def test_max_beta(self):
beta = .8
gamma = 7.5
m = 0
J = 25
K = 2
M = 51
data = self.data_simu
graph = data.get_graph()
q_Z = np.zeros((M, K, J), dtype=np.float64)
neighbours_indexes = vt.create_neighbours(graph)
beta = vt.beta_maximization(beta, q_Z, neighbours_indexes, gamma)
def test_gradient(self):
beta = .8
gamma = 7.5
m = 0
J = 25
K = 2
M = 51
data = self.data_simu
graph = data.get_graph()
q_Z = np.zeros((M, K, J), dtype=np.float64)
neighbours_indexes = vt.create_neighbours(graph)
labels_neigh = vt.sum_over_neighbours(neighbours_indexes, q_Z)
Gr = vt.beta_gradient(beta, q_Z, labels_neigh, neighbours_indexes, gamma)
def test_free_energy(self):
""" Test of vem tool to compute free energy """
M = 51
D = 3
N = 325
J = 25
K = 2
TR = 1.
Thrf = 25.
dt = .5
gamma_h = 1000
data = self.data_simu
Y = data.bold
graph = data.get_graph()
onsets = data.paradigm.get_joined_onsets()
durations = data.paradigm.stimDurations
P = vt.PolyMat(N, 4, TR)
L = vt.polyFit(Y, TR, 4, P)
y_tilde = Y - np.dot(P, L)
TT, m_h = getCanoHRF(Thrf, dt)
order = 2
D2 = vt.buildFiniteDiffMatrix(order, D)
R = np.dot(D2, D2) / pow(dt, 2*order)
invR = np.linalg.inv(R)
Det_invR = np.linalg.det(invR)
q_Z = 0.5 * np.ones((M, K, J), dtype=np.float64)
neighbours_indexes = vt.create_neighbours(graph)
Beta = np.ones((M), dtype=np.float64)
sigma_epsilone = np.ones(J)
_, occurence_matrix, _ = vt.create_conditions(onsets, durations, M, N, D, TR, dt)
Gamma = np.identity(N)
Det_Gamma = np.linalg.det(Gamma)
XGamma = np.zeros((M, D, N), dtype=np.float64)
m_A = np.zeros((J, M), dtype=np.float64)
Sigma_A = np.zeros((M, M, J), np.float64)
mu_M = np.zeros((M, K), dtype=np.float64)
sigma_M = np.ones((M, K), dtype=np.float64)
m_H = np.array(m_h[:D]).astype(np.float64)
Sigma_H = np.ones((D, D), dtype=np.float64)
free_energy = vt.free_energy_computation(m_A, Sigma_A, m_H, Sigma_H, D,
q_Z, y_tilde, occurence_matrix,
sigma_epsilone, Gamma, M, J, N,
K, mu_M, sigma_M, neighbours_indexes,
Beta, Sigma_H, np.linalg.inv(R),
R, Det_Gamma, gamma_h)
def test_expectZ(self):
M = 51
J = 25
K = 2
data = self.data_simu
graph = data.get_graph()
m_A = np.zeros((J, M), dtype=np.float64)
Sigma_A = np.zeros((M, M, J), np.float64)
mu_M = np.zeros((M, K), dtype=np.float64)
sigma_M = np.ones((M, K), dtype=np.float64)
beta = .8
Beta = beta * np.ones((M), dtype=np.float64)
q_Z = np.zeros((M, K, J), dtype=np.float64)
Z_tilde = q_Z.copy()
zerosK = np.zeros(K)
neighbours_indexes = vt.create_neighbours(graph)
q_Z = vt.labels_expectation(Sigma_A, m_A, sigma_M, mu_M, Beta, q_Z,
neighbours_indexes, M, K)
def Main_vbjde_physio(graph, Y, Onsets, durations, Thrf, K, TR, beta, dt,
scale=1, estimateSigmaH=True, estimateSigmaG=True,
sigmaH=0.05, sigmaG=0.05, gamma_h=0, gamma_g=0,
NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False,
contrasts=[], computeContrast=False,
idx_first_tag=0, simulation=None, sigmaMu=None,
estimateH=True, estimateG=True, estimateA=True,
estimateC=True, estimateZ=True, estimateNoise=True,
estimateMP=True, estimateLA=True, use_hyperprior=False,
positivity=False, constraint=False,
phy_params=PHY_PARAMS_KHALIDOV11, prior='omega', zc=False):
logger.info("EM for ASL!")
np.random.seed(6537540)
logger.info("data shape: ")
logger.info(Y.shape)
Thresh = 1e-5
D, M = np.int(np.ceil(Thrf / dt)) + 1, len(Onsets)
#D, M = np.int(np.ceil(Thrf / dt)), len(Onsets)
N, J = Y.shape[0], Y.shape[1]
Crit_AH, Crit_CG, cTime, rerror, FE = 1, 1, [], [], []
EP, EPlh, Ent = [],[],[]
Crit_H, Crit_G, Crit_Z, Crit_A, Crit_C = 1, 1, 1, 1, 1
cAH, cCG, AH1, CG1 = [], [], [], []
cA, cC, cH, cG, cZ = [], [], [], [], []
h_norm, g_norm = [], []
SUM_q_Z = [[] for m in xrange(M)]
mua1 = [[] for m in xrange(M)]
muc1 = [[] for m in xrange(M)]
# Beta data
MaxItGrad = 200
gradientStep = 0.005
gamma = 7.5
maxNeighbours, neighboursIndexes = vt.create_neighbours(graph, J)
# Control-tag
w = np.ones((N))
w[idx_first_tag + 1::2] = -1
W = np.diag(w)
# Conditions
X, XX, condition_names = vt.create_conditions_block(Onsets, durations, M, N, D, TR, dt)
#X, XX, condition_names = vt.create_conditions(Onsets, M, N, D, TR, dt)
if zc:
XX = XX[:, :, 1:-1] # XX shape (S, M, N, D)
D = D - 2
AH1, CG1 = np.zeros((J, M, D)), np.zeros((J, M, D))
# Covariance matrix
#R = vt.covariance_matrix(2, D, dt)
_, R_inv = genGaussianSmoothHRF(False, D, dt, 1., 2)
R = np.linalg.inv(R_inv)
# Noise matrix
Gamma = np.identity(N)
# Noise initialization
sigma_eps = np.ones(J)
# Labels
logger.info("Labels are initialized by setting active probabilities "
"to ones ...")
q_Z = np.ones((M, K, J), dtype=np.float64) / 2.
#q_Z = np.zeros((M, K, J), dtype=np.float64)
#q_Z[:, 1, :] = 1
q_Z1 = copy.deepcopy(q_Z)
Z_tilde = copy.deepcopy(q_Z)
# H and G
TT, m_h = getCanoHRF(Thrf, dt)
H = np.array(m_h[1:D+1]).astype(np.float64)
H /= np.linalg.norm(H)
G = copy.deepcopy(H)
Hb = create_physio_brf(phy_params, response_dt=dt, response_duration=Thrf)
Hb /= np.linalg.norm(Hb)
Gb = create_physio_prf(phy_params, response_dt=dt, response_duration=Thrf)
Gb /= np.linalg.norm(Gb)
if prior=='balloon':
H = Hb.copy()
G = Gb.copy()
Mu = Hb.copy()
H1 = copy.deepcopy(H)
Sigma_H = np.zeros((D, D), dtype=np.float64)
G1 = copy.deepcopy(G)
Sigma_G = copy.deepcopy(Sigma_H)
normOh = False
normg = False
if prior=='hierarchical' or prior=='omega':
Omega = linear_rf_operator(len(H), phy_params, dt, calculating_brf=False)
if prior=='omega':
Omega0 = Omega.copy()
OmegaH = np.dot(Omega, H)
G = np.dot(Omega, H)
if normOh or normg:
Omega /= np.linalg.norm(OmegaH)
OmegaH /=np.linalg.norm(OmegaH)
G /= np.linalg.norm(G)
# Initialize model parameters
Beta = beta * np.ones((M), dtype=np.float64)
P = vt.PolyMat(N, 4, TR)
L = vt.polyFit(Y, TR, 4, P)
alpha = np.zeros((J), dtype=np.float64)
WP = np.append(w[:, np.newaxis], P, axis=1)
AL = np.append(alpha[np.newaxis, :], L, axis=0)
y_tilde = Y - WP.dot(AL)
# Parameters Gaussian mixtures
mu_Ma = np.append(np.zeros((M, 1)), np.ones((M, 1)), axis=1).astype(np.float64)
mu_Mc = mu_Ma.copy()
sigma_Ma = np.ones((M, K), dtype=np.float64) * 0.3
sigma_Mc = sigma_Ma.copy()
# Params RLs
m_A = np.zeros((J, M), dtype=np.float64)
for j in xrange(0, J):
m_A[j, :] = (np.random.normal(mu_Ma, np.sqrt(sigma_Ma)) * q_Z[:, :, j]).sum(axis=1).T
m_A1 = m_A.copy()
Sigma_A = np.ones((M, M, J)) * np.identity(M)[:, :, np.newaxis]
m_C = m_A.copy()
m_C1 = m_C.copy()
Sigma_C = Sigma_A.copy()
# Precomputations
WX = W.dot(XX).transpose(1, 0, 2)
Gamma_X = np.tensordot(Gamma, XX, axes=(1, 1))
X_Gamma_X = np.tensordot(XX.T, Gamma_X, axes=(1, 0)) # shape (D, M, M, D)
Gamma_WX = np.tensordot(Gamma, WX, axes=(1, 1))
XW_Gamma_WX = np.tensordot(WX.T, Gamma_WX, axes=(1, 0)) # shape (D, M, M, D)
Gamma_WP = Gamma.dot(WP)
WP_Gamma_WP = WP.T.dot(Gamma_WP)
sigma_eps_m = np.maximum(sigma_eps, eps)
cov_noise = sigma_eps_m[:, np.newaxis, np.newaxis]
###########################################################################
############################################# VBJDE
t1 = time.time()
ni = 0
#while ((ni < NitMin + 1) or (((Crit_AH > Thresh) or (Crit_CG > Thresh)) \
# and (ni < NitMax))):
#while ((ni < NitMin + 1) or (((Crit_AH > Thresh)) \
# and (ni < NitMax))):
while ((ni < NitMin + 1) or (((Crit_FE > Thresh * np.ones_like(Crit_FE)).any()) \
and (ni < NitMax))):
logger.info("-------- Iteration n° " + str(ni + 1) + " --------")
if PLOT and ni >= 0: # Plotting HRF and PRF
logger.info("Plotting HRF and PRF for current iteration")
vt.plot_response_functions_it(ni, NitMin, M, H, G, Mu, prior)
# Managing types of prior
priorH_cov_term = np.zeros_like(R_inv)
priorG_cov_term = np.zeros_like(R_inv)
matrix_covH = R_inv.copy()
matrix_covG = R_inv.copy()
if prior=='balloon':
logger.info(" prior balloon")
#matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1])
#matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1])
priorH_mean_term = np.dot(matrix_covH / sigmaH, Hb)
priorG_mean_term = np.dot(matrix_covG / sigmaG, Gb)
elif prior=='omega':
logger.info(" prior omega")
#matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1])
priorH_mean_term = np.dot(np.dot(Omega.T, matrix_covG / sigmaG), G)
priorH_cov_term = np.dot(np.dot(Omega.T, matrix_covG / sigmaG), Omega)
priorG_mean_term = np.dot(matrix_covG / sigmaG, OmegaH)
elif prior=='hierarchical':
logger.info(" prior hierarchical")
matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1])
matrix_covG = np.eye(R_inv.shape[0], R_inv.shape[1])
priorH_mean_term = Mu / sigmaH
priorG_mean_term = np.dot(Omega, Mu / sigmaG)
else:
logger.info(" NO prior")
priorH_mean_term = np.zeros_like(H)
priorG_mean_term = np.zeros_like(G)
#####################
# EXPECTATION
#####################
# HRF H
if estimateH:
logger.info("E H step ...")
