def solve(y,
A,
At,
tol_fun=1e-4,
tol_x=1e-6,
max_iter=1000,
verbose=True,
x0=None,
regularisation=None,
confidence_array=None):
"""
Solve the regularised least squares problem
argmin_x 0.5*|| sqrt(W) ( Ax-y ) ||_2^2 + Omega(x)
with the Omega described by 'regularisation' and W is the confidence_array
Check the documentation of commit.solvers.init_regularisation to see how to
solve a specific problem.
"""
if regularisation is None:
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, x.size)
else:
omega, prox = regularisation2omegaprox(regularisation)
if x0 is None:
x0 = np.zeros(A.shape[1])
if confidence_array is not None:
confidence_array = np.sqrt(confidence_array)
return fista(y, A, At, tol_fun, tol_x, max_iter, verbose, x0, omega, prox,
confidence_array)
def solve(y,
A,
At,
tol_fun=1e-4,
tol_x=1e-6,
max_iter=1000,
verbose=1,
x0=None,
regularisation=None):
"""
Solve the regularised least squares problem
argmin_x 0.5*||Ax-y||_2^2 + Omega(x)
with the Omega described by 'regularisation'.
Check the documentation of commit.solvers.init_regularisation to see how to
solve a specific problem.
"""
if regularisation is None:
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, x.size)
else:
omega, prox = regularisation2omegaprox(regularisation)
if x0 is None:
x0 = np.ones(A.shape[1])
return fista(y, A, At, tol_fun, tol_x, max_iter, verbose, x0, omega, prox)
def evaluate_model(y, A, x, regularisation=None):
if regularisation is None:
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, len(x))
else:
omega, _ = regularisation2omegaprox(regularisation)
return 0.5 * np.linalg.norm(A.dot(x) - y)**2 + omega(x)
def evaluate_model(y, A, x, regularisation = None):
if regularisation is None:
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, len(x))
else:
omega, _ = regularisation2omegaprox(regularisation)
return 0.5*np.linalg.norm(A.dot(x)-y)**2 + omega(x)
def solve(y, A, At, tol_fun = 1e-4, tol_x = 1e-6, max_iter = 1000, verbose = 1, x0 = None, regularisation = None):
"""
Solve the regularised least squares problem
argmin_x 0.5*||Ax-y||_2^2 + Omega(x)
with the Omega described by 'regularisation'.
Check the documentation of commit.solvers.init_regularisation to see how to
solve a specific problem.
"""
if regularisation is None:
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, x.size)
else:
omega, prox = regularisation2omegaprox(regularisation)
if x0 is None:
x0 = np.zeros(A.shape[1])
return fista( y, A, At, tol_fun, tol_x, max_iter, verbose, x0, omega, prox)
def regularisation2omegaprox(regularisation):
lambdaIC = float(regularisation.get('lambdaIC'))
lambdaEC = float(regularisation.get('lambdaEC'))
lambdaISO = float(regularisation.get('lambdaISO'))
if lambdaIC < 0.0 or lambdaEC < 0.0 or lambdaISO < 0.0:
raise ValueError('Negative regularisation parameters are not allowed')
normIC = regularisation.get('normIC')
normEC = regularisation.get('normEC')
normISO = regularisation.get('normISO')
if not normIC in list_regnorms:
raise ValueError(
'normIC must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}'
)
if not normEC in list_regnorms:
raise ValueError(
'normEC must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}'
)
if not normISO in list_regnorms:
raise ValueError(
'normISO must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}'
)
## NNLS case
if (lambdaIC == 0.0 and lambdaEC == 0.0
and lambdaISO == 0.0) or (normIC == non_negative
and normEC == non_negative
and normISO == non_negative):
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, len(x))
return omega, prox
## All other cases
# Intracellular Compartment
startIC = regularisation.get('startIC')
sizeIC = regularisation.get('sizeIC')
if lambdaIC == 0.0:
omegaIC = lambda x: 0.0
proxIC = lambda x: x
elif normIC == norm2:
omegaIC = lambda x: lambdaIC * np.linalg.norm(x[startIC:sizeIC])
proxIC = lambda x: projection_onto_l2_ball(x, lambdaIC, startIC, sizeIC
)
elif normIC == norm1:
omegaIC = lambda x: lambdaIC * sum(x[startIC:sizeIC])
proxIC = lambda x: soft_thresholding(x, lambdaIC, startIC, sizeIC)
elif normIC == non_negative:
omegaIC = lambda x: 0.0
proxIC = lambda x: non_negativity(x, startIC, sizeIC)
elif normIC == group_sparsity:
weightsIC = regularisation.get('weightsIC')
structureIC = regularisation.get('structureIC')
if regularisation.get(
'group_is_ordered'
): # This option will be deprecated in future release
warnings.warn(
'The ordered group structure will be deprecated. Check the documentation of commit.solvers.init_regularisation.',
DeprecationWarning)
bundles = np.insert(structureIC, 0, 0)
structureIC = np.array([
np.arange(sum(bundles[:k + 1]),
sum(bundles[:k + 1]) + bundles[k + 1])
for k in range(len(bundles) - 1)
]) # check how it works with bundles=[2,5,4]
regularisation['structureIC'] = structureIC
regularisation[
'group_is_ordered'] = False # the group structure is overwritten, hence the flag has to be changed
del bundles
if not len(structureIC) == len(weightsIC):
raise ValueError('Number of groups and weights do not coincide.')
