def cross_val_score_GLasso(data, fold=5, alpha=0.01):
n = data.shape[0]
m = int(n / fold)
score = {}
score['log_lik'] = 0
score['AIC'] = 0
score['non_zero'] = 0
for i in range(1, fold + 1):
test_index = np.arange((i - 1) * m, i * m)
#print(test_index)
train_index = np.delete(np.arange(0, n), test_index)
test_data = data[test_index, :]
train_data = data[train_index, :]
cov = sample_cov(test_data)
model = GraphicalLasso(alpha=alpha)
model.fit(train_data)
prec = model.precision_
score['log_lik'] += log_likelihood(cov, prec) / fold
score['AIC'] += AIC(cov, prec, n - m) / fold
score['non_zero'] += L0_penal(prec) / fold
return score
def glasso_results(data_grid, K, K_obs, ells, alpha):
gl = GLsk(alpha=alpha, mode='cd', assume_centered=False, max_iter=500)
tic = time.time()
iters = []
precisions = []
for d in data_grid.transpose(2, 0, 1):
gl.fit(d)
iters.append(gl.n_iter_)
precisions.append(gl.precision_)
tac = time.time()
iterations = np.max(iters)
precisions = np.array(precisions)
ss = utils.structure_error(K, precisions) #, thresholding=1, eps=1e-5)
MSE_observed = None
MSE_precision = utils.error_norm(K, precisions, upper_triangular=True)
MSE_latent = None
mean_rank_error = None
res = dict(n_dim_obs=K.shape[1],
time=tac - tic,
iterations=iterations,
MSE_precision=MSE_precision,
MSE_observed=MSE_observed,
MSE_latent=MSE_latent,
mean_rank_error=mean_rank_error,
likelihood=likelihood_score(data_grid.transpose(2, 0, 1),
precisions),
note=None,
estimator=gl)
res = dict(res, **ss)
return res
def test_gowl_vs_glasso_duality_gap_3(self):
"""
Duality Gap goes negative in this case. Should that happen?
"""
np.random.seed(680)
p = 10
blocks = [
Block(dim=p,
idx=0,
block_min_size=2,
block_max_size=6,
block_value=0.9),
Block(dim=p,
idx=1,
block_min_size=2,
block_max_size=6,
block_value=-0.9),
Block(dim=p,
idx=3,
block_min_size=2,
block_max_size=6,
block_value=-0.5),
]
theta_star, blocks, theta_blocks = generate_theta_star_gowl(p=p,
alpha=0.5,
noise=0.1,
blocks=blocks)
lam1 = 0.001 # controls sparsity
lam2 = 0.01 # encourages equality of coefficients
rho = oscar_weights(lam1, lam2, (p ** 2 - p) / 2)
theta_star = theta_star[0]
sigma = np.linalg.inv(theta_star)
n = 100
X = np.random.multivariate_normal(np.zeros(p), sigma, n)
X = standardize(X)
S = np.cov(X.T)
theta_0 = np.linalg.inv(S)
model = GOWLModel(X, S, theta_0, lam1, lam2, 'backtracking', max_iters=100000)
model.fit()
theta_gowl = model.theta_hat
gl = GraphicalLasso(max_iter=200)
gl.fit(S)
theta_glasso = gl.get_precision()
print('Non zero entries in precision matrix {}'.format(np.count_nonzero(theta_gowl)))
plot_multiple_theta_matrices_2d([theta_blocks, theta_star, theta_glasso, theta_gowl],
[f"Blocks: {len(blocks)}", 'True Theta', 'GLASSO', 'GOWL'])
_fit_evaluations(theta_star, theta_glasso, 3, 'GLASSO')
_fit_evaluations(theta_star, theta_gowl, 3, 'GOWL')
y_hat_gowl = spectral_clustering(theta=theta_gowl, K=4)
y_hat_glasso = spectral_clustering(theta=theta_glasso, K=4)
y_true = spectral_clustering(theta=theta_blocks, K=4).flatten()
_cluster_evaluations(y_true, y_hat_gowl, 'GOWL')
_cluster_evaluations(y_true, y_hat_glasso, 'GLASSO')
def get_optimal_cov_estimator(time_series):
from sklearn.covariance import GraphicalLassoCV
estimator = GraphicalLassoCV(cv=5, assume_centered=True)
print("\nSearching for best Lasso estimator...\n")
try:
estimator.fit(time_series)
return estimator
except BaseException:
ix = 0
print("\nModel did not converge on first attempt. "
"Varying tolerance...\n")
while not hasattr(estimator, 'covariance_') and \
not hasattr(estimator, 'precision_') and ix < 3:
for tol in [0.1, 0.01, 0.001, 0.0001]:
print(f"Tolerance={tol}")
estimator = GraphicalLassoCV(cv=5,
max_iter=200,
tol=tol,
assume_centered=True)
try:
estimator.fit(time_series)
return estimator
except BaseException:
ix += 1
continue
if not hasattr(estimator, 'covariance_') and not hasattr(
estimator, 'precision_'):
print("Unstable Lasso estimation. Applying shrinkage to empirical "
"covariance...")
