def step(self, w, index):
"""The step size to use in descent methods.
From the interface "StepSize".
Parameters
----------
w : list of numpy arrays
The point at which to determine the step size.
index : int
Non-negative integer. The variable which the step is for.
"""
all_lipschitz = True
L = 0.0
# Add Lipschitz constants from the loss functions.
fi = self._f[index]
for j in range(len(fi)):
fij = fi[j]
for k in range(len(fij)):
fijk = fij[k]
if isinstance(fijk, properties.Gradient):
if not isinstance(fijk,
properties.LipschitzContinuousGradient):
all_lipschitz = False
break
else:
L += fijk.L(w[index])
elif isinstance(fijk, mb_properties.MultiblockGradient):
if not isinstance(
fijk, mb_properties.
MultiblockLipschitzContinuousGradient):
all_lipschitz = False
break
else:
L += fijk.L([w[index], w[j]], 0)
if not all_lipschitz:
break
for i in range(len(self._f)):
fij = self._f[i][index]
if i != index: # Do not visit these twice.
for k in range(len(fij)):
fijk = fij[k]
if isinstance(fijk, properties.Gradient):
# We shouldn't do anything here, right? This means that
# this (block i) is e.g. the y in a logistic
# regression.
pass
elif isinstance(fijk, mb_properties.MultiblockGradient):
if not isinstance(
fijk, mb_properties.
MultiblockLipschitzContinuousGradient):
all_lipschitz = False
break
else:
L += fijk.L([w[i], w[index]], 1)
# Add Lipschitz constants from the penalties.
di = self._d[index]
for k in range(len(di)):
if not isinstance(di[k], properties.LipschitzContinuousGradient):
all_lipschitz = False
break
else:
L += di[k].L() # w[index])
Ni = self._N[index]
for k in range(len(Ni)):
if not isinstance(Ni[k], properties.LipschitzContinuousGradient):
all_lipschitz = False
break
else:
L += Ni[k].L() # w[index])
step = 0.0
if all_lipschitz and L >= consts.TOLERANCE:
step = 1.0 / L
else:
# If all functions did not have Lipschitz continuous gradients,
# try to find the step size through backtracking line search.
class F(properties.Function, properties.Gradient):
def __init__(self, func, w, index):
self.func = func
self.w = w
self.index = index
def f(self, x):
# Temporarily replace the index:th variable with x.
w_old = self.w[self.index]
self.w[self.index] = x
f = self.func.f(w)
self.w[self.index] = w_old
return f
def grad(self, x):
# Temporarily replace the index:th variable with x.
w_old = self.w[self.index]
self.w[self.index] = x
g = self.func.grad(w, index)
self.w[self.index] = w_old
return g
func = F(self, w, index)
p = -self.grad(w, index)
from parsimony.algorithms.utils import BacktrackingLineSearch
import parsimony.functions.penalties as penalties
line_search = BacktrackingLineSearch(
condition=penalties.SufficientDescentCondition, max_iter=30)
a = np.sqrt(1.0 / self.X[index].shape[1]) # Arbitrarily "small".
step = line_search.run(func,
w[index],
p,
rho=0.5,
a=a,
condition_params={"c": 1e-4})
return step
def step(self, w, index):
# return 0.0001
all_lipschitz = True
# Add the Lipschitz constants.
L = 0.0
fi = self.functions[index]
for j in range(len(fi)):
if j != index and fi[j] is not None:
fij = fi[j]
if isinstance(fij, properties.LipschitzContinuousGradient):
L += fij.L()
elif isinstance(
fij,
mb_properties.MultiblockLipschitzContinuousGradient):
L += fij.L(w, index)
else:
all_lipschitz = False
break
if all_lipschitz:
fii = self.functions[index][index]
for k in range(len(fii)):
if fi[j] is None:
continue
if isinstance(fii[k], properties.LipschitzContinuousGradient):
L += fii[k].L()
elif isinstance(
fii[k],
mb_properties.MultiblockLipschitzContinuousGradient):
L += fii[k].L(w, index)
else:
all_lipschitz = False
break
if all_lipschitz and L > 0.0:
t = 1.0 / L
else:
# If all functions did not have Lipschitz continuous gradients,
# try to find the step size through backtracking line search.
class F(properties.Function, properties.Gradient):
def __init__(self, func, w, index):
self.func = func
self.w = w
self.index = index
def f(self, x):
# Temporarily replace the index:th variable with x.
w_old = self.w[self.index]
self.w[self.index] = x
f = self.func.f(w)
self.w[self.index] = w_old
return f
def grad(self, x):
# Temporarily replace the index:th variable with x.
w_old = self.w[self.index]
self.w[self.index] = x
g = self.func.grad(w, index)
self.w[self.index] = w_old
return g
func = F(self, w, index)
p = -self.grad(w, index)
from algorithms import BacktrackingLineSearch
import parsimony.functions.penalties as penalties
line_search = BacktrackingLineSearch(
condition=penalties.SufficientDescentCondition, max_iter=30)
a = np.sqrt(1.0 / self.X[index].shape[1]) # Arbitrarily "small".
t = line_search(func, w[index], p, rho=0.5, a=a, c=1e-4)
return t