group_norm = regularisation.get('group_norm')
if not group_norm in list_group_sparsity_norms:
raise ValueError(
'Wrong norm in the structured sparsity term. Choose between %s.'
% str(list_group_sparsity_norms))
omegaIC = lambda x: omega_group_sparsity(x, structureIC, weightsIC,
lambdaIC, group_norm)
proxIC = lambda x: prox_group_sparsity(x, structureIC, weightsIC,
lambdaIC, group_norm)
else:
raise ValueError(
'Type of regularisation for IC compartment not recognized.')
# Extracellular Compartment
startEC = regularisation.get('startEC')
sizeEC = regularisation.get('sizeEC')
if lambdaEC == 0.0:
omegaEC = lambda x: 0.0
proxEC = lambda x: x
elif normEC == norm2:
omegaEC = lambda x: lambdaEC * np.linalg.norm(x[startEC:sizeEC])
proxEC = lambda x: projection_onto_l2_ball(x, lambdaEC, startEC, sizeEC
)
elif normEC == norm1:
omegaEC = lambda x: lambdaEC * sum(x[startEC:sizeEC])
proxEC = lambda x: soft_thresholding(x, lambdaEC, startEC, sizeEC)
elif normEC == non_negative:
omegaEC = lambda x: 0.0
proxEC = lambda x: non_negativity(x, startEC, sizeEC)
else:
raise ValueError(
'Type of regularisation for EC compartment not recognized.')
# Isotropic Compartment
startISO = regularisation.get('startISO')
sizeISO = regularisation.get('sizeISO')
if lambdaISO == 0.0:
omegaISO = lambda x: 0.0
proxISO = lambda x: x
elif normISO == norm2:
omegaISO = lambda x: lambdaISO * np.linalg.norm(x[startISO:sizeISO])
proxISO = lambda x: projection_onto_l2_ball(x, lambdaISO, startISO,
sizeISO)
elif normISO == norm1:
omegaISO = lambda x: lambdaISO * sum(x[startISO:sizeISO])
proxISO = lambda x: soft_thresholding(x, lambdaISO, startISO, sizeISO)
elif normISO == non_negative:
omegaISO = lambda x: 0.0
proxISO = lambda x: non_negativity(x, startISO, sizeISO)
else:
raise ValueError(
'Type of regularisation for ISO compartment not recognized.')