Ht, Sigma_H = vt.expectation_H_asl(Sigma_A, m_A, m_C, G, XX, W, Gamma,
Gamma_X, X_Gamma_X, J, y_tilde,
cov_noise, matrix_covH, sigmaH,
priorH_mean_term, priorH_cov_term)
if constraint:
if not np.linalg.norm(Ht)==1:
logger.info(" constraint l2-norm = 1")
H = vt.constraint_norm1_b(Ht, Sigma_H)
#H = Ht / np.linalg.norm(Ht)
else:
logger.info(" l2-norm already 1!!!!!")
H = Ht.copy()
Sigma_H = np.zeros_like(Sigma_H)
else:
H = Ht.copy()
h_norm = np.append(h_norm, np.linalg.norm(H))
print 'h_norm = ', h_norm
Crit_H = (np.linalg.norm(H - H1) / np.linalg.norm(H1)) ** 2
cH += [Crit_H]
H1[:] = H[:]
if prior=='omega':
OmegaH = np.dot(Omega0, H)
Omega = Omega0
if normOh:
Omega /= np.linalg.norm(OmegaH)
OmegaH /= np.linalg.norm(OmegaH)
if ni > 0:
free_energyH = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyH < free_energy:
logger.info("free energy has decreased after E-H step from %f to %f", free_energy, free_energyH)
# A
if estimateA:
logger.info("E A step ...")
m_A, Sigma_A = vt.expectation_A_asl(H, G, m_C, W, XX, Gamma, Gamma_X, q_Z,
mu_Ma, sigma_Ma, J, y_tilde,
Sigma_H, sigma_eps_m)
cA += [(np.linalg.norm(m_A - m_A1) / np.linalg.norm(m_A1)) ** 2]
m_A1[:, :] = m_A[:, :]
if ni > 0:
free_energyA = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyA < free_energyH:
logger.info("free energy has decreased after E-A step from %f to %f", free_energyH, free_energyA)
# PRF G
if estimateG:
logger.info("E G step ...")
Gt, Sigma_G = vt.expectation_G_asl(Sigma_C, m_C, m_A, H, XX, W, WX, Gamma,
Gamma_WX, XW_Gamma_WX, J, y_tilde,
cov_noise, matrix_covG, sigmaG,
priorG_mean_term, priorG_cov_term)
if constraint and normg:
if not np.linalg.norm(Gt)==1:
logger.info(" constraint l2-norm = 1")
G = vt.constraint_norm1_b(Gt, Sigma_G, positivity=positivity)
#G = Gt / np.linalg.norm(Gt)
else:
logger.info(" l2-norm already 1!!!!!")
G = Gt.copy()
Sigma_G = np.zeros_like(Sigma_G)
else:
G = Gt.copy()
g_norm = np.append(g_norm, np.linalg.norm(G))
print 'g_norm = ', g_norm
cG += [(np.linalg.norm(G - G1) / np.linalg.norm(G1)) ** 2]
G1[:] = G[:]
if ni > 0:
free_energyG = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyG < free_energyA:
logger.info("free energy has decreased after E-G step from %f to %f", free_energyA, free_energyG)
# C
if estimateC:
logger.info("E C step ...")
m_C, Sigma_C = vt.expectation_C_asl(G, H, m_A, W, XX, Gamma, Gamma_X, q_Z,
mu_Mc, sigma_Mc, J, y_tilde,
Sigma_G, sigma_eps_m)
cC += [(np.linalg.norm(m_C - m_C1) / np.linalg.norm(m_C1)) ** 2]
m_C1[:, :] = m_C[:, :]
if ni > 0:
free_energyC = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyC < free_energyG:
logger.info("free energy has decreased after E-C step from %f to %f", free_energyG, free_energyC)
# Q labels
if estimateZ:
logger.info("E Q step ...")
q_Z, Z_tilde = vt.expectation_Q_asl(Sigma_A, m_A, Sigma_C, m_C,
sigma_Ma, mu_Ma, sigma_Mc, mu_Mc,
Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K)
#q_Z0, Z_tilde0 = vt.expectation_Q_async(Sigma_A, m_A, Sigma_C, m_C,
# sigma_Ma, mu_Ma, sigma_Mc, mu_Mc,
# Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K)
#print 'synchronous vs asynchronous: ', np.abs(q_Z - q_Z0).sum()
cZ += [(np.linalg.norm(q_Z - q_Z1) / (np.linalg.norm(q_Z1) + eps)) ** 2]
q_Z1 = q_Z
if ni > 0:
free_energyQ = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyQ < free_energyC:
logger.info("free energy has decreased after E-Q step from %f to %f", free_energyC, free_energyQ)
# crit. AH and CG
logger.info("crit. AH and CG")
AH = m_A[:, :, np.newaxis] * H[np.newaxis, np.newaxis, :]
CG = m_C[:, :, np.newaxis] * G[np.newaxis, np.newaxis, :]
Crit_AH = (np.linalg.norm(AH - AH1) / (np.linalg.norm(AH1) + eps)) ** 2
cAH += [Crit_AH]
AH1 = AH.copy()
Crit_CG = (np.linalg.norm(CG - CG1) / (np.linalg.norm(CG1) + eps)) ** 2
cCG += [Crit_CG]
CG1 = CG.copy()
logger.info("Crit_AH = " + str(Crit_AH))
logger.info("Crit_CG = " + str(Crit_CG))
#####################
# MAXIMIZATION
#####################
if prior=='balloon':
logger.info(" prior balloon")
AuxH = H - Hb
AuxG = G - Gb
elif prior=='omega':
logger.info(" prior omega")
AuxH = H.copy()
AuxG = G - np.dot(Omega, H) #/np.linalg.norm(np.dot(Omega, H))
elif prior=='hierarchical':
logger.info(" prior hierarchical")
AuxH = H - Mu
AuxG = G - np.dot(Omega, Mu)
else:
logger.info(" NO prior")
AuxH = H.copy()
AuxG = G.copy()
# Variance HRF: sigmaH
if estimateSigmaH:
logger.info("M sigma_H step ...")
sigmaH = vt.maximization_sigma_asl(D, Sigma_H, matrix_covH, AuxH, use_hyperprior, gamma_h)
logger.info('sigmaH = ' + str(sigmaH))
if ni > 0:
free_energyVh = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyVh < free_energyQ:
logger.info("free energy has decreased after v_h computation from %f to %f", free_energyQ, free_energyVh)
# Variance PRF: sigmaG
if estimateSigmaG:
logger.info("M sigma_G step ...")
sigmaG = vt.maximization_sigma_asl(D, Sigma_G, matrix_covG, AuxG, use_hyperprior, gamma_g)
logger.info('sigmaG = ' + str(sigmaG))
if ni > 0:
free_energyVg = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyVg < free_energyVh:
logger.info("free energy has decreased after v_g computation from %f to %f", free_energyVh, free_energyVg)
# Mu: True HRF in the hierarchical prior case
if prior=='hierarchical':
logger.info("M sigma_G step ...")
Mu = vt.maximization_Mu_asl(H, G, matrix_covH, matrix_covG,
sigmaH, sigmaG, sigmaMu, Omega, R_inv)
logger.info('sigmaG = ' + str(sigmaG))
if ni > 0:
free_energyMu = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyMu < free_energyVg:
logger.info("free energy has decreased after v_g computation from %f to %f", free_energyVg, free_energyMu)
# (mu,sigma)
if estimateMP:
logger.info("M (mu,sigma) a and c step ...")
mu_Ma, sigma_Ma = vt.maximization_mu_sigma_asl(q_Z, m_A, Sigma_A)
mu_Mc, sigma_Mc = vt.maximization_mu_sigma_asl(q_Z, m_C, Sigma_C)
if ni > 0:
free_energyMP = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyMP < free_energyVg:
logger.info("free energy has decreased after GMM parameters computation from %f to %f", free_energyVg, free_energyMP)
# Drift L, alpha
if estimateLA:
logger.info("M L, alpha step ...")
AL = vt.maximization_LA_asl(Y, m_A, m_C, XX, WP, W, WP_Gamma_WP, H, G, Gamma)
y_tilde = Y - WP.dot(AL)
if ni > 0:
free_energyLA = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyLA < free_energyMP:
logger.info("free energy has decreased after drifts computation from %f to %f", free_energyMP, free_energyLA)
# Beta
if estimateBeta:
logger.info("M beta step ...")
