta_seq) > 1 or len(gamma_seq) >1:
print "select alpha,beta and gamma"
alpha_star, beta_star, gamma_star, cv_MSE_lasso = L21solver.select_alpha_beta_gamma_stft_tree_group_cv_active_set(
M,G_list, G_ind, X,
active_set_J_ini,
DipoleGroup,DipoleGroupWeight,
alpha_seq, beta_seq, gamma_seq, cv_partition_ind,
n_orient=n_dip_per_pos,
wsize=wsize, tstep = tstep,
maxit=maxit, tol = tol,
Maxit_J = Maxit_J, Incre_Group_Numb = Incre_Group_Numb,
dual_tol = dual_tol,
Flag_backtrack = Flag_backtrack, L0 = L0, eta = eta,
Flag_verbose=Flag_verbose)
else:
alpha_star, beta_star, gamma_star = alpha_seq[0], beta_seq[0], gamma_seq[0]
# randomly initialize Z0, make sure the imaginary part is zero
Z0 = np.zeros([active_set_z0.sum(), n_coefs*p])*1j \
+ np.random.randn(active_set_z0.sum(), n_coefs*p)*1E-20
tmp_result = L21solver.solve_stft_regression_tree_group_active_set(
M, G_list, G_ind, X,
alpha_star, beta_star, gamma_star,
DipoleGroup, DipoleGroupWeight,
Z0, active_set_z0,
active_set_J_ini, n_orient=n_dip_per_pos,
wsize=wsize, tstep=tstep, maxit=maxit, tol=tol,
Maxit_J=Maxit_J, Incre_Group_Numb=Incre_Group_Numb,
dual_tol=dual_tol,
Flag_backtrack = Flag_backtrack, L0 = L0, eta = eta,
Flag_verbose=Flag_verbose)
if tmp_result is None:
raise Exception("No active dipoles found. alpha is too big.")
Z = tmp_result['Z']
active_set = tmp_result['active_set']
active_t_ind = np.ones(n_step, dtype = np.bool)
# the following part is copied from tf_mixed_norm in v0.11
if mask is not None:
active_set_tmp = np.zeros(len(mask), dtype=np.bool)
active_set_tmp[mask] = active_set
active_set = active_set_tmp
del active_set_tmp
# =====================================================================
delta_star = None # even if L2_option ==0, we will stil return an empty delta_star
#re-run the regression with a given active set
if L2_option == 1 or L2_option == 2:
# if only L2 solution is needed, do some initialization,
if L2_option == 2:
if coef_non_zero_mat is None:
raise ValueError("if L2_option == 2, coef_non_zero_mat must not be empty!")
active_set= active_set_z0.copy()
active_t_ind = np.ones(n_step, dtype = np.bool)
if Z0_l2 is None:
# make sure the imaginary part is zero
Z = np.zeros([active_set_z0.sum(), n_coefs*p])*1j \
+ np.random.randn(active_set_z0.sum(), n_coefs*p)*1E-20
else:
Z = Z0_l2
alpha_star, beta_star, gamma_star = None, None, None
if L2_option == 1:
coef_non_zero_mat = np.abs(Z)>0
if delta_seq is None:
delta_seq = np.array([1E-12,1E-10,1E-8])
if len(delta_seq) > 1:
Z0 = Z.copy()
Z0 = Z0[:, np.tile(active_t_ind,p*n_freq)]
delta_star, cv_MSE_L2 = L2solver.select_delta_stft_regression_cv(M,G_list, G_ind, X,
Z0, active_set, active_t_ind,
coef_non_zero_mat,
delta_seq,cv_partition_ind,
wsize=wsize, tstep = tstep,
maxit=maxit, tol = tol,
Flag_backtrack = Flag_backtrack, L0 = L0, eta = eta,
Flag_verbose = Flag_verbose)
else:
delta_star = delta_seq[0]
# L2 optimization
Z, obj = L2solver.solve_stft_regression_L2_tsparse(M,G_list, G_ind, X, Z, active_set,
active_t_ind, coef_non_zero_mat,
wsize=wsize, tstep = tstep, delta = delta_star,
maxit=maxit, tol = tol,
Flag_backtrack = Flag_backtrack, L0 = L0, eta = eta,
Flag_verbose = Flag_verbose)
# =========================================================================
# reweighting should be done after the debiasing!!!
# Reapply weights to have correct unit, To Be modifiled
# it seems that in MNE0.11, source_weighting is the inverse of the original source weighting
# MNE 0.8 (verified in their 0.81 code "X /= source_weighting[active_set][:, None]")
#Z /= source_weighting[active_set][:, None]
# MNE 0.11
Z = _reapply_source_weighting(Z, source_weighting, active_set, n_dip_per_pos)
Z_full = np.zeros([active_set.sum(),p, n_freq, n_step], dtype = np.complex)
Z_full[:,:,:,active_t_ind] = np.reshape(Z,[active_set.sum(), p,
n_freq,active_t_ind.sum()])
Z_full = np.reshape(Z_full, [active_set.sum(),-1])
# do not compute stc_list
# tmin = evoked_list[0].times[0]
# stc_tstep = 1.0 / info['sfreq']
# stc_list = list()
# for r in range(n_trials):
# tmp_stc_data = np.zeros([active_set.sum(),n_times])
# tmp_Z = np.zeros([active_set.sum(), n_coefs],dtype = np.complex)
# for i in range(p):
# tmp_Z += Z_full[:,i*n_coefs:(i+1)*n_coefs]* X[r,i]
# # if it is a trial by_trial model, add the model for the single trial
# tmp_stc_data = phiT(tmp_Z)
# tmp_stc = _make_sparse_stc(tmp_stc_data, active_set, fwd_list[G_ind[r]], tmin, stc_tstep)
# stc_list.append(tmp_stc)
# logger.info('[done]')
return Z_full, active_set, active_t_ind, alpha_star, beta_star, gamma_star, delta_star, cv_MSE_lasso, cv_MSE_L2