omega = lambda x: omegaIC(x) + omegaEC(x) + omegaISO(x)
prox = lambda x: non_negativity(proxIC(proxEC(proxISO(x))), 0, x.size
) # non negativity is redunduntly forced
return omega, prox
def regularisation2omegaprox(regularisation):
lambdaIC = float(regularisation.get('lambdaIC'))
lambdaEC = float(regularisation.get('lambdaEC'))
lambdaISO = float(regularisation.get('lambdaISO'))
if lambdaIC < 0.0 or lambdaEC < 0.0 or lambdaISO < 0.0:
raise ValueError('Negative regularisation parameters are not allowed')
normIC = regularisation.get('normIC')
normEC = regularisation.get('normEC')
normISO = regularisation.get('normISO')
if not normIC in list_regnorms:
raise ValueError('normIC must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}')
if not normEC in list_regnorms:
raise ValueError('normEC must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}')
if not normISO in list_regnorms:
raise ValueError('normISO must be one of commit.solvers.{group_sparsity,non_negative,norm1,norm2}')
## NNLS case
if (lambdaIC == 0.0 and lambdaEC == 0.0 and lambdaISO == 0.0) or (normIC == non_negative and normEC == non_negative and normISO == non_negative):
omega = lambda x: 0.0
prox = lambda x: non_negativity(x, 0, len(x))
return omega, prox
## All other cases
# Intracellular Compartment
startIC = regularisation.get('startIC')
sizeIC = regularisation.get('sizeIC')
if lambdaIC == 0.0:
omegaIC = lambda x: 0.0
proxIC = lambda x: x
elif normIC == norm2:
omegaIC = lambda x: lambdaIC * np.linalg.norm(x[startIC:sizeIC])
proxIC = lambda x: projection_onto_l2_ball(x, lambdaIC, startIC, sizeIC)
elif normIC == norm1:
omegaIC = lambda x: lambdaIC * sum( x[startIC:sizeIC] )
proxIC = lambda x: soft_thresholding(x, lambdaIC, startIC, sizeIC)
elif normIC == non_negative:
omegaIC = lambda x: 0.0
proxIC = lambda x: non_negativity(x, startIC, sizeIC)
elif normIC == group_sparsity:
structureIC = regularisation.get('structureIC')
groupWeightIC = regularisation.get('weightsIC')
if not len(structureIC) == len(groupWeightIC):
raise ValueError('Number of groups and weights do not coincide.')
group_norm = regularisation.get('group_norm')
if not group_norm in list_group_sparsity_norms:
raise ValueError('Wrong norm in the structured sparsity term. Choose between %s.' % str(list_group_sparsity_norms))
# convert to new data structure (needed for faster access)
N = np.sum([g.size for g in structureIC])
groupIdxIC = np.zeros( (N,), dtype=np.int32 )
groupSizeIC = np.zeros( (structureIC.size,), dtype=np.int32 )
pos = 0
for i, g in enumerate(structureIC) :
groupSizeIC[i] = g.size
groupIdxIC[pos:(pos+g.size)] = g[:]
pos += g.size
omegaIC = lambda x: omega_group_sparsity( x, groupIdxIC, groupSizeIC, groupWeightIC, lambdaIC, group_norm )
proxIC = lambda x: prox_group_sparsity( x, groupIdxIC, groupSizeIC, groupWeightIC, lambdaIC, group_norm )
else:
raise ValueError('Type of regularisation for IC compartment not recognized.')
# Extracellular Compartment
startEC = regularisation.get('startEC')
sizeEC = regularisation.get('sizeEC')
if lambdaEC == 0.0:
omegaEC = lambda x: 0.0
proxEC = lambda x: x
elif normEC == norm2:
omegaEC = lambda x: lambdaEC * np.linalg.norm(x[startEC:sizeEC])
proxEC = lambda x: projection_onto_l2_ball(x, lambdaEC, startEC, sizeEC)
elif normEC == norm1:
omegaEC = lambda x: lambdaEC * sum( x[startEC:sizeEC] )
proxEC = lambda x: soft_thresholding(x, lambdaEC, startEC, sizeEC)
elif normEC == non_negative:
omegaEC = lambda x: 0.0
proxEC = lambda x: non_negativity(x, startEC, sizeEC)
else:
raise ValueError('Type of regularisation for EC compartment not recognized.')
# Isotropic Compartment
startISO = regularisation.get('startISO')
sizeISO = regularisation.get('sizeISO')
if lambdaISO == 0.0:
omegaISO = lambda x: 0.0
proxISO = lambda x: x
elif normISO == norm2:
omegaISO = lambda x: lambdaISO * np.linalg.norm(x[startISO:sizeISO])
proxISO = lambda x: projection_onto_l2_ball(x, lambdaISO, startISO, sizeISO)
elif normISO == norm1:
omegaISO = lambda x: lambdaISO * sum( x[startISO:sizeISO] )
proxISO = lambda x: soft_thresholding(x, lambdaISO, startISO, sizeISO)
elif normISO == non_negative:
omegaISO = lambda x: 0.0
proxISO = lambda x: non_negativity(x, startISO, sizeISO)
else:
raise ValueError('Type of regularisation for ISO compartment not recognized.')
omega = lambda x: omegaIC(x) + omegaEC(x) + omegaISO(x)
prox = lambda x: non_negativity(proxIC(proxEC(proxISO(x))),0,x.size) # non negativity is redunduntly forced
return omega, prox