"""
Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2)
Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3)
Beta = vt.maximization_beta_m2(Beta.copy(), q_Z, Qtilde_sumneighbour,
Qtilde, neighboursIndexes, maxNeighbours,
gamma, MaxItGrad, gradientStep)
"""
Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2)
Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3)
for m in xrange(0, M):
Beta[m] = vt.maximization_beta_m2_scipy_asl(Beta[m].copy(), q_Z[m, :, :],
Qtilde_sumneighbour[m, :, :],
Qtilde[m, :, :], neighboursIndexes,
maxNeighbours, gamma, MaxItGrad, gradientStep)
logger.info(Beta)
if ni > 0:
free_energyB = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX)
if free_energyB < free_energyLA:
logger.info("free energy has decreased after Beta computation from %f to %f", \
free_energyLA, free_energyB)
if 0:
plt.close('all')
for m in xrange(0, M):
range_b = np.arange(-10., 20., 0.1)
beta_plotting = np.zeros_like(range_b)
for ib, b in enumerate(range_b):
beta_plotting[ib] = vt.beta_function(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :],
neighboursIndexes, gamma)
#print beta_plotting
plt.figure(1)
plt.hold('on')
plt.plot(range_b, beta_plotting)
plt.show()
# Sigma noise
if estimateNoise:
logger.info("M sigma noise step ...")
sigma_eps = vt.maximization_sigma_noise_asl(XX, m_A, Sigma_A, H, m_C, Sigma_C, \
G, Sigma_H, Sigma_G, W, y_tilde, Gamma, \
Gamma_X, Gamma_WX, N)
if PLOT:
for m in xrange(M):
SUM_q_Z[m] += [q_Z[m, 1, :].sum()]
mua1[m] += [mu_Ma[m, 1]]
muc1[m] += [mu_Mc[m, 1]]
free_energy = vt.Compute_FreeEnergy(y_tilde, m_A, Sigma_A, mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C, Sigma_C, mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps, XX, W,
J, D, M, N, K, use_hyperprior, Gamma_X, Gamma_WX, plot=True)
if ni > 0:
if free_energy < free_energyB:
logger.info("free energy has decreased after Noise computation from %f to %f", free_energyB, free_energy)
if ni > 0:
if free_energy < FE[-1]:
logger.info("WARNING! free energy has decreased in this iteration from %f to %f", FE[-1], free_energy)
FE += [free_energy]
#EP += [EPt]
#EPlh += [EPt_lh]
#Ent += [Entropy]
if ni > NitMin:
#Crit_FE = np.abs((FE[-1] - FE[-2]) / FE[-2])
FE0 = np.array(FE)
Crit_FE = np.abs((FE0[-5:] - FE0[-6:-1]) / FE0[-6:-1])
print Crit_FE
print (Crit_FE > Thresh * np.ones_like(Crit_FE)).any()
else:
Crit_FE = 100
ni += 1
cTime += [time.time() - t1]
logger.info("Computing reconstruction error")
StimulusInducedSignal = vt.computeFit_asl(H, m_A, G, m_C, W, XX)
rerror = np.append(rerror, \
np.mean(((Y - StimulusInducedSignal) ** 2).sum(axis=0)) \
/ np.mean((Y ** 2).sum(axis=0)))
CompTime = time.time() - t1
# Normalize if not done already
if not constraint or not normg:
logger.info("l2-norm of H and G to 1 if not constraint")
Hnorm = np.linalg.norm(H)
H /= Hnorm
Sigma_H /= Hnorm**2
m_A *= Hnorm
Gnorm = np.linalg.norm(G)
G /= Gnorm
Sigma_G /= Gnorm**2
m_C *= Gnorm
if zc:
H = np.concatenate(([0], H, [0]))
G = np.concatenate(([0], G, [0]))
## Compute contrast maps and variance
if computeContrast and len(contrasts) > 0:
logger.info("Computing contrasts ... ")
CONTRAST_A, CONTRASTVAR_A, \
CONTRAST_C, CONTRASTVAR_C = vt.compute_contrasts(condition_names,
contrasts, m_A, m_C,
Sigma_A, Sigma_C, M, J)
else:
CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C = 0, 0, 0, 0
###########################################################################
########################################## PLOTS and SNR computation
if PLOT:
logger.info("plotting...")
print 'FE = ', FE
vt.plot_convergence(ni, M, cA, cC, cH, cG, cAH, cCG, SUM_q_Z, mua1, muc1, FE)
logger.info("Nb iterations to reach criterion: %d", ni)
logger.info("Computational time = %s min %s s",
str(np.int(CompTime // 60)), str(np.int(CompTime % 60)))
logger.info("Iteration time = %s min %s s",
str(np.int((CompTime // ni) // 60)), str(np.int((CompTime / ni) % 60)))
logger.info("perfusion baseline mean = %f", np.mean(AL[0, :]))
logger.info("perfusion baseline var = %f", np.var(AL[0, :]))
logger.info("drifts mean = %f", np.mean(AL[1:, :]))
logger.info("drifts var = %f", np.var(AL[1:, :]))
logger.info("noise mean = %f", np.mean(sigma_eps))
logger.info("noise var = %f", np.var(sigma_eps))
SNR10 = 20 * (np.log10(np.linalg.norm(Y) / \
np.linalg.norm(Y - StimulusInducedSignal - WP.dot(AL))))
logger.info("SNR = %d", SNR10)
return ni, m_A, H, m_C, G, Z_tilde, sigma_eps, \
mu_Ma, sigma_Ma, mu_Mc, sigma_Mc, Beta, AL[1:, :], np.dot(P, AL[1:, :]), \
AL[0, :], Sigma_A, Sigma_C, Sigma_H, Sigma_G, rerror, \
CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C, \
cA[:], cH[2:], cC[2:], cG[2:], cZ[2:], cAH[2:], cCG[2:], \
cTime, FE #, EP, EPlh, Ent
def Main_vbjde_physio(graph, Y, Onsets, durations, Thrf, K, TR, beta, dt,
scale=1, estimateSigmaH=True, estimateSigmaG=True,
sigmaH=0.05, sigmaG=0.05, gamma_h=0, gamma_g=0,
NitMax=-1, NitMin=1, estimateBeta=True, PLOT=False,
contrasts=[], computeContrast=False,
idx_first_tag=0, simulation=None, sigmaMu=None,
estimateH=True, estimateG=True, estimateA=True,
estimateC=True, estimateZ=True, estimateNoise=True,
estimateMP=True, estimateLA=True, use_hyperprior=False,
positivity=False, constraint=False,
phy_params=PHY_PARAMS_KHALIDOV11, prior='omega', zc=False):
logger.info("EM for ASL!")
np.random.seed(6537540)
logger.info("data shape: ")
logger.info(Y.shape)
Thresh = 1e-5
D, M = np.int(np.ceil(Thrf / dt)) + 1, len(Onsets)
#D, M = np.int(np.ceil(Thrf / dt)), len(Onsets)
n_sess, N, J = Y.shape[0], Y.shape[1], Y.shape[2]
Crit_AH, Crit_CG, cTime, rerror, FE = 1, 1, [], [], []
EP, EPlh, Ent = [],[],[]
Crit_H, Crit_G, Crit_Z, Crit_A, Crit_C = 1, 1, 1, 1, 1
cAH, cCG, AH1, CG1 = [], [], [], []
cA, cC, cH, cG, cZ = [], [], [], [], []
h_norm, g_norm = [], []
SUM_q_Z = [[] for m in xrange(M)]
mua1 = [[] for m in xrange(M)]
muc1 = [[] for m in xrange(M)]
sigmaH = sigmaH * J / 100
print sigmaH
gamma_h = gamma_h * 100 / J
print gamma_h
# Beta data
MaxItGrad = 200
gradientStep = 0.005
gamma = 7.5
print 'gamma = ', gamma
print 'voxels = ', J
maxNeighbours, neighboursIndexes = vt.create_neighbours(graph, J)
print 'graph.shape = ', graph.shape
# Conditions
print 'Onsets: ', Onsets
print 'durations = ', durations
print 'creating conditions...'
X, XX, condition_names = vt.create_conditions_block_ms(Onsets, durations,
M, N, D, n_sess, TR, dt)
# Covariance matrix
#R = vt.covariance_matrix(2, D, dt)
_, R_inv = genGaussianSmoothHRF(zc, D, dt, 1., 2)
R = np.linalg.inv(R_inv)
if zc:
XX = XX[:, :, :, 1:-1] # XX shape (S, M, N, D)
D = D - 2
AH1, CG1 = np.zeros((J, M, D)), np.zeros((J, M, D))
print 'HRF length = ', D
print 'Condition number = ', M
print 'Number of scans = ', N
print 'Number of voxels = ', J
print 'Number of sessions = ', n_sess
print 'XX.shape = ', XX.shape
# Noise matrix
Gamma = np.identity(N)
# Noise initialization
sigma_eps = np.ones((n_sess, J))
# Labels
logger.info("Labels are initialized by setting active probabilities "
"to ones ...")
q_Z = np.ones((M, K, J), dtype=np.float64) / 2.
