def _update_cholesky(self, emp_covs, maxiter=10, eps=1.0e-4, verbose=0):
"""
Core of spice: cholesky update
Parameters
----------
emp_covs: array of shape (n, p, p),
the sample covariances for each group of obervations
maxiter: int, optional
max. number iterations
eps: float, optional
threshold value on precision change to declare convergence
verbose: integer, optional
verbosity mode
"""
chol_precs_old = self.chol_precs.copy()
delta = eps * np.sum(np.sum(chol_precs_old ** 2, axis=-1), axis=-1).min()
# implement a L21 norm
initial_abs_precs = np.sqrt(np.sum(self.precisions ** 2, axis=0))
# Regularized 1/initial_abs_prec:
abs_inv_prec0 = emp_covs.shape[0] / (initial_abs_precs + eps ** 2)
# Put the diagonal to 0
p = abs_inv_prec0.shape[0]
abs_inv_prec0.flat[:: p + 1] = 0
for i in range(maxiter):
# L21: Call the L1 problem for all chol with the same
# penalty (initial_abs_prec)
for emp_cov, precision, chol_prec in zip(emp_covs, self.precisions, self.chol_precs):
_choleski_update_l1(emp_cov, precision, abs_inv_prec0, self.l21, chol_prec=chol_prec)
diff = np.sum(np.sum((chol_precs_old - self.chol_precs) ** 2, axis=-1), axis=-1).min()
if diff < delta:
if verbose:
print i, diff, delta
break
chol_precs_old = self.chol_precs.copy()
# Don't forget to update the precision
for precision, chol_prec in zip(self.precisions, self.chol_precs):
precision[...] = np.dot(chol_prec.T, chol_prec)
def _update_cholesky(self, emp_cov, maxiter=10, eps=1.0e-4, regularization=1e-8, verbose=0):
"""
Core of spice: cholesky update
Parameters
----------
emp_cov: array of shape (n, n),
the sample covariance of the obervations
maxiter: int, optional
max. number iterations
eps: float, optional
threshold value on precision change to declare convergence
regularization: float, optional
regularization of the inverse
verbose: integer, optional
verbosity mode
"""
chol_prec_old = self.chol_prec.copy()
delta = eps * np.sum(chol_prec_old ** 2)
initial_abs_prec = np.absolute(self.precision)
# Regularized 1/initial_abs_prec:
abs_inv_prec0 = 1 / (initial_abs_prec + regularization)
# Put the diagonal to zero
p = abs_inv_prec0.shape[0]
abs_inv_prec0.flat[:: p + 1] = 0
for i in range(maxiter):
_choleski_update_l1(emp_cov, self.precision, abs_inv_prec0, self.l1, chol_prec=self.chol_prec)
diff = np.sum((chol_prec_old - self.chol_prec) ** 2)
if diff < delta:
if verbose:
print i, diff, delta
break
chol_prec_old = self.chol_prec.copy()
# Don't forget to update the precision
self.precision = np.dot(self.chol_prec.T, self.chol_prec)