from sklearn.covariance import (
GraphicalLasso,
empirical_covariance,
shrunk_covariance,
)
try:
emp_cov = empirical_covariance(time_series, assume_centered=True)
for i in np.arange(0.8, 0.99, 0.01):
print(f"Shrinkage={i}:")
shrunk_cov = shrunk_covariance(emp_cov, shrinkage=i)
alphaRange = 10.0**np.arange(-8, 0)
for alpha in alphaRange:
print(f"Auto-tuning alpha={alpha}...")
estimator_shrunk = GraphicalLasso(alpha,
assume_centered=True)
try:
estimator_shrunk.fit(shrunk_cov)
return estimator_shrunk
except BaseException:
continue
except BaseException:
return None
else:
return estimator
def predict(self,
data: pd.DataFrame,
alpha: float = 0.01,
max_iter: int = 2000,
**kwargs) -> nx.Graph:
"""Predict the graph structure """
edge_model = GraphicalLasso(alpha=alpha, max_iter=max_iter)
edge_model.fit(data.values)
return nx.relabel_nodes(nx.DiGraph(edge_model.get_precision()),
{idx: i
for idx, i in enumerate(data.columns)})
def get_mean_cov(x, y):
model = GraphicalLasso()
ones = (y == 1).astype(bool)
x2 = x[ones]
model.fit(x2)
p1 = model.precision_
m1 = model.location_
onesb = (y == 0).astype(bool)
x2b = x[onesb]
model.fit(x2b)
p2 = model.precision_
m2 = model.location_
ms = np.stack([m1, m2])
ps = np.stack([p1, p2])
return ms, ps
def predict(self, data, alpha=0.01, max_iter=2000, **kwargs):
""" Predict the graph skeleton.
Args:
data (pandas.DataFrame): observational data
alpha (float): regularization parameter
max_iter (int): maximum number of iterations
Returns:
networkx.Graph: Graph skeleton
"""
edge_model = GraphicalLasso(alpha=alpha, max_iter=max_iter)
edge_model.fit(data.values)
return nx.relabel_nodes(nx.DiGraph(edge_model.get_precision()),
{idx: i
for idx, i in enumerate(data.columns)})
def get_mean_cov(x, y):
#print(x.shape)
ms_list = []
ps_list = []
# Label equals to One
ones = (y == 1).astype(bool)
model = GraphicalLasso()
x2 = x[ones]
kmeans = GaussianMixture(n_components=3,
init_params='random',
covariance_type='full')
new_label = kmeans.fit_predict(x2)
for elem in range(3):
index = np.where(new_label == elem)
tmp_df = x2[index]
#print(tmp_df.shape)
model.fit(tmp_df)
p1 = model.precision_
m1 = model.location_
ms_list.append(m1)
ps_list.append(p1)
# Label equals to Zero
onesb = (y == 0).astype(bool)
x2b = x[onesb]
kmeans = GaussianMixture(n_components=3,
init_params='random',
covariance_type='full')
new_label = kmeans.fit_predict(x2b)
model = GraphicalLasso()
for elem in range(3):
index = np.where(new_label == elem)
tmp_df = x2b[index]
model.fit(tmp_df)
p1 = model.precision_
m1 = model.location_
ms_list.append(m1)
ps_list.append(p1)
ms = np.stack(ms_list)
ps = np.stack(ps_list)
return ms, ps
class GraphicalLassoComputer(SklearnComputer):
def fit(self):
if not self.is_fitted:
all_x = [
elem.reshape(-1) for a_list in self.data.values()
for elem in a_list
]
e = None
for alpha in np.logspace(-1, 5, 10):
try:
self.estimator = GraphicalLasso(assume_centered=False,
alpha=alpha)
self.estimator.fit(all_x)
self.is_fitted = True
return
except Exception as e:
logger.error(f"Graphical lasso failed with alpha={alpha}")
raise e
def get_mean_cov(x,y):
max_label = y.astype(int).max()
ps = []
ms = []
for i in range(max_label + 1):
model = GraphicalLasso()
label_i = (y==i).astype(bool)
x2 = x[label_i]
model.fit(x2)
ps.append(model.precision_)
ms.append(model.location_)
ms = np.stack(ms)
ps = np.stack(ps)
return ms,ps
def get_mean_cov3(x, y):
#print(x.shape)
ms_list = []
ps_list = []
# Label equals to One
ones = (y == 1).astype(bool)
model = GraphicalLasso()
x2 = x[ones]
kmeans = KMeans(n_clusters=3, random_state=0, algorithm='elkan').fit(x2)
new_label = kmeans.labels_