#q_Z = np.zeros((M, K, J), dtype=np.float64)
#q_Z[:, 1, :] = 1
q_Z1 = copy.deepcopy(q_Z)
Z_tilde = copy.deepcopy(q_Z)
# H and G
TT, m_h = getCanoHRF(Thrf, dt)
H = np.array(m_h[:D]).astype(np.float64)
H /= np.linalg.norm(H)
Hb = create_physio_brf(phy_params, response_dt=dt, response_duration=Thrf)
Hb /= np.linalg.norm(Hb)
if prior=='balloon':
H = Hb.copy()
H1 = copy.deepcopy(H)
Sigma_H = np.zeros((D, D), dtype=np.float64)
# Initialize model parameters
Beta = beta * np.ones((M), dtype=np.float64)
n_drift = 4
P = np.zeros((n_sess, N, n_drift+1), dtype=np.float64)
L = np.zeros((n_drift+1, J, n_sess), dtype=np.float64)
for s in xrange(0, n_sess):
P[s, :, :] = vt.PolyMat(N, n_drift, TR)
L[:, :, s] = vt.polyFit(Y[s, :, :], TR, n_drift, P[s, :, :])
print 'P shape = ', P.shape
print 'L shape = ', L.shape
WP = P.copy()
AL = L.copy()
PL = np.einsum('ijk,kli->ijl', P, L)
y_tilde = Y - PL
# Parameters Gaussian mixtures
mu_Ma = np.append(np.zeros((M, 1)), np.ones((M, 1)), axis=1).astype(np.float64)
sigma_Ma = np.ones((M, K), dtype=np.float64) * 0.3
# Params RLs
m_A = np.zeros((n_sess, J, M), dtype=np.float64)
for s in xrange(0, n_sess):
for j in xrange(0, J):
m_A[s, j, :] = (np.random.normal(mu_Ma, np.sqrt(sigma_Ma)) * q_Z[:, :, j]).sum(axis=1).T
m_A1 = m_A.copy()
Sigma_A = np.ones((M, M, J, n_sess)) * np.identity(M)[:, :, np.newaxis, np.newaxis]
G = np.zeros_like(H)
m_C = np.zeros_like(m_A)
Sigma_G = np.zeros_like(Sigma_H)
Sigma_C = np.zeros_like(Sigma_A)
mu_Mc = np.zeros_like(mu_Ma)
sigma_Mc = np.ones_like(sigma_Ma)
W = np.zeros_like(Gamma) # (N, N)
# Precomputations
print 'W shape is ', W.shape
WX = W.dot(XX).transpose(1, 2, 0, 3) # shape (S, M, N, D)
Gamma_X = np.zeros((N, n_sess, M, D), dtype=np.float64) # shape (N, S, M, D)
X_Gamma_X = np.zeros((D, M, n_sess, M, D), dtype=np.float64) # shape (D, M, S, M, D)
Gamma_WX = np.zeros((N, n_sess, M, D), dtype=np.float64) # shape (N, S, M, D)
XW_Gamma_WX = np.zeros((D, M, n_sess, M, D), dtype=np.float64) # shape (D, M, S, M, D)
Gamma_WP = np.zeros((N, n_sess, n_drift+1), dtype=np.float64) # shape (N, S, M, D)
WP_Gamma_WP = np.zeros((n_sess, n_drift+1, n_drift+1), dtype=np.float64) # shape (D, M, S, M, D)
for s in xrange(0, n_sess):
Gamma_X[:, s, :, :] = np.tensordot(Gamma, XX[s, :, :, :], axes=(1, 1))
X_Gamma_X[:, :, s, :, :] = np.tensordot(XX[s, :, :, :].T, Gamma_X[:, s, :, :], axes=(1, 0))
Gamma_WX[:, s, :, :] = np.tensordot(Gamma, WX[s, :, :, :], axes=(1, 1))
XW_Gamma_WX[:, :, s, :, :] = np.tensordot(WX[s, :, :, :].T, Gamma_WX[:, s, :, :], axes=(1, 0))
Gamma_WP[:, s, :] = Gamma.dot(WP[s, :, :]) # (N, n_drift)
WP_Gamma_WP[s, :, :] = WP[s, :, :].T.dot(Gamma_WP[:, s, :]) # (n_drift, n_drift)
sigma_eps_m = np.maximum(sigma_eps, eps) # (n_sess, J)
cov_noise = sigma_eps_m[:, :, np.newaxis, np.newaxis] # (n_sess, J, 1, 1)
###########################################################################
############################################# VBJDE
t1 = time.time()
ni = 0
#while ((ni < NitMin + 1) or (((Crit_AH > Thresh) or (Crit_CG > Thresh)) \
# and (ni < NitMax))):
#while ((ni < NitMin + 1) or (((Crit_AH > Thresh)) \
# and (ni < NitMax))):
while ((ni < NitMin + 1) or (((Crit_FE > Thresh * np.ones_like(Crit_FE)).any()) \
and (ni < NitMax))):
logger.info("-------- Iteration n° " + str(ni + 1) + " --------")
if PLOT and ni >= 0: # Plotting HRF and PRF
logger.info("Plotting HRF and PRF for current iteration")
vt.plot_response_functions_it(ni, NitMin, M, H, G)
# Managing types of prior
priorH_cov_term = np.zeros_like(R_inv)
matrix_covH = R_inv.copy()
if prior=='balloon':
logger.info(" prior balloon")
#matrix_covH = np.eye(R_inv.shape[0], R_inv.shape[1])
priorH_mean_term = np.dot(matrix_covH / sigmaH, Hb)
else:
logger.info(" NO prior")
priorH_mean_term = np.zeros_like(H)
priorG_mean_term = np.zeros_like(G)
#####################
# EXPECTATION
#####################
# HRF H
if estimateH:
logger.info("E H step ...")
Ht, Sigma_H = vt.expectation_H_ms(Sigma_A, m_A, m_C, G, XX, W, Gamma,
Gamma_X, X_Gamma_X, J, y_tilde,
cov_noise, matrix_covH, sigmaH,
priorH_mean_term, priorH_cov_term, N, M, D, n_sess)
if constraint:
if not np.linalg.norm(Ht)==1:
logger.info(" constraint l2-norm = 1")
H = vt.constraint_norm1_b(Ht, Sigma_H)
#H = Ht / np.linalg.norm(Ht)
else:
logger.info(" l2-norm already 1!!!!!")
H = Ht.copy()
Sigma_H = np.zeros_like(Sigma_H)
else:
H = Ht.copy()
h_norm = np.append(h_norm, np.linalg.norm(H))
print 'h_norm = ', h_norm
Crit_H = (np.linalg.norm(H - H1) / np.linalg.norm(H1)) ** 2
cH += [Crit_H]
H1[:] = H[:]
# A
if estimateA:
logger.info("E A step ...")
m_A, Sigma_A = vt.expectation_A_ms(m_A, Sigma_A, H, G, m_C, W, XX,
Gamma, Gamma_X, q_Z,
mu_Ma, sigma_Ma, J, y_tilde,
Sigma_H, sigma_eps_m, N, M, D, n_sess)
cA += [(np.linalg.norm(m_A - m_A1) / np.linalg.norm(m_A1)) ** 2]
m_A1[:, :, :] = m_A[:, :, :]
# Q labels
if estimateZ:
logger.info("E Q step ...")
q_Z, Z_tilde = vt.expectation_Q_ms(Sigma_A, m_A, Sigma_C, m_C,
sigma_Ma, mu_Ma, sigma_Mc, mu_Mc,
Beta, Z_tilde, q_Z, neighboursIndexes, graph, M, J, K, n_sess)
if 0:
import matplotlib.pyplot as plt
plt.close('all')
fig = plt.figure(1)
for m in xrange(M):
ax = fig.add_subplot(2, M, m + 1)
im = ax.matshow(m_A[:, :, m].mean(0).reshape(20, 20))
plt.colorbar(im, ax=ax)
ax = fig.add_subplot(2, M, m + 3)
im = ax.matshow(q_Z[m, 1, :].reshape(20, 20))
plt.colorbar(im, ax=ax)
fig = plt.figure(2)
for m in xrange(M):
for s in xrange(n_sess):
ax = fig.add_subplot(M, n_sess, n_sess * m + s + 1)
im = ax.matshow(m_A[s, :, m].reshape(20, 20))
plt.colorbar(im, ax=ax)
plt.show()
cZ += [(np.linalg.norm(q_Z - q_Z1) / (np.linalg.norm(q_Z1) + eps)) ** 2]
q_Z1 = q_Z
if ni > 0:
free_energyE = 0
for s in xrange(n_sess):
free_energyE += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s],
mu_Ma, sigma_Ma, H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :],
W, J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :],
Gamma_WX[:, s, :, :], bold=True, S=n_sess)
if free_energyE < free_energy:
logger.info("free energy has decreased after E step from %f to %f", free_energy, free_energyE)
# crit. AH and CG
logger.info("crit. AH and CG")
AH = m_A[:, :, :, np.newaxis] * H[np.newaxis, np.newaxis, :]
Crit_AH = (np.linalg.norm(AH - AH1) / (np.linalg.norm(AH1) + eps)) ** 2
cAH += [Crit_AH]
AH1 = AH.copy()
logger.info("Crit_AH = " + str(Crit_AH))
#####################
# MAXIMIZATION
#####################
if prior=='balloon':
logger.info(" prior balloon")
AuxH = H - Hb
AuxG = G - Gb
else:
logger.info(" NO prior")
AuxH = H.copy()
AuxG = G.copy()
# Variance HRF: sigmaH
if estimateSigmaH:
logger.info("M sigma_H step ...")
sigmaH = vt.maximization_sigma_asl(D, Sigma_H, matrix_covH, AuxH, use_hyperprior, gamma_h)
logger.info('sigmaH = ' + str(sigmaH))
if ni > 0:
free_energyVh = 0
for s in xrange(n_sess):
free_energyVh += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W,
J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess)
if free_energyVh < free_energyE:
logger.info("free energy has decreased after v_h computation from %f to %f", free_energyE, free_energyVh)
# (mu,sigma)
if estimateMP:
logger.info("M (mu,sigma) a and c step ...")
#print 'q_Z = ', q_Z
#print q_Z.shape
mu_Ma, sigma_Ma = vt.maximization_mu_sigma_ms(q_Z, m_A, Sigma_A, M, J, n_sess, K)
print 'mu_Ma = ', mu_Ma
print 'sigma_Ma = ', sigma_Ma
if ni > 0:
free_energyMP = 0
for s in xrange(n_sess):
free_energyMP += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W,
J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess)
if free_energyMP < free_energyVh:
logger.info("free energy has decreased after GMM parameters computation from %f to %f", free_energyVh, free_energyMP)
# Drift L, alpha
if estimateLA:
logger.info("M L, alpha step ...")
for s in xrange(n_sess):
AL[:, :, s] = vt.maximization_LA_asl(Y[s, :, :], m_A[s, :, :], m_C[s, :, :], XX[s, :, :, :],
WP[s, :, :], W, WP_Gamma_WP[s, :, :], H, G, Gamma)
PL = np.einsum('ijk,kli->ijl', WP, AL)
y_tilde = Y - PL
if ni > 0:
free_energyLA = 0
for s in xrange(n_sess):
free_energyLA += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W,
J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess)
if free_energyLA < free_energyMP:
logger.info("free energy has decreased after drifts computation from %f to %f", free_energyMP, free_energyLA)
# Beta
if estimateBeta:
logger.info("M beta step ...")
"""Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2)
Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3)
Beta = vt.maximization_beta_m2(Beta.copy(), q_Z, Qtilde_sumneighbour,
Qtilde, neighboursIndexes, maxNeighbours,
gamma, MaxItGrad, gradientStep)
logger.info(Beta)
"""
logger.info("M beta step ...")
