def centralized_graphical_lasso(X, D, alpha=0.01, max_iter=100, convg_threshold=0.001):
""" This function computes the graphical lasso algorithm as outlined in Sparse inverse covariance estimation with the
graphical lasso (2007).
inputs:
X: the data matrix, size (nxd)
alpha: the coefficient of penalization, higher values means more sparseness.
max_iter: maximum number of iterations
convg_threshold: Stop the algorithm when the duality gap is below a certain threshold.
"""
if alpha == 0:
return cov_estimator(X)
n_features = X.shape[1]
mle_estimate_ = cov_estimator(X)
covariance_ = mle_estimate_.copy()
precision_ = np.linalg.pinv(mle_estimate_)
indices = np.arange(n_features)
for i in xrange(max_iter):
for n in range(n_features):
sub_estimate = covariance_[indices != n].T[indices != n]
row = mle_estimate_[n, indices != n]
# solve the lasso problem
# Not now DAAAAAAAAARLING! lez do the generalized lasso instead
# _, _, coefs_ = lars_path( sub_estimate, row, Xy = row, Gram = sub_estimate,
# alpha_min = alpha/(n_features-1.),
# method = "lars")
# coefs_ = coefs_[:,-1] #just the last please.
# clf = linear_model.Lasso(alpha=alpha)
# clf.fit(sub_estimate, row)
# coefs_ = clf.coef_
coefs_ = generalized_lasso(sub_estimate, row, D, alpha)
# update the precision matrix.
precision_[n, n] = 1.0 / (covariance_[n, n] - np.dot(covariance_[indices != n, n], coefs_))
precision_[indices != n, n] = -precision_[n, n] * coefs_
precision_[n, indices != n] = -precision_[n, n] * coefs_
temp_coefs = np.dot(sub_estimate, coefs_)
covariance_[n, indices != n] = temp_coefs
covariance_[indices != n, n] = temp_coefs
print "Finished iteration %s" % i
# if test_convergence( old_estimate_, new_estimate_, mle_estimate_, convg_threshold):
if np.abs(_dual_gap(mle_estimate_, precision_, alpha)) < convg_threshold:
break
else:
# this triggers if not break command occurs
print "The algorithm did not coverge. Try increasing the max number of iterations."
return covariance_, precision_
from generalized_lasso import generalized_lasso
from graphical_lasso import centralized_graphical_lasso
from matplotlib.pylab import *
import gett.io
print 'Testing generalized_lasso'
A = randn(4,40)
y = randn(4)
D = rand(3,40)
def lasso_fun(x):
return norm(dot(A,x) - y) + abs(dot(D, x).sum())
res = generalized_lasso(A, y, D, 1)
print 'Lasso result, evaluated in lasso function: %s' % lasso_fun(res)
print 'Random number, evaluated in lasso function: %s' % lasso_fun(randn(len(res)))
print 'Testing centralized_graphical_lasso'
# Read the heart failure eqtl dataset!
#samples, genenames, Mexp = gett.io.read_expression_matrix(open('../hf_eqtl/full_exp_varcutoff_50.txt'))
print 'Finished reading'
Mexp = randn(400,20000)
D = eye(Mexp.shape[0])
covariance, precision = centralized_graphical_lasso(Mexp.T, D, max_iter=1000)
print covariance
print precision