for elem in range(3):
index = np.where(new_label == elem)
tmp_df = x2[index]
#print(tmp_df.shape)
model.fit(tmp_df)
p1 = model.precision_
m1 = model.location_
ms_list.append(m1)
ps_list.append(p1)
# Label equals to Zero
onesb = (y == 0).astype(bool)
x2b = x[onesb]
kmeans = KMeans(n_clusters=3, random_state=0, algorithm='elkan').fit(x2b)
new_label = kmeans.labels_
model = GraphicalLasso()
for elem in range(3):
index = np.where(new_label == elem)
tmp_df = x2b[index]
model.fit(tmp_df)
p1 = model.precision_
m1 = model.location_
ms_list.append(m1)
ps_list.append(p1)
ms = np.stack(ms_list)
ps = np.stack(ps_list)
return ms, ps
def test_SGL_scikit():
"""
test single Graphical Lasso solver vs. scikit-learn
"""
p = 10
N = 100
Sigma, Theta = generate_precision_matrix(p=p,
M=2,
style='erdos',
gamma=2.8,
prob=0.1,
scale=False,
nxseed=None)
S, samples = sample_covariance_matrix(
Sigma, N) # sample from multivar_norm(Sigma)
lambda1 = 0.01
singleGL = GraphicalLasso(alpha=lambda1,
tol=1e-6,
max_iter=500,
verbose=False)
model = singleGL.fit(samples.T) # transpose because of sklearn format
sol_scikit = model.precision_
Omega_0 = np.eye(p)
sol, info = ADMM_SGL(S,
lambda1,
Omega_0,
tol=1e-7,
rtol=1e-5,
verbose=True,
latent=False)
# run into max_iter
sol2, info2 = ADMM_SGL(S,
lambda1,
Omega_0,
stopping_criterion='kkt',
tol=1e-20,
max_iter=200,
verbose=True,
latent=False)
assert_array_almost_equal(sol_scikit, sol['Theta'], 3)
assert_array_almost_equal(sol_scikit, sol2['Theta'], 3)
return
def glasso(subsamples, alpha, precision_tol=1e-4, glasso_params={}):
"""Run the graphical lasso from scikit learn over the given
subsamples, at the given regularization level.
Parameters:
- subsamples (np.array): the subsample array
- alpha (float): the regularization parameter at which to run
the estimator, taken as 1/lambda, i.e, lower values mean
sparser
Returns:
- estimates (np.array): The adjacency matrices of the graphs
estimated for each subsample
"""
(N, _, p) = subsamples.shape
precisions = np.zeros((len(subsamples), p, p))
g = GraphicalLasso(alpha=1 / alpha, **glasso_params)
for j, sample in enumerate(subsamples):
precision = g.fit(sample).precision_
precisions[j, :, :] = precision - np.diag(np.diag(precision))
estimates = (abs(precisions) > precision_tol).astype(int)
return estimates
def get_conn_matrix(time_series, conn_model, dir_path, node_size, smooth,
dens_thresh, network, ID, roi, min_span_tree, disp_filt,
parc, prune, atlas_select, uatlas_select, label_names,
coords, c_boot, norm, binary):
from nilearn.connectome import ConnectivityMeasure
from sklearn.covariance import GraphicalLassoCV
conn_matrix = None
if conn_model == 'corr' or conn_model == 'cor' or conn_model == 'correlation':
# credit: nilearn
print('\nComputing correlation matrix...\n')
conn_measure = ConnectivityMeasure(kind='correlation')
conn_matrix = conn_measure.fit_transform([time_series])[0]
elif conn_model == 'partcorr' or conn_model == 'parcorr' or conn_model == 'partialcorrelation':
# credit: nilearn
print('\nComputing partial correlation matrix...\n')
conn_measure = ConnectivityMeasure(kind='partial correlation')
conn_matrix = conn_measure.fit_transform([time_series])[0]
elif conn_model == 'cov' or conn_model == 'covariance' or conn_model == 'covar' or conn_model == 'sps' or conn_model == 'sparse' or conn_model == 'precision':
# Fit estimator to matrix to get sparse matrix
estimator_shrunk = None
estimator = GraphicalLassoCV(cv=5)
try:
print('\nComputing covariance...\n')
estimator.fit(time_series)
except:
print(
'Unstable Lasso estimation--Attempting to re-run by first applying shrinkage...'