Qtilde = np.concatenate((Z_tilde, np.zeros((M, K, 1), dtype=Z_tilde.dtype)), axis=2)
Qtilde_sumneighbour = Qtilde[:, :, neighboursIndexes].sum(axis=3)
for m in xrange(0, M):
Beta[m] = vt.maximization_beta_m2_scipy_asl(Beta[m].copy(), q_Z[m, :, :], Qtilde_sumneighbour[m, :, :],
Qtilde[m, :, :], neighboursIndexes, maxNeighbours,
gamma, MaxItGrad, gradientStep)
logger.info(Beta)
if ni > 0:
free_energyB = 0
for s in xrange(n_sess):
free_energyB += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W,
J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], bold=True, S=n_sess)
if free_energyB < free_energyLA:
logger.info("free energy has decreased after Beta computation from %f to %f", \
free_energyLA, free_energyB)
if 0 and ni < 5:
plt.close('all')
for m in xrange(0, M):
range_b = np.arange(-10., 20., 0.1)
beta_plotting = np.zeros_like(range_b)
grad_plotting = np.zeros_like(range_b)
for ib, b in enumerate(range_b):
beta_plotting[ib] = vt.fun(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :],
neighboursIndexes, gamma)
grad_plotting[ib] = vt.grad_fun(b, q_Z[m, :, :], Qtilde_sumneighbour[m, :, :],
neighboursIndexes, gamma)
#print beta_plotting
plt.figure(1)
plt.hold('on')
plt.plot(range_b, beta_plotting)
plt.figure(2)
plt.hold('on')
plt.plot(range_b, grad_plotting)
plt.show()
# Sigma noise
if estimateNoise:
logger.info("M sigma noise step ...")
for s in xrange(n_sess):
sigma_eps[s, :] = vt.maximization_sigma_noise_asl(XX[s, :, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], H, m_C[s, :, :], Sigma_C[:, :, :, s], \
G, Sigma_H, Sigma_G, W, y_tilde[s, :, :], Gamma, \
Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :], N)
if PLOT:
for m in xrange(M):
SUM_q_Z[m] += [q_Z[m, 1, :].sum()]
mua1[m] += [mu_Ma[m, 1]]
free_energy = 0
for s in xrange(n_sess):
if s==n_sess-1:
plotFE = True
else:
plotFE = False
free_energy += vt.Compute_FreeEnergy(y_tilde[s, :, :], m_A[s, :, :], Sigma_A[:, :, :, s], mu_Ma, sigma_Ma,
H, Sigma_H, AuxH, R, R_inv, sigmaH, sigmaG,
m_C[s, :, :], Sigma_C[:, :, :, s], mu_Mc, sigma_Mc, G, Sigma_G,
AuxG, q_Z, neighboursIndexes, Beta, Gamma,
gamma, gamma_h, gamma_g, sigma_eps[s, :], XX[s, :, :, :], W,
J, D, M, N, K, use_hyperprior, Gamma_X[:, s, :, :], Gamma_WX[:, s, :, :],
plot=plotFE, bold=True, S=n_sess)
if ni > 0:
if free_energy < free_energyB:
logger.info("free energy has decreased after Noise computation from %f to %f", free_energyB, free_energy)
if ni > 0:
if free_energy < FE[-1]:
logger.info("WARNING! free energy has decreased in this iteration from %f to %f", FE[-1], free_energy)
FE += [free_energy]
if ni > 5:
#Crit_FE = np.abs((FE[-1] - FE[-2]) / FE[-2])
FE0 = np.array(FE)
Crit_FE = np.abs((FE0[-5:] - FE0[-6:-1]) / FE0[-6:-1])
print Crit_FE
print (Crit_FE > Thresh * np.ones_like(Crit_FE)).any()
else:
Crit_FE = 100
ni += 1
cTime += [time.time() - t1]
logger.info("Computing reconstruction error")
StimulusInducedSignal = vt.computeFit_asl(H, m_A[s, :, :], G, m_C[s, :, :], W, XX[s, :, :, :])
rerror = np.append(rerror, \
np.mean(((Y[s, :, :] - StimulusInducedSignal) ** 2).sum(axis=0)) \
/ np.mean((Y[s, :, :] ** 2).sum(axis=0)))
CompTime = time.time() - t1
# Normalize if not done already
if not constraint: # or not normg:
logger.info("l2-norm of H and G to 1 if not constraint")
Hnorm = np.linalg.norm(H)
H /= Hnorm
Sigma_H /= Hnorm**2
m_A *= Hnorm
if zc:
H = np.concatenate(([0], H, [0]))
## Compute contrast maps and variance
if computeContrast and len(contrasts) > 0:
logger.info("Computing contrasts ... ")
CONTRAST_A, CONTRASTVAR_A, \
CONTRAST_C, CONTRASTVAR_C = vt.compute_contrasts(condition_names,
contrasts, m_A[s, :, :], m_C[s, :, :],
Sigma_A[:, :, :, s], Sigma_C[:, :, :, s], M, J)
else:
CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C = 0, 0, 0, 0
###########################################################################
########################################## PLOTS and SNR computation
logger.info("Nb iterations to reach criterion: %d", ni)
logger.info("Computational time = %s min %s s",
str(np.int(CompTime // 60)), str(np.int(CompTime % 60)))
logger.info("Iteration time = %s min %s s",
str(np.int((CompTime // ni) // 60)), str(np.int((CompTime / ni) % 60)))
logger.info("perfusion baseline mean = %f", np.mean(AL[0, :, s]))
logger.info("perfusion baseline var = %f", np.var(AL[0, :, s]))
logger.info("drifts mean = %f", np.mean(AL[1:, :, s]))
logger.info("drifts var = %f", np.var(AL[1:, :, s]))
logger.info("noise mean = %f", np.mean(sigma_eps[s, :]))
logger.info("noise var = %f", np.var(sigma_eps[s, :]))
SNR10 = 20 * (np.log10(np.linalg.norm(Y[s, :, :]) / \
np.linalg.norm(Y[s, :, :] - StimulusInducedSignal - PL[s, :, :])))
logger.info("SNR = %d", SNR10)
return ni, m_A.mean(0), H, m_C.mean(0), G, Z_tilde, sigma_eps[s, :], \
mu_Ma, sigma_Ma, mu_Mc, sigma_Mc, Beta, AL[:, :, s], PL[s, :, :], \
np.zeros_like(AL[0, :, s]), Sigma_A[:, :, :, s], Sigma_C[:, :, :, s], Sigma_H, Sigma_G, rerror, \
CONTRAST_A, CONTRASTVAR_A, CONTRAST_C, CONTRASTVAR_C, \
cA[:], cH[2:], cC[2:], cG[2:], cZ[2:], cAH[2:], cCG[2:], \
cTime, FE
def test_create_neighbours(self):
graph = self.data_simu.get_graph()
neighbours_indexes = vt.create_neighbours(graph)
def jde_vem_bold(graph, bold_data, onsets, durations, hrf_duration, nb_classes,
tr, beta, dt, estimate_sigma_h=True, sigma_h=0.05,
it_max=-1, it_min=0, estimate_beta=True, contrasts=None,
compute_contrasts=False, hrf_hyperprior=0, estimate_hrf=True,
constrained=False, zero_constraint=True, drifts_type="poly",
seed=6537546):
"""This is the main function that computes the VEM analysis on BOLD data.
This function uses optimized python functions.
Parameters
----------
graph : ndarray of lists
represents the neighbours indexes of each voxels index
bold_data : ndarray, shape (nb_scans, nb_voxels)
raw data
onsets : dict
dictionnary of onsets
durations : # TODO
# TODO
hrf_duration : float
hrf total time duration (in s)
nb_classes : int
the number of classes to classify the nrls. This parameter is provided
for development purposes as most of the algorithm implies two classes
tr : float
time of repetition
beta : float
the initial value of beta
dt : float
hrf temporal precision
estimate_sigma_h : bool, optional
toggle estimation of sigma H
sigma_h : float, optional
initial or fixed value of sigma H
it_max : int, optional
maximal computed iteration number
it_min : int, optional
minimal computed iteration number
estimate_beta : bool, optional
toggle the estimation of beta
contrasts : OrderedDict, optional
dict of contrasts to compute
compute_contrasts : bool, optional
if True, compute the contrasts defined in contrasts
hrf_hyperprior : float
# TODO
estimate_hrf : bool, optional
if True, estimate the HRF for each parcel, if False use the canonical HRF
constrained : bool, optional
if True, add a constrains the l2 norm of the HRF to 1
drifts_type : str, optional
set the drifts basis type used. Can be "poly" for polynomial or "cos"
for cosine
seed : int, optional
seed used by numpy to initialize random generator number
Returns
-------
loop : int
number of iterations before convergence
nrls_mean : ndarray, shape (nb_voxels, nb_conditions)
Neural response level mean value
hrf_mean : ndarray, shape (hrf_len,)
Hemodynamic response function mean value
hrf_covar : ndarray, shape (hrf_len, hrf_len)
Covariance matrix of the HRF
labels_proba : ndarray, shape (nb_conditions, nb_classes, nb_voxels)
probability of voxels being in one class
noise_var : ndarray, shape (nb_voxels,)
estimated noise variance
nrls_class_mean : ndarray, shape (nb_conditions, nb_classes)
estimated mean value of the gaussians of the classes
nrls_class_var : ndarray, shape (nb_conditions, nb_classes)
estimated variance of the gaussians of the classes
beta : ndarray, shape (nb_conditions,)
estimated beta
drift_coeffs : ndarray, shape (# TODO)
estimated coefficient of the drifts
drift : ndarray, shape (# TODO)
estimated drifts
contrasts_mean : ndarray, shape (nb_voxels, len(contrasts))
Contrasts computed from NRLs
contrasts_var : ndarray, shape (nb_voxels, len(contrasts))
Variance of the contrasts
compute_time : list
computation time of each iteration
compute_time_mean : float
computation mean time over iterations
nrls_covar : ndarray, shape (nb_conditions, nb_conditions, nb_voxels)
# TODO
stimulus_induced_signal : ndarray, shape (nb_scans, nb_voxels)
# TODO
mahalanobis_zero : float
Mahalanobis distance between estimated hrf_mean and the null vector
mahalanobis_cano : float
Mahalanobis distance between estimated hrf_mean and the canonical HRF
mahalanobis_diff : float
difference between mahalanobis_cano and mahalanobis_diff
mahalanobis_prod : float
product of mahalanobis_cano and mahalanobis_diff
ppm_a_nrl : ndarray, shape (nb_voxels,)
The posterior probability map using an alpha
ppm_g_nrl : ndarray, shape (nb_voxels,)
# TODO
ppm_a_contrasts : ndarray, shape (nb_voxels,)
# TODO
ppm_g_contrasts : ndarray, shape (nb_voxels,)
# TODO
variation_coeff : float
coefficient of variation of the HRF
free_energy : list
# TODO
Notes
-----
See `A novel definition of the multivariate coefficient of variation
<http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000030/abstract>`_
article for more information about the coefficient of variation.
