algorithm=algorithms.proximal.StaticCONESTA(),
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_conesta"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A,
algorithm=algorithms.proximal.CONESTA(),
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_inter_conesta"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A, penalty_start=1,
algorithm=algorithms.proximal.CONESTA(),
algorithm_params=algorithm_params)
Al1tv = l1tv.linear_operator_from_shape(shape, np.prod(shape))
MODELS["2d_l1l2tv_inexactfista"] = \
estimators.LogisticRegressionL1L2TVInexactFISTA(
l1, l2, tv, Al1tv,
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_inter_inexactfista"] = \
estimators.LogisticRegressionL1L2TVInexactFISTA(
l1, l2, tv, Al1tv,
penalty_start=1,
algorithm_params=algorithm_params)
## Get data structure from mesh
# build a cylinder mesh with the same topology than the 2D grid
xyz, tri = mesh.cylinder(shape[1], shape[0])
def test_smoothed_l1tv(self):
import numpy as np
from parsimony.functions import CombinedFunction
import parsimony.algorithms.proximal as proximal
import parsimony.functions as functions
import parsimony.functions.penalties as penalties
import parsimony.functions.nesterov.tv as tv
import parsimony.functions.nesterov.l1tv as l1tv
import parsimony.utils.start_vectors as start_vectors
import parsimony.datasets.simulate as simulate
np.random.seed(42)
px = 10
py = 1
pz = 1
shape = (pz, py, px)
n, p = 5, np.prod(shape)
l = 0.618
k = 0.01
g = 1.1
start_vector = start_vectors.RandomStartVector(normalise=True)
beta = start_vector.get_vector(p)
alpha = 1.0
Sigma = alpha * np.eye(p, p) \
+ (1.0 - alpha) * np.random.randn(p, p)
mean = np.zeros(p)
M = np.random.multivariate_normal(mean, Sigma, n)
e = np.random.randn(n, 1)
snr = 100.0
mu = 5e-3
A = tv.linear_operator_from_shape(shape)
# X, y, beta_star = l1_l2_tvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e,
# A=A, mu=mu, snr=snr)
funs = [simulate.grad.L1(l),
simulate.grad.L2Squared(k),
simulate.grad.TotalVariation(g, A)]
lr = simulate.LinearRegressionData(funs, M, e, snr=snr,
intercept=False)
X, y, beta_star = lr.load(beta)
eps = 1e-8
max_iter = 810
alg = proximal.FISTA(eps=eps, max_iter=max_iter)
function = CombinedFunction()
function.add_loss(functions.losses.LinearRegression(X, y, mean=False))
function.add_penalty(penalties.L2Squared(l=k))
A = l1tv.linear_operator_from_shape(shape, p)
function.add_prox(l1tv.L1TV(l, g, A=A, mu=mu, penalty_start=0))
# A = tv.linear_operator_from_shape(shape)
# function.add_penalty(tv.TotalVariation(l=g, A=A, mu=mu,
# penalty_start=0))
# function.add_prox(penalties.L1(l=l))
beta_start = start_vector.get_vector(p)
beta = alg.run(function, beta_start)
berr = np.linalg.norm(beta - beta_star)
# print "berr:", berr
# assert berr < 5e-1
assert_less(berr, 5e-1, "The found regression vector is not correct.")
f_parsimony = function.f(beta)
f_star = function.f(beta_star)
ferr = abs(f_parsimony - f_star)
# print "ferr:", ferr
# assert ferr < 5e-3
assert_less(ferr, 5e-3, "The found regression vector is not correct.")
algorithm=algorithms.proximal.StaticCONESTA(),
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_conesta"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A,
algorithm=algorithms.proximal.CONESTA(),
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_inter_conesta"] = \
estimators.LogisticRegressionL1L2TV(
l1, l2, tv, A, penalty_start=1,
algorithm=algorithms.proximal.CONESTA(),
algorithm_params=algorithm_params)
Al1tv = l1tv.linear_operator_from_shape(shape, np.prod(shape))
MODELS["2d_l1l2tv_inexactfista"] = \
estimators.LogisticRegressionL1L2TVInexactFISTA(
l1, l2, tv, Al1tv,
algorithm_params=algorithm_params)
MODELS["2d_l1l2tv_inter_inexactfista"] = \
estimators.LogisticRegressionL1L2TVInexactFISTA(
l1, l2, tv, Al1tv,
penalty_start=1,
algorithm_params=algorithm_params)
## Get data structure from mesh
# build a cylinder mesh with the same topology than the 2D grid
xyz, tri = mesh.cylinder(shape[1], shape[0])
def test_smoothed_l1tv(self):
import numpy as np
from parsimony.functions import CombinedFunction
import parsimony.algorithms.proximal as proximal
import parsimony.functions as functions
import parsimony.functions.penalties as penalties
import parsimony.functions.nesterov.tv as tv
import parsimony.functions.nesterov.l1tv as l1tv
import parsimony.datasets.simulate.l1_l2_tvmu as l1_l2_tvmu
import parsimony.utils.start_vectors as start_vectors
import parsimony.datasets.simulate as simulate
np.random.seed(42)
px = 10
py = 1
pz = 1
shape = (pz, py, px)
n, p = 5, np.prod(shape)
l = 0.618
k = 0.01
g = 1.1
start_vector = start_vectors.RandomStartVector(normalise=True)
beta = start_vector.get_vector(p)
alpha = 1.0
Sigma = alpha * np.eye(p, p) \
+ (1.0 - alpha) * np.random.randn(p, p)
mean = np.zeros(p)
M = np.random.multivariate_normal(mean, Sigma, n)
e = np.random.randn(n, 1)
snr = 100.0
mu = 5e-3
A = tv.linear_operator_from_shape(shape)
# X, y, beta_star = l1_l2_tvmu.load(l=l, k=k, g=g, beta=beta, M=M, e=e,
# A=A, mu=mu, snr=snr)
funs = [
simulate.grad.L1(l),
simulate.grad.L2Squared(k),
simulate.grad.TotalVariation(g, A)
]
lr = simulate.LinearRegressionData(funs,
M,
e,
snr=snr,
intercept=False)
X, y, beta_star = lr.load(beta)
eps = 1e-8
max_iter = 810
alg = proximal.FISTA(eps=eps, max_iter=max_iter)
function = CombinedFunction()
function.add_function(
functions.losses.LinearRegression(X, y, mean=False))
function.add_penalty(penalties.L2Squared(l=k))
A = l1tv.linear_operator_from_shape(shape, p)
function.add_prox(l1tv.L1TV(l, g, A=A, mu=mu, penalty_start=0))
# A = tv.linear_operator_from_shape(shape)
# function.add_penalty(tv.TotalVariation(l=g, A=A, mu=mu,
# penalty_start=0))
# function.add_prox(penalties.L1(l=l))
beta_start = start_vector.get_vector(p)
beta = alg.run(function, beta_start)
berr = np.linalg.norm(beta - beta_star)
# print "berr:", berr
assert berr < 5e-1
f_parsimony = function.f(beta)
f_star = function.f(beta_star)
ferr = abs(f_parsimony - f_star)
# print "ferr:", ferr
assert ferr < 5e-3