)
try:
from sklearn.covariance import GraphicalLasso, empirical_covariance, shrunk_covariance
emp_cov = empirical_covariance(time_series)
for i in np.arange(0.8, 0.99, 0.01):
shrunk_cov = shrunk_covariance(emp_cov, shrinkage=i)
alphaRange = 10.0**np.arange(-8, 0)
for alpha in alphaRange:
try:
estimator_shrunk = GraphicalLasso(alpha)
estimator_shrunk.fit(shrunk_cov)
print(
"Retrying covariance matrix estimate with alpha=%s"
% alpha)
if estimator_shrunk is None:
pass
else:
break
except:
print(
"Covariance estimation failed with shrinkage at alpha=%s"
% alpha)
continue
except ValueError:
print(
'Unstable Lasso estimation! Shrinkage failed. A different connectivity model may be needed.'
)
if estimator is None and estimator_shrunk is None:
raise RuntimeError('\nERROR: Covariance estimation failed.')
if conn_model == 'sps' or conn_model == 'sparse' or conn_model == 'precision':
if estimator_shrunk is None:
print(
'\nFetching precision matrix from covariance estimator...\n'
)
conn_matrix = -estimator.precision_
else:
print(
'\nFetching shrunk precision matrix from covariance estimator...\n'
)
conn_matrix = -estimator_shrunk.precision_
elif conn_model == 'cov' or conn_model == 'covariance' or conn_model == 'covar':
if estimator_shrunk is None:
print(
'\nFetching covariance matrix from covariance estimator...\n'
)
conn_matrix = estimator.covariance_
else:
conn_matrix = estimator_shrunk.covariance_
elif conn_model == 'QuicGraphicalLasso':
try:
from inverse_covariance import QuicGraphicalLasso
except ImportError:
print('Cannot run QuicGraphLasso. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLasso
# credit: skggm
model = QuicGraphicalLasso(init_method='cov',
lam=0.5,
mode='default',
verbose=1)
print('\nCalculating QuicGraphLasso precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'QuicGraphLassoCV':
try:
from inverse_covariance import QuicGraphicalLassoCV
except ImportError:
print('Cannot run QuicGraphLassoCV. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLassoCV
# credit: skggm
model = QuicGraphicalLassoCV(init_method='cov', verbose=1)
print(
'\nCalculating QuicGraphLassoCV precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'QuicGraphicalLassoEBIC':
try:
from inverse_covariance import QuicGraphicalLassoEBIC
except ImportError:
print('Cannot run QuicGraphLassoEBIC. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLassoEBIC
# credit: skggm
model = QuicGraphicalLassoEBIC(init_method='cov', verbose=1)
print(
'\nCalculating QuicGraphLassoEBIC precision matrix using skggm...\n'
)
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'AdaptiveQuicGraphLasso':
try:
from inverse_covariance import AdaptiveQuicGraphicalLasso, QuicGraphicalLassoEBIC
except ImportError:
print('Cannot run AdaptiveGraphLasso. Skggm not installed!')
# Compute the sparse inverse covariance via
# AdaptiveGraphLasso + QuicGraphLassoEBIC + method='binary'
# credit: skggm
model = AdaptiveQuicGraphicalLasso(
estimator=QuicGraphicalLassoEBIC(init_method='cov', ),
method='binary',
)
print(
'\nCalculating AdaptiveQuicGraphLasso precision matrix using skggm...\n'
)
model.fit(time_series)
conn_matrix = -model.estimator_.precision_
else:
raise ValueError(
'\nERROR! No connectivity model specified at runtime. Select a valid estimator using the '
'-mod flag.')