"""
logger.info("VEM started.")
if not contrasts:
contrasts = OrderedDict()
np.random.seed(seed)
nb_2_norm = 1
normalizing = False
regularizing = False
if it_max <= 0:
it_max = 100
gamma = 7.5
thresh_free_energy = 1e-4
# Initialize sizes vectors
hrf_len = np.int(np.ceil(hrf_duration / dt)) + 1
nb_conditions = len(onsets)
nb_scans = bold_data.shape[0]
nb_voxels = bold_data.shape[1]
X, occurence_matrix, condition_names = vt.create_conditions(
onsets, durations, nb_conditions, nb_scans, hrf_len, tr, dt
)
neighbours_indexes = vt.create_neighbours(graph)
order = 2
if regularizing:
regularization = np.ones(hrf_len)
regularization[hrf_len//3:hrf_len//2] = 2
regularization[hrf_len//2:2*hrf_len//3] = 5
regularization[2*hrf_len//3:3*hrf_len//4] = 7
regularization[3*hrf_len//4:] = 10
# regularization[hrf_len//2:] = 10
else:
regularization = None
d2 = vt.buildFiniteDiffMatrix(order, hrf_len, regularization)
hrf_regu_prior_inv = d2.T.dot(d2) / pow(dt, 2 * order)
if estimate_hrf and zero_constraint:
hrf_len = hrf_len - 2
hrf_regu_prior_inv = hrf_regu_prior_inv[1:-1, 1:-1]
occurence_matrix = occurence_matrix[:, :, 1:-1]
noise_struct = np.identity(nb_scans)
free_energy = [1.]
free_energy_crit = [1.]
compute_time = []
noise_var = np.ones(nb_voxels)
labels_proba = np.zeros((nb_conditions, nb_classes, nb_voxels), dtype=np.float64)
logger.info("Labels are initialized by setting everything to {}".format(1./nb_classes))
labels_proba[:, :, :] = 1./nb_classes
m_h = getCanoHRF(hrf_duration, dt)[1][:hrf_len]
hrf_mean = np.array(m_h).astype(np.float64)
if estimate_hrf:
hrf_covar = np.identity(hrf_len, dtype=np.float64)
else:
hrf_covar = np.zeros((hrf_len, hrf_len), dtype=np.float64)
beta = beta * np.ones((nb_conditions), dtype=np.float64)
beta_list = []
beta_list.append(beta.copy())
if drifts_type == "poly":
drift_basis = vt.poly_drifts_basis(nb_scans, 4, tr)
elif drifts_type == "cos":
drift_basis = vt.cosine_drifts_basis(nb_scans, 64, tr)
drift_coeffs = vt.drifts_coeffs_fit(bold_data, drift_basis)
drift = drift_basis.dot(drift_coeffs)
bold_data_drift = bold_data - drift
# Parameters Gaussian mixtures
nrls_class_mean = 2 * np.ones((nb_conditions, nb_classes))
nrls_class_mean[:, 0] = 0
nrls_class_var = 0.3 * np.ones((nb_conditions, nb_classes), dtype=np.float64)
nrls_mean = (np.random.normal(
nrls_class_mean, nrls_class_var)[:, :, np.newaxis] * labels_proba).sum(axis=1).T
nrls_covar = (np.identity(nb_conditions)[:, :, np.newaxis] + np.zeros((1, 1, nb_voxels)))
start_time = time.time()
loop = 0
while (loop <= it_min or
((np.asarray(free_energy_crit[-5:]) > thresh_free_energy).any()
and loop < it_max)):
logger.info("{:-^80}".format(" Iteration n°"+str(loop+1)+" "))
logger.info("Expectation A step...")
logger.debug("Before: nrls_mean = %s, nrls_covar = %s", nrls_mean, nrls_covar)
nrls_mean, nrls_covar = vt.nrls_expectation(
hrf_mean, nrls_mean, occurence_matrix, noise_struct, labels_proba,
nrls_class_mean, nrls_class_var, nb_conditions, bold_data_drift, nrls_covar,
hrf_covar, noise_var)
logger.debug("After: nrls_mean = %s, nrls_covar = %s", nrls_mean, nrls_covar)
logger.info("Expectation Z step...")
logger.debug("Before: labels_proba = %s, labels_proba = %s", labels_proba, labels_proba)
labels_proba = vt.labels_expectation(
nrls_covar, nrls_mean, nrls_class_var, nrls_class_mean, beta,
labels_proba, neighbours_indexes, nb_conditions, nb_classes,
nb_voxels, parallel=True)
logger.debug("After: labels_proba = %s, labels_proba = %s", labels_proba, labels_proba)
if estimate_hrf:
logger.info("Expectation H step...")
logger.debug("Before: hrf_mean = %s, hrf_covar = %s", hrf_mean, hrf_covar)
hrf_mean, hrf_covar = vt.hrf_expectation(
nrls_covar, nrls_mean, occurence_matrix, noise_struct,
hrf_regu_prior_inv, sigma_h, nb_voxels, bold_data_drift, noise_var)
if constrained:
hrf_mean = vt.norm1_constraint(hrf_mean, hrf_covar)
hrf_covar[:] = 0
logger.debug("After: hrf_mean = %s, hrf_covar = %s", hrf_mean, hrf_covar)
# Normalizing H at each nb_2_norm iterations:
if not constrained and normalizing:
# Normalizing is done before sigma_h, nrls_class_mean and nrls_class_var estimation
# we should not include them in the normalisation step
if (loop + 1) % nb_2_norm == 0:
hrf_norm = np.linalg.norm(hrf_mean)
hrf_mean /= hrf_norm
hrf_covar /= hrf_norm ** 2
nrls_mean *= hrf_norm
nrls_covar *= hrf_norm ** 2
if estimate_hrf and estimate_sigma_h:
logger.info("Maximization sigma_H step...")
logger.debug("Before: sigma_h = %s", sigma_h)
if hrf_hyperprior > 0:
sigma_h = vt.maximization_sigmaH_prior(hrf_len, hrf_covar,
hrf_regu_prior_inv,
hrf_mean, hrf_hyperprior)
else:
sigma_h = vt.maximization_sigmaH(hrf_len, hrf_covar,
hrf_regu_prior_inv, hrf_mean)
logger.debug("After: sigma_h = %s", sigma_h)
logger.info("Maximization (mu,sigma) step...")
logger.debug("Before: nrls_class_mean = %s, nrls_class_var = %s",
nrls_class_mean, nrls_class_var)
nrls_class_mean, nrls_class_var = vt.maximization_class_proba(
labels_proba, nrls_mean, nrls_covar
)
logger.debug("After: nrls_class_mean = %s, nrls_class_var = %s",
nrls_class_mean, nrls_class_var)
logger.info("Maximization L step...")
logger.debug("Before: drift_coeffs = %s", drift_coeffs)
drift_coeffs = vt.maximization_drift_coeffs(
bold_data, nrls_mean, occurence_matrix, hrf_mean, noise_struct, drift_basis
)
logger.debug("After: drift_coeffs = %s", drift_coeffs)
drift = drift_basis.dot(drift_coeffs)
bold_data_drift = bold_data - drift
if estimate_beta:
logger.info("Maximization beta step...")
for cond_nb in xrange(0, nb_conditions):
beta[cond_nb], success = vt.beta_maximization(
beta[cond_nb]*np.ones((1,)), labels_proba[cond_nb, :, :],
neighbours_indexes, gamma
)
beta_list.append(beta.copy())
logger.debug("beta = %s", str(beta))
logger.info("Maximization sigma noise step...")
noise_var = vt.maximization_noise_var(
occurence_matrix, hrf_mean, hrf_covar, nrls_mean, nrls_covar,
noise_struct, bold_data_drift, nb_scans
)
#### Computing Free Energy ####
free_energy.append(vt.free_energy_computation(
nrls_mean, nrls_covar, hrf_mean, hrf_covar, hrf_len, labels_proba,
bold_data_drift, occurence_matrix, noise_var, noise_struct, nb_conditions,
nb_voxels, nb_scans, nb_classes, nrls_class_mean, nrls_class_var, neighbours_indexes,
beta, sigma_h, np.linalg.inv(hrf_regu_prior_inv), hrf_regu_prior_inv, gamma, hrf_hyperprior
))
free_energy_crit.append(abs((free_energy[-2] - free_energy[-1]) /
free_energy[-2]))
logger.info("Convergence criteria: %f (Threshold = %f)",
free_energy_crit[-1], thresh_free_energy)
loop += 1
compute_time.append(time.time() - start_time)
compute_time_mean = compute_time[-1] / loop
mahalanobis_zero = np.nan
mahalanobis_cano = np.nan
mahalanobis_diff = np.nan
mahalanobis_prod = np.nan
variation_coeff = np.nan
if estimate_hrf and not constrained and not normalizing:
hrf_norm = np.linalg.norm(hrf_mean)
hrf_mean /= hrf_norm
hrf_covar /= hrf_norm ** 2
sigma_h /= hrf_norm ** 2
nrls_mean *= hrf_norm
nrls_covar *= hrf_norm ** 2
nrls_class_mean *= hrf_norm
nrls_class_var *= hrf_norm ** 2
mahalanobis_zero = mahalanobis(hrf_mean, np.zeros_like(hrf_mean),
np.linalg.inv(hrf_covar))
mahalanobis_cano = mahalanobis(hrf_mean, m_h, np.linalg.inv(hrf_covar))
mahalanobis_diff = mahalanobis_cano - mahalanobis_zero
mahalanobis_prod = mahalanobis_cano * mahalanobis_zero
variation_coeff = np.sqrt((hrf_mean.T.dot(hrf_covar).dot(hrf_mean))
/(hrf_mean.T.dot(hrf_mean))**2)
if estimate_hrf and zero_constraint:
hrf_mean = np.concatenate(([0], hrf_mean, [0]))
# when using the zero constraint the hrf covariance is fill with
# arbitrary zeros around the matrix, this is maybe a bad idea if we need
# it for later computation...
hrf_covar = np.concatenate(
(np.zeros((hrf_covar.shape[0], 1)), hrf_covar, np.zeros((hrf_covar.shape[0], 1))),
axis=1
)
hrf_covar = np.concatenate(
(np.zeros((1, hrf_covar.shape[1])), hrf_covar, np.zeros((1, hrf_covar.shape[1]))),
axis=0
)
if estimate_hrf:
(delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under, delay) = vt.fit_hrf_two_gammas(
hrf_mean, dt, hrf_duration
)
else:
(delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under, delay) = (None, None, None,
None, None, None)
ppm_a_nrl, ppm_g_nrl = vt.ppms_computation(
nrls_mean, np.diagonal(nrls_covar), nrls_class_mean, nrls_class_var,
threshold_a="intersect"
)
#+++++++++++++++++++++++ calculate contrast maps and variance +++++++++++++++++++++++#
nb_contrasts = len(contrasts)
if compute_contrasts and nb_contrasts > 0:
logger.info('Computing contrasts ...')