if conn_matrix.shape < (2, 2):
raise RuntimeError(
'\nERROR! Matrix estimation selection yielded an empty or 1-dimensional graph. '
'Check time-series for errors or try using a different atlas')
coords = np.array(coords)
label_names = np.array(label_names)
return conn_matrix, conn_model, dir_path, node_size, smooth, dens_thresh, network, ID, roi, min_span_tree, disp_filt, parc, prune, atlas_select, uatlas_select, label_names, coords, c_boot, norm, binary
ALPHA = 2 * np.logspace(start=-3, stop=-1, num=15, base=10)
FPR_GL = np.zeros(len(ALPHA))
TPR_GL = np.zeros(len(ALPHA))
DFPR_GL = np.zeros(len(ALPHA))
DTPR_GL = np.zeros(len(ALPHA))
for a in np.arange(len(ALPHA)):
singleGL = GraphicalLasso(alpha=ALPHA[a],
tol=1e-6,
max_iter=200,
verbose=False)
singleGL_sol = np.zeros((K, p, p))
for k in np.arange(K):
#model = quic.fit(S[k,:,:], verbose = 1)
model = singleGL.fit(sample[k, :, :].T)
singleGL_sol[k, :, :] = model.precision_
TPR_GL[a] = discovery_rate(singleGL_sol, Theta)['TPR']
FPR_GL[a] = discovery_rate(singleGL_sol, Theta)['FPR']
DTPR_GL[a] = discovery_rate(singleGL_sol, Theta)['TPR_DIFF']
DFPR_GL[a] = discovery_rate(singleGL_sol, Theta)['FPR_DIFF']
#%%
# solve again for optimal (l1, l2)
l1opt = L1[ix]
l2opt = L2[ix]
print("Optimal lambda values: (l1,l2) = ", (l1opt, l2opt))
Omega_0 = get_K_identity(K, p)
Theta_0 = get_K_identity(K, p)
ns = nitk.NeighbourhoodSelection(l)
ns.fit(X)
tpr, fpr, prec = nitk.methods.calculate_matrix_accuracy(
K, ns.precision_)
neighbourhood_selection_tpr.append(tpr)
neighbourhood_selection_fpr.append(fpr)
neighbourhood_selection_precision.append(prec)
glasso_tpr = []
glasso_fpr = []
glasso_precision = []
for l in ls:
try:
gl = GraphicalLasso(l)
gl.fit(X)
tpr, fpr, prec = nitk.methods.calculate_matrix_accuracy(
K, gl.precision_)
glasso_tpr.append(tpr)
glasso_fpr.append(fpr)
glasso_precision.append(prec)
except FloatingPointError as e:
print(e)
space_tpr = []
space_fpr = []
space_precision = []
for l in ls:
s = nitk.SPACE(l)
s.fit(X)
X = self.update_X(Y, Z, cov)
Y = self.soft_threshold(X + Z, self.alpha / self.rho)
Z = Z + self.alpha * (X - Y)
self.cov = np.linalg.inv(Y)
self.precision = Y
return self
if __name__ == "__main__":
A = load_boston().data
A = sp.stats.zscore(A, axis=0)
# ---sklearn---
model = GraphicalLasso(alpha=0.4, verbose=True)
model.fit(A)
cov = np.cov(A.T)
cov_ = model.covariance_
pre_ = model.precision_
model = GraphicalLassoADMM()
res = model.fit(A)
#print(res.precision)
#print(cov_)
# 普通の共分散行列
plt.imshow(cov, interpolation='nearest', vmin=0, vmax=1, cmap='jet')
plt.colorbar()
plt.figure()
# sklearnのglasso
ALPHA = 2 * np.logspace(start=-3, stop=-1, num=20, base=10)
FPR_GL = np.zeros(len(ALPHA))
TPR_GL = np.zeros(len(ALPHA))
DFPR_GL = np.zeros(len(ALPHA))
DTPR_GL = np.zeros(len(ALPHA))
for a in np.arange(len(ALPHA)):
singleGL = GraphicalLasso(alpha=ALPHA[a],
tol=1e-6,
max_iter=200,
verbose=False)
singleGL_sol = np.zeros((K, p, p))
for k in np.arange(K):
model = singleGL.fit(sample_train[k, :, :].T)
singleGL_sol[k, :, :] = model.precision_
TPR_GL[a] = discovery_rate(singleGL_sol, Theta)['TPR']
FPR_GL[a] = discovery_rate(singleGL_sol, Theta)['FPR']
DTPR_GL[a] = discovery_rate(singleGL_sol, Theta)['TPR_DIFF']
DFPR_GL[a] = discovery_rate(singleGL_sol, Theta)['FPR_DIFF']
#%% solve again for optimal (l1, l2)
l1opt = L1[ix]
l2opt = L2[ix]
print("Optimal lambda values: (l1,l2) = ", (l1opt, l2opt))
Omega_0 = get_K_identity(K, p)
Theta_0 = get_K_identity(K, p)
def get_conn_matrix(time_series, conn_model, dir_path, node_size, smooth, dens_thresh, network, ID, roi, min_span_tree,
disp_filt, parc, prune, atlas, uatlas, labels, coords, norm, binary,
hpass, extract_strategy):
"""
Computes a functional connectivity matrix based on a node-extracted time-series array.
Includes a library of routines across Nilearn, scikit-learn, and skggm packages, among others.
Parameters
----------
time_series : array
2D m x n array consisting of the time-series signal for each ROI node where m = number of scans and
n = number of ROI's.
conn_model : str
Connectivity estimation model (e.g. corr for correlation, cov for covariance, sps for precision covariance,
partcorr for partial correlation). sps type is used by default.
dir_path : str
Path to directory containing subject derivative data for given run.
node_size : int
Spherical centroid node size in the case that coordinate-based centroids
are used as ROI's.
smooth : int
Smoothing width (mm fwhm) to apply to time-series when extracting signal from ROI's.
dens_thresh : bool
Indicates whether a target graph density is to be used as the basis for
thresholding.
network : str
Resting-state network based on Yeo-7 and Yeo-17 naming (e.g. 'Default') used to filter nodes in the study of
brain subgraphs.
ID : str
A subject id or other unique identifier.
roi : str
File path to binarized/boolean region-of-interest Nifti1Image file.
min_span_tree : bool
Indicates whether local thresholding from the Minimum Spanning Tree
should be used.
disp_filt : bool
Indicates whether local thresholding using a disparity filter and
'backbone network' should be used.
parc : bool
Indicates whether to use parcels instead of coordinates as ROI nodes.
prune : bool
Indicates whether to prune final graph of disconnected nodes/isolates.
atlas : str
Name of atlas parcellation used.
uatlas : str
File path to atlas parcellation Nifti1Image in MNI template space.
labels : list
List of string labels corresponding to ROI nodes.
coords : list
List of (x, y, z) tuples corresponding to a coordinate atlas used or
which represent the center-of-mass of each parcellation node.
norm : int
Indicates method of normalizing resulting graph.
binary : bool
Indicates whether to binarize resulting graph edges to form an
unweighted graph.
hpass : bool
High-pass filter values (Hz) to apply to node-extracted time-series.
extract_strategy : str
The name of a valid function used to reduce the time-series region extraction.
Returns
-------
conn_matrix : array
Adjacency matrix stored as an m x n array of nodes and edges.
conn_model : str
Connectivity estimation model (e.g. corr for correlation, cov for covariance, sps for precision covariance,
partcorr for partial correlation). sps type is used by default.
dir_path : str
Path to directory containing subject derivative data for given run.
node_size : int
Spherical centroid node size in the case that coordinate-based centroids
are used as ROI's for tracking.
smooth : int
Smoothing width (mm fwhm) to apply to time-series when extracting signal from ROI's.
dens_thresh : bool
Indicates whether a target graph density is to be used as the basis for
thresholding.
network : str
Resting-state network based on Yeo-7 and Yeo-17 naming (e.g. 'Default') used to filter nodes in the study of
brain subgraphs.
ID : str
A subject id or other unique identifier.
roi : str
File path to binarized/boolean region-of-interest Nifti1Image file.
min_span_tree : bool
Indicates whether local thresholding from the Minimum Spanning Tree
should be used.
disp_filt : bool
Indicates whether local thresholding using a disparity filter and
'backbone network' should be used.
parc : bool
Indicates whether to use parcels instead of coordinates as ROI nodes.
prune : bool
Indicates whether to prune final graph of disconnected nodes/isolates.
atlas : str
Name of atlas parcellation used.
uatlas : str
File path to atlas parcellation Nifti1Image in MNI template space.
labels : list
List of string labels corresponding to graph nodes.
coords : list
List of (x, y, z) tuples corresponding to a coordinate atlas used or
which represent the center-of-mass of each parcellation node.
norm : int
Indicates method of normalizing resulting graph.
binary : bool
Indicates whether to binarize resulting graph edges to form an
unweighted graph.
hpass : bool
High-pass filter values (Hz) to apply to node-extracted time-series.
extract_strategy : str
The name of a valid function used to reduce the time-series region extraction.
References
----------
.. [1] Varoquaux, G., & Craddock, R. C. (2013). Learning and comparing functional connectomes
across subjects. NeuroImage. https://doi.org/10.1016/j.neuroimage.2013.04.007
.. [2] Jason Laska, Manjari Narayan, 2017. skggm 0.2.7: A scikit-learn compatible package
for Gaussian and related Graphical Models. doi:10.5281/zenodo.830033
"""
from nilearn.connectome import ConnectivityMeasure
from sklearn.covariance import GraphicalLassoCV
conn_matrix = None
if conn_model == 'corr' or conn_model == 'cor' or conn_model == 'correlation':
# credit: nilearn
print('\nComputing correlation matrix...\n')
conn_measure = ConnectivityMeasure(kind='correlation')
conn_matrix = conn_measure.fit_transform([time_series])[0]
elif conn_model == 'partcorr' or conn_model == 'parcorr' or conn_model == 'partialcorrelation':
# credit: nilearn
print('\nComputing partial correlation matrix...\n')
conn_measure = ConnectivityMeasure(kind='partial correlation')
conn_matrix = conn_measure.fit_transform([time_series])[0]
elif conn_model == 'cov' or conn_model == 'covariance' or conn_model == 'covar' or conn_model == 'sps' or \
conn_model == 'sparse' or conn_model == 'precision':
# Fit estimator to matrix to get sparse matrix
estimator_shrunk = None
estimator = GraphicalLassoCV(cv=5)
try:
print('\nComputing covariance...\n')
estimator.fit(time_series)
except:
print('Unstable Lasso estimation--Attempting to re-run by first applying shrinkage...')