(contrasts_mean,
contrasts_var,
contrasts_class_mean,
contrasts_class_var) = vt.contrasts_mean_var_classes(
contrasts, condition_names, nrls_mean, nrls_covar,
nrls_class_mean, nrls_class_var, nb_contrasts, nb_classes, nb_voxels
)
ppm_a_contrasts, ppm_g_contrasts = vt.ppms_computation(
contrasts_mean, contrasts_var, contrasts_class_mean, contrasts_class_var
)
logger.info('Done computing contrasts.')
else:
(contrasts_mean, contrasts_var, contrasts_class_mean,
contrasts_class_var, ppm_a_contrasts, ppm_g_contrasts) = (None, None,
None, None,
None, None)
#+++++++++++++++++++++++ calculate contrast maps and variance +++++++++++++++++++++++#
logger.info("Nb iterations to reach criterion: %d", loop)
logger.info("Computational time = %s min %s s",
*(str(int(x)) for x in divmod(compute_time[-1], 60)))
logger.debug('nrls_class_mean: %s', nrls_class_mean)
logger.debug('nrls_class_var: %s', nrls_class_var)
logger.debug("sigma_H = %s", str(sigma_h))
logger.debug("beta = %s", str(beta))
stimulus_induced_signal = vt.computeFit(hrf_mean, nrls_mean, X, nb_voxels, nb_scans)
snr = 20 * np.log(
np.linalg.norm(bold_data.astype(np.float))
/ np.linalg.norm((bold_data - stimulus_induced_signal - drift).astype(np.float))
)
snr /= np.log(10.)
logger.info('snr comp = %f', snr)
# ,FreeEnergyArray
return (loop, nrls_mean, hrf_mean, hrf_covar, labels_proba, noise_var,
nrls_class_mean, nrls_class_var, beta, drift_coeffs, drift,
contrasts_mean, contrasts_var, compute_time[2:], compute_time_mean,
nrls_covar, stimulus_induced_signal, mahalanobis_zero,
mahalanobis_cano, mahalanobis_diff, mahalanobis_prod, ppm_a_nrl,
ppm_g_nrl, ppm_a_contrasts, ppm_g_contrasts, variation_coeff,
free_energy[1:], free_energy_crit[1:], beta_list[1:],
delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under, delay)
def jde_vem_bold(graph,
bold_data,
onsets,
durations,
hrf_duration,
nb_classes,
tr,
beta,
dt,
estimate_sigma_h=True,
sigma_h=0.05,
it_max=-1,
it_min=0,
estimate_beta=True,
contrasts=None,
compute_contrasts=False,
hrf_hyperprior=0,
estimate_hrf=True,
constrained=False,
zero_constraint=True,
drifts_type="poly",
seed=6537546):
"""This is the main function that computes the VEM analysis on BOLD data.
This function uses optimized python functions.
Parameters
----------
graph : ndarray of lists
represents the neighbours indexes of each voxels index
bold_data : ndarray, shape (nb_scans, nb_voxels)
raw data
onsets : dict
dictionnary of onsets
durations : # TODO
# TODO
hrf_duration : float
hrf total time duration (in s)
nb_classes : int
the number of classes to classify the nrls. This parameter is provided
for development purposes as most of the algorithm implies two classes
tr : float
time of repetition
beta : float
the initial value of beta
dt : float
hrf temporal precision
estimate_sigma_h : bool, optional
toggle estimation of sigma H
sigma_h : float, optional
initial or fixed value of sigma H
it_max : int, optional
maximal computed iteration number
it_min : int, optional
minimal computed iteration number
estimate_beta : bool, optional
toggle the estimation of beta
contrasts : OrderedDict, optional
dict of contrasts to compute
compute_contrasts : bool, optional
if True, compute the contrasts defined in contrasts
hrf_hyperprior : float
# TODO
estimate_hrf : bool, optional
if True, estimate the HRF for each parcel, if False use the canonical HRF
constrained : bool, optional
if True, add a constrains the l2 norm of the HRF to 1
zero_constraint : bool, optional
if True, add zeros to the beginning and the end of the estimated HRF.
drifts_type : str, optional
set the drifts basis type used. Can be "poly" for polynomial or "cos"
for cosine
seed : int, optional
seed used by numpy to initialize random generator number
Returns
-------
loop : int
number of iterations before convergence
nrls_mean : ndarray, shape (nb_voxels, nb_conditions)
Neural response level mean value
hrf_mean : ndarray, shape (hrf_len,)
Hemodynamic response function mean value
hrf_covar : ndarray, shape (hrf_len, hrf_len)
Covariance matrix of the HRF
labels_proba : ndarray, shape (nb_conditions, nb_classes, nb_voxels)
probability of voxels being in one class
noise_var : ndarray, shape (nb_voxels,)
estimated noise variance
nrls_class_mean : ndarray, shape (nb_conditions, nb_classes)
estimated mean value of the gaussians of the classes
nrls_class_var : ndarray, shape (nb_conditions, nb_classes)
estimated variance of the gaussians of the classes
beta : ndarray, shape (nb_conditions,)
estimated beta
drift_coeffs : ndarray, shape (# TODO)
estimated coefficient of the drifts
drift : ndarray, shape (# TODO)
estimated drifts
contrasts_mean : ndarray, shape (nb_voxels, len(contrasts))
Contrasts computed from NRLs
contrasts_var : ndarray, shape (nb_voxels, len(contrasts))
Variance of the contrasts
compute_time : list
computation time of each iteration
compute_time_mean : float
computation mean time over iterations
nrls_covar : ndarray, shape (nb_conditions, nb_conditions, nb_voxels)
# TODO
stimulus_induced_signal : ndarray, shape (nb_scans, nb_voxels)
# TODO
mahalanobis_zero : float
Mahalanobis distance between estimated hrf_mean and the null vector
mahalanobis_cano : float
Mahalanobis distance between estimated hrf_mean and the canonical HRF
mahalanobis_diff : float
difference between mahalanobis_cano and mahalanobis_diff
mahalanobis_prod : float
product of mahalanobis_cano and mahalanobis_diff
ppm_a_nrl : ndarray, shape (nb_voxels,)
The posterior probability map using an alpha
ppm_g_nrl : ndarray, shape (nb_voxels,)
# TODO
ppm_a_contrasts : ndarray, shape (nb_voxels,)
# TODO
ppm_g_contrasts : ndarray, shape (nb_voxels,)
# TODO
variation_coeff : float
coefficient of variation of the HRF
free_energy : list
# TODO
Notes
-----
See `A novel definition of the multivariate coefficient of variation
<http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000030/abstract>`_
article for more information about the coefficient of variation.
"""
logger.info("VEM started.")
if not contrasts:
contrasts = OrderedDict()
np.random.seed(seed)
nb_2_norm = 1
normalizing = False
regularizing = False
if it_max <= 0:
it_max = 100
gamma = 7.5
# Initialize sizes vectors
hrf_len = np.int(np.ceil(hrf_duration / dt)) + 1
nb_conditions = len(onsets)
nb_scans = bold_data.shape[0]
nb_voxels = bold_data.shape[1]
X, occurence_matrix, condition_names = vt.create_conditions(
onsets, durations, nb_conditions, nb_scans, hrf_len, tr, dt)
neighbours_indexes = vt.create_neighbours(graph)
order = 2
if regularizing:
regularization = np.ones(hrf_len)
regularization[hrf_len // 3:hrf_len // 2] = 2
regularization[hrf_len // 2:2 * hrf_len // 3] = 5
regularization[2 * hrf_len // 3:3 * hrf_len // 4] = 7
regularization[3 * hrf_len // 4:] = 10
# regularization[hrf_len//2:] = 10
else:
regularization = None
d2 = vt.buildFiniteDiffMatrix(order, hrf_len, regularization)
hrf_regu_prior_inv = d2.T.dot(d2) / pow(dt, 2 * order)
if estimate_hrf and zero_constraint:
hrf_len = hrf_len - 2
hrf_regu_prior_inv = hrf_regu_prior_inv[1:-1, 1:-1]
occurence_matrix = occurence_matrix[:, :, 1:-1]
noise_struct = np.identity(nb_scans)
noise_var = np.ones(nb_voxels)
if nb_classes != 2:
logger.warn('The number of classes is different to two.')
labels_proba = np.zeros((nb_conditions, nb_classes, nb_voxels),
dtype=np.float64)
logger.info("Labels are initialized by setting everything to {}".format(
1. / nb_classes))
labels_proba[:, :, :] = 1. / nb_classes
m_h = getCanoHRF(hrf_duration, dt)[1][:hrf_len]
hrf_mean = np.array(m_h).astype(np.float64)
if estimate_hrf:
hrf_covar = np.identity(hrf_len, dtype=np.float64)
else:
hrf_covar = np.zeros((hrf_len, hrf_len), dtype=np.float64)
beta = beta * np.ones(nb_conditions, dtype=np.float64)
beta_list = [beta.copy()]
if drifts_type == "poly":
drift_basis = vt.poly_drifts_basis(nb_scans, 4, tr)
elif drifts_type == "cos":
drift_basis = vt.cosine_drifts_basis(nb_scans, 64, tr)
else:
raise Exception('drift type "%s" is not supported' % drifts_type)
drift_coeffs = vt.drifts_coeffs_fit(bold_data, drift_basis)
drift = drift_basis.dot(drift_coeffs)
bold_data_drift = bold_data - drift
# Parameters Gaussian mixtures
nrls_class_mean = 2 * np.ones((nb_conditions, nb_classes))
nrls_class_mean[:, 0] = 0
nrls_class_var = 0.3 * np.ones(
(nb_conditions, nb_classes), dtype=np.float64)
nrls_mean = (
np.random.normal(nrls_class_mean, nrls_class_var)[:, :, np.newaxis] *
labels_proba).sum(axis=1).T
nrls_covar = np.identity(nb_conditions)[:, :, np.newaxis] + np.zeros(
(1, 1, nb_voxels))
thresh_free_energy = 1e-4
free_energy = [1.]