try:
from sklearn.covariance import GraphicalLasso, empirical_covariance, shrunk_covariance
emp_cov = empirical_covariance(time_series)
for i in np.arange(0.8, 0.99, 0.01):
shrunk_cov = shrunk_covariance(emp_cov, shrinkage=i)
alphaRange = 10.0 ** np.arange(-8, 0)
for alpha in alphaRange:
try:
estimator_shrunk = GraphicalLasso(alpha)
estimator_shrunk.fit(shrunk_cov)
print(f"Retrying covariance matrix estimate with alpha={alpha}")
if estimator_shrunk is None:
pass
else:
break
except:
print(f"Covariance estimation failed with shrinkage at alpha={alpha}")
continue
except ValueError:
print('Unstable Lasso estimation! Shrinkage failed. A different connectivity model may be needed.')
if estimator is None and estimator_shrunk is None:
raise RuntimeError('\nERROR: Covariance estimation failed.')
if conn_model == 'sps' or conn_model == 'sparse' or conn_model == 'precision':
if estimator_shrunk is None:
print('\nFetching precision matrix from covariance estimator...\n')
conn_matrix = -estimator.precision_
else:
print('\nFetching shrunk precision matrix from covariance estimator...\n')
conn_matrix = -estimator_shrunk.precision_
elif conn_model == 'cov' or conn_model == 'covariance' or conn_model == 'covar':
if estimator_shrunk is None:
print('\nFetching covariance matrix from covariance estimator...\n')
conn_matrix = estimator.covariance_
else:
conn_matrix = estimator_shrunk.covariance_
elif conn_model == 'QuicGraphicalLasso':
try:
from inverse_covariance import QuicGraphicalLasso
except ImportError:
print('Cannot run QuicGraphLasso. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLasso
# credit: skggm
model = QuicGraphicalLasso(
init_method='cov',
lam=0.5,
mode='default',
verbose=1)
print('\nCalculating QuicGraphLasso precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'QuicGraphicalLassoCV':
try:
from inverse_covariance import QuicGraphicalLassoCV
except ImportError:
print('Cannot run QuicGraphLassoCV. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLassoCV
# credit: skggm
model = QuicGraphicalLassoCV(
init_method='cov',
verbose=1)
print('\nCalculating QuicGraphLassoCV precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'QuicGraphicalLassoEBIC':
try:
from inverse_covariance import QuicGraphicalLassoEBIC
except ImportError:
print('Cannot run QuicGraphLassoEBIC. Skggm not installed!')
# Compute the sparse inverse covariance via QuicGraphLassoEBIC
# credit: skggm
model = QuicGraphicalLassoEBIC(
init_method='cov',
verbose=1)
print('\nCalculating QuicGraphLassoEBIC precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.precision_
elif conn_model == 'AdaptiveQuicGraphicalLasso':
try:
from inverse_covariance import AdaptiveQuicGraphicalLasso, QuicGraphicalLassoEBIC
except ImportError:
print('Cannot run AdaptiveGraphLasso. Skggm not installed!')
# Compute the sparse inverse covariance via
# AdaptiveGraphLasso + QuicGraphLassoEBIC + method='binary'
# credit: skggm
model = AdaptiveQuicGraphicalLasso(
estimator=QuicGraphicalLassoEBIC(
init_method='cov',
),
method='binary',
)
print('\nCalculating AdaptiveQuicGraphLasso precision matrix using skggm...\n')
model.fit(time_series)
conn_matrix = -model.estimator_.precision_
else:
raise ValueError('\nERROR! No connectivity model specified at runtime. Select a valid estimator using the '
'-mod flag.')