free_energy_crit = [1.]
compute_time = []
start_time = time.time()
loop = 0
while (loop <= it_min
or ((np.asarray(free_energy_crit[-5:]) > thresh_free_energy).any()
and loop < it_max)):
logger.info("{:-^80}".format(" Iteration n°" + str(loop + 1) + " "))
logger.info("Expectation A step...")
logger.debug("Before: nrls_mean = %s, nrls_covar = %s", nrls_mean,
nrls_covar)
nrls_mean, nrls_covar = vt.nrls_expectation(
hrf_mean, nrls_mean, occurence_matrix, noise_struct, labels_proba,
nrls_class_mean, nrls_class_var, nb_conditions, bold_data_drift,
nrls_covar, hrf_covar, noise_var)
logger.debug("After: nrls_mean = %s, nrls_covar = %s", nrls_mean,
nrls_covar)
logger.info("Expectation Z step...")
logger.debug("Before: labels_proba = %s, labels_proba = %s",
labels_proba, labels_proba)
labels_proba = vt.labels_expectation(nrls_covar,
nrls_mean,
nrls_class_var,
nrls_class_mean,
beta,
labels_proba,
neighbours_indexes,
nb_conditions,
nb_classes,
nb_voxels,
parallel=True)
logger.debug("After: labels_proba = %s, labels_proba = %s",
labels_proba, labels_proba)
if estimate_hrf:
logger.info("Expectation H step...")
logger.debug("Before: hrf_mean = %s, hrf_covar = %s", hrf_mean,
hrf_covar)
hrf_mean, hrf_covar = vt.hrf_expectation(
nrls_covar, nrls_mean, occurence_matrix, noise_struct,
hrf_regu_prior_inv, sigma_h, nb_voxels, bold_data_drift,
noise_var)
if constrained:
hrf_mean = vt.norm1_constraint(hrf_mean, hrf_covar)
hrf_covar[:] = 0
logger.debug("After: hrf_mean = %s, hrf_covar = %s", hrf_mean,
hrf_covar)
# Normalizing H at each nb_2_norm iterations:
if not constrained and normalizing:
# Normalizing is done before sigma_h, nrls_class_mean and nrls_class_var estimation
# we should not include them in the normalisation step
if (loop + 1) % nb_2_norm == 0:
hrf_norm = np.linalg.norm(hrf_mean)
hrf_mean /= hrf_norm
hrf_covar /= hrf_norm**2
nrls_mean *= hrf_norm
nrls_covar *= hrf_norm**2
if estimate_hrf and estimate_sigma_h:
logger.info("Maximization sigma_H step...")
logger.debug("Before: sigma_h = %s", sigma_h)
if hrf_hyperprior > 0:
sigma_h = vt.maximization_sigmaH_prior(hrf_len, hrf_covar,
hrf_regu_prior_inv,
hrf_mean,
hrf_hyperprior)
else:
sigma_h = vt.maximization_sigmaH(hrf_len, hrf_covar,
hrf_regu_prior_inv, hrf_mean)
logger.debug("After: sigma_h = %s", sigma_h)
logger.info("Maximization (mu,sigma) step...")
logger.debug("Before: nrls_class_mean = %s, nrls_class_var = %s",
nrls_class_mean, nrls_class_var)
nrls_class_mean, nrls_class_var = vt.maximization_class_proba(
labels_proba, nrls_mean, nrls_covar)
logger.debug("After: nrls_class_mean = %s, nrls_class_var = %s",
nrls_class_mean, nrls_class_var)
logger.info("Maximization L step...")
logger.debug("Before: drift_coeffs = %s", drift_coeffs)
drift_coeffs = vt.maximization_drift_coeffs(bold_data, nrls_mean,
occurence_matrix, hrf_mean,
noise_struct, drift_basis)
logger.debug("After: drift_coeffs = %s", drift_coeffs)
drift = drift_basis.dot(drift_coeffs)
bold_data_drift = bold_data - drift
if estimate_beta:
logger.info("Maximization beta step...")
for cond_nb in xrange(0, nb_conditions):
beta[cond_nb], success = vt.beta_maximization(
beta[cond_nb] * np.ones((1, )),
labels_proba[cond_nb, :, :], neighbours_indexes, gamma)
beta_list.append(beta.copy())
logger.debug("beta = %s", str(beta))
logger.info("Maximization sigma noise step...")
noise_var = vt.maximization_noise_var(occurence_matrix, hrf_mean,
hrf_covar, nrls_mean, nrls_covar,
noise_struct, bold_data_drift,
nb_scans)
# Computing Free Energy
free_energy.append(
vt.free_energy_computation(
nrls_mean, nrls_covar, hrf_mean, hrf_covar, hrf_len,
labels_proba, bold_data_drift, occurence_matrix, noise_var,
noise_struct, nb_conditions, nb_voxels, nb_scans, nb_classes,
nrls_class_mean, nrls_class_var,
neighbours_indexes, beta, sigma_h,
np.linalg.inv(hrf_regu_prior_inv), hrf_regu_prior_inv, gamma,
hrf_hyperprior))
free_energy_crit.append(
abs((free_energy[-2] - free_energy[-1]) / free_energy[-2]))
logger.info("Convergence criteria: %f (Threshold = %f)",
free_energy_crit[-1], thresh_free_energy)
loop += 1
compute_time.append(time.time() - start_time)
compute_time_mean = compute_time[-1] / loop
mahalanobis_zero = np.nan
mahalanobis_cano = np.nan
mahalanobis_diff = np.nan
mahalanobis_prod = np.nan
variation_coeff = np.nan
if estimate_hrf and not constrained and not normalizing:
hrf_norm = np.linalg.norm(hrf_mean)
hrf_mean /= hrf_norm
hrf_covar /= hrf_norm**2
sigma_h /= hrf_norm**2
nrls_mean *= hrf_norm
nrls_covar *= hrf_norm**2
nrls_class_mean *= hrf_norm
nrls_class_var *= hrf_norm**2
mahalanobis_zero = mahalanobis(hrf_mean, np.zeros_like(hrf_mean),
np.linalg.inv(hrf_covar))
mahalanobis_cano = mahalanobis(hrf_mean, m_h, np.linalg.inv(hrf_covar))
mahalanobis_diff = mahalanobis_cano - mahalanobis_zero
mahalanobis_prod = mahalanobis_cano * mahalanobis_zero
variation_coeff = np.sqrt((hrf_mean.T.dot(hrf_covar).dot(hrf_mean)) /
(hrf_mean.T.dot(hrf_mean))**2)
if estimate_hrf and zero_constraint:
hrf_mean = np.concatenate(([0], hrf_mean, [0]))
# when using the zero constraint the hrf covariance is fill with
# arbitrary zeros around the matrix, this is maybe a bad idea if we need
# it for later computation...
hrf_covar = np.concatenate((np.zeros(
(hrf_covar.shape[0], 1)), hrf_covar,
np.zeros((hrf_covar.shape[0], 1))),
axis=1)
hrf_covar = np.concatenate((np.zeros(
(1, hrf_covar.shape[1])), hrf_covar,
np.zeros((1, hrf_covar.shape[1]))),
axis=0)
if estimate_hrf:
(delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under,
delay) = vt.fit_hrf_two_gammas(hrf_mean, dt, hrf_duration)
else:
(delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under,
delay) = (None, None, None, None, None, None)
ppm_a_nrl, ppm_g_nrl = vt.ppms_computation(nrls_mean,
np.diagonal(nrls_covar),
nrls_class_mean,
nrls_class_var,
threshold_a="intersect")
# Calculate contrast maps and variance
nb_contrasts = len(contrasts)
if compute_contrasts and nb_contrasts > 0:
logger.info('Computing contrasts ...')
(contrasts_mean, contrasts_var, contrasts_class_mean,
contrasts_class_var) = vt.contrasts_mean_var_classes(
contrasts, condition_names, nrls_mean, nrls_covar,
nrls_class_mean, nrls_class_var, nb_contrasts, nb_classes,
nb_voxels)
ppm_a_contrasts, ppm_g_contrasts = vt.ppms_computation(
contrasts_mean, contrasts_var, contrasts_class_mean,
contrasts_class_var)
logger.info('Done computing contrasts.')
else:
(contrasts_mean, contrasts_var, contrasts_class_mean,
contrasts_class_var, ppm_a_contrasts,
ppm_g_contrasts) = (None, None, None, None, None, None)
logger.info("Number of iterations to reach criterion: %d", loop)
logger.info("Computational time = {t[0]:.0f} min {t[1]:.0f} s".format(
t=divmod(compute_time[-1], 60)))
logger.debug('nrls_class_mean: %s', nrls_class_mean)
logger.debug('nrls_class_var: %s', nrls_class_var)
logger.debug("sigma_H = %s", str(sigma_h))
logger.debug("beta = %s", str(beta))
stimulus_induced_signal = vt.computeFit(hrf_mean, nrls_mean, X, nb_voxels,
nb_scans)
snr = 20 * np.log(
np.linalg.norm(bold_data.astype(np.float)) / np.linalg.norm(
(bold_data_drift - stimulus_induced_signal).astype(np.float)))
snr /= np.log(10.)
logger.info('SNR comp = %f', snr)
return (loop, nrls_mean, hrf_mean, hrf_covar, labels_proba, noise_var,
nrls_class_mean, nrls_class_var, beta, drift_coeffs, drift,
contrasts_mean, contrasts_var, compute_time[2:], compute_time_mean,
nrls_covar, stimulus_induced_signal, mahalanobis_zero,
mahalanobis_cano, mahalanobis_diff, mahalanobis_prod, ppm_a_nrl,
ppm_g_nrl, ppm_a_contrasts, ppm_g_contrasts, variation_coeff,
free_energy[1:], free_energy_crit[1:], beta_list[1:],
delay_of_response, delay_of_undershoot, dispersion_of_response,
dispersion_of_undershoot, ratio_resp_under, delay)