# Enforce symmetry
conn_matrix = np.maximum(conn_matrix, conn_matrix.T)
if conn_matrix.shape < (2, 2):
raise RuntimeError('\nERROR! Matrix estimation selection yielded an empty or 1-dimensional graph. '
'Check time-series for errors or try using a different atlas')
coords = np.array(coords)
labels = np.array(labels)
del time_series
return (conn_matrix, conn_model, dir_path, node_size, smooth, dens_thresh, network, ID, roi, min_span_tree,
disp_filt, parc, prune, atlas, uatlas, labels, coords, norm, binary, hpass, extract_strategy)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.covariance import GraphicalLasso
filename = "expr_ceph_utah_1000.txt"
data = pd.read_csv(filename, delimiter='\t', index_col=0)
n_rows = data.shape[0]
n_cols = data.shape[1]
cov_matrix = np.cov(data.T)
np.savetxt("cov_matrix.csv", cov_matrix, delimiter=',')
model = GraphicalLasso(alpha=0.55)
model.fit(data)
prec_matrix = model.get_precision()
# print(prec_matrix)
np.savetxt("precision_matrix.csv", prec_matrix, delimiter=',')
n = n_cols
adj_matrix = np.zeros((n, n))
n_edges = 0
for i in range(n):
for j in range(i, n):
if prec_matrix[i, j] != 0:
adj_matrix[i, j] = 1
adj_matrix[j, i] = 1
n_edges += 1
np.savetxt("glasso_adj_matrix.csv", adj_matrix, delimiter=',')
degree_list = np.sum(adj_matrix, axis=0) - 1
def block_glasso(data, eps=1e-8, COLLECT=True):
criterion = nn.MSELoss() # input, target
theta_true, X = data
# #############################################################################
# Estimate the covariance
print('Using the lars method')
S = np.dot(X.T, X) / args.M
# model = GraphicalLassoCV(cv=2, alphas=5, n_refinements=5, tol=1e-6,
# max_iter=100, mode='lars', n_jobs=-1)
model = GraphicalLasso(alpha=args.rho,
mode='lars',
tol=1e-7,
enet_tol=1e-6,
max_iter=args.MAX_EPOCH,
verbose=True,
assume_centered=True)
# model = GraphLasso(alpha=args.rho, mode='lars', tol=1e-8, enet_tol=1e-6,
# max_iter=100, verbose=False, assume_centered=False)
# print('Using the cd method')
# model = GraphicalLassoCV(cv=2, alphas=5, n_refinements=5, tol=1e-6,
# max_iter=100, mode='cd', n_jobs=-1)
model.fit(X)
cov_ = model.covariance_
theta_pred = model.precision_
# #############################################################################
fdr, tpr, fpr, shd, nnz, nnz_true, ps = metrics.report_metrics(
theta_true, theta_pred)
cond_theta_pred, cond_theta_true = np.linalg.cond(
theta_pred), np.linalg.cond(theta_true)
num_itr = model.n_iter_
rho_obtained = args.rho # the L1 penalty parameter
print('Accuracy metrics: fdr ', fdr, ' tpr ', tpr, ' fpr ', fpr, ' shd ',
shd, ' nnz ', nnz, ' nnz_true ', nnz_true, ' sign_match ', ps,
' pred_cond ', cond_theta_pred, ' true_cond ', cond_theta_true,
'total itr: ', num_itr, ' penalty_rho: ', rho_obtained)
# Getting the NMSE and objective value
# results of convergence
res_conv = []
theta_true = convert_to_torch(theta_true, TESTING_FLAG=True)
theta_pred = convert_to_torch(theta_pred, TESTING_FLAG=True)
S = convert_to_torch(S, TESTING_FLAG=True)
obj_true = get_obj_val(theta_true, S)
if COLLECT:
theta_pred_diag = torch.diag_embed(
torch.diagonal(theta_pred, offset=0, dim1=-2, dim2=-1))
theta_true_diag = torch.diag_embed(
torch.diagonal(theta_true, offset=0, dim1=-2, dim2=-1))
cv_loss, cv_loss_off_diag, obj_pred = get_convergence_loss(
theta_pred, theta_true), get_convergence_loss(
theta_pred - theta_pred_diag,
theta_true - theta_true_diag), get_obj_val(theta_pred, S)
res_conv.append([cv_loss, obj_pred, obj_true, cv_loss_off_diag])
return [
fdr, tpr, fpr, shd, nnz, nnz_true, ps, cond_theta_pred,
cond_theta_true, num_itr, rho_obtained
], res_conv # result of convergence
ix2 = np.unravel_index(np.nanargmin(AIC), AIC.shape)
lambda1 = L1[ix]
lambda2 = L2[ix]
print("Optimal lambda values: (l1,l2) = ", (lambda1, lambda2))
#%%
singleGL = GraphicalLasso(alpha=1.5 * lambda1,
tol=1e-2,
max_iter=4000,
verbose=True)
res = np.zeros((K, p, p))
for k in np.arange(K):
#model = quic.fit(S[k,:,:], verbose = 1)
model = singleGL.fit(samples[k, :, :])
res[k, :, :] = model.precision_
results['GLASSO'] = {'Theta': res}
#%%
start = time()
sol, info = ADMM_MGL(S, lambda1, lambda2, reg, Omega_0, rho = 1, max_iter = 100, \
eps_admm = 1e-5, verbose = True, measure = True)
end = time()
print(f"Running time for ADMM was {end-start} seconds")
results['ADMM'] = {'Theta': sol['Theta']}