def test_smooth_1D_l2(self):
from parsimony.functions import CombinedFunction
import parsimony.functions as functions
import parsimony.functions.nesterov.grouptv as grouptv
import parsimony.datasets.simulate.l1_l2_grouptvmu as l1_l2_grouptvmu
import parsimony.utils.weights as weights
np.random.seed(1337)
n, p = 10, 15
shape = (1, 1, p)
l = 0.0
k = 0.1 # Must have some regularisation for all variables.
g = 0.9
start_vector = weights.RandomUniformWeights(normalise=True)
beta = start_vector.get_weights(p)
rects = [[(0, 5)], [(4, 10)], [(13, 15)]]
# 0 [ 5 ] 0
# 1 [ 5 ] 0
# 2 [ 5 ] 0
# 3 [ 5 ] 0
# 4 [ 4 ] 0 / 1
beta[:5, :] = 5.0 # 5 [ 3 ] 1
beta[4, :] = 4.0 # 6 [ 3 ] 1
beta[5:10, :] = 3.0 # 7 [ 3 ] 1
beta[13:15, :] = 7.0 # 8 [ 3 ] 1
# 9 [ 3 ] 1
# 0 [ x ] -
# 1 [ x ] -
# 2 [ x ] -
# 3 [ 7 ] 2
# 4 [ 7 ] 2
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
A = grouptv.linear_operator_from_rects(rects, shape)
mu_min = 5e-8
X, y, beta_star = l1_l2_grouptvmu.load(l=l, k=k, g=g, beta=beta,
M=M, e=e, A=A, mu=mu_min,
snr=snr)
eps = 1e-5
max_iter = 12000
beta_start = start_vector.get_weights(p)
mus = [5e-2, 5e-4, 5e-6, 5e-8]
fista = FISTA(eps=eps, max_iter=max_iter / len(mus))
beta_parsimony = beta_start
for mu in mus:
function = CombinedFunction()
function.add_loss(functions.losses.LinearRegression(X, y,
mean=False))
function.add_penalty(grouptv.GroupTotalVariation(l=g,
A=A, mu=mu,
penalty_start=0))
function.add_penalty(functions.penalties.L2Squared(l=k,
penalty_start=0))
beta_parsimony = fista.run(function, beta_parsimony)
berr = np.linalg.norm(beta_parsimony - beta_star)
# print "berr:", berr
assert berr < 5e-2
f_parsimony = function.f(beta_parsimony)
f_star = function.f(beta_star)
ferr = abs(f_parsimony - f_star)
# print "ferr:", ferr
assert ferr < 5e-5
def test_smooth_2D_l1(self):
from parsimony.functions import CombinedFunction
import parsimony.functions as functions
import parsimony.functions.nesterov.grouptv as grouptv
import parsimony.datasets.simulate.l1_l2_grouptvmu as l1_l2_grouptvmu
import parsimony.utils.weights as weights
np.random.seed(1337)
n, p = 10, 18
shape = (1, 3, 6)
l = 0.618
k = 0.0
g = 1.618
start_vector = weights.ZerosWeights()
beta = start_vector.get_weights(p)
rects = [[(0, 1), (0, 3)], [(1, 2), (3, 6)]]
beta = np.reshape(beta, shape[1:])
beta[0:2, 0:4] = 1.0
beta[1:3, 3:6] = 2.0
beta[1, 3] = 1.5
beta = np.reshape(beta, (p, 1))
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
A = grouptv.linear_operator_from_rects(rects, shape)
mu_min = 5e-8
X, y, beta_star = l1_l2_grouptvmu.load(l=l, k=k, g=g, beta=beta,
M=M, e=e, A=A, mu=mu_min,
snr=snr)
eps = 1e-5
max_iter = 10000
beta_start = start_vector.get_weights(p)
mus = [5e-2, 5e-4, 5e-6, 5e-8]
fista = FISTA(eps=eps, max_iter=max_iter / len(mus))
beta_parsimony = beta_start
for mu in mus:
function = CombinedFunction()
function.add_loss(functions.losses.LinearRegression(X, y,
mean=False))
function.add_penalty(grouptv.GroupTotalVariation(l=g,
A=A, mu=mu,
penalty_start=0))
function.add_prox(functions.penalties.L1(l=l, penalty_start=0))
beta_parsimony = fista.run(function, beta_parsimony)
berr = np.linalg.norm(beta_parsimony - beta_star)
# print "berr:", berr
assert berr < 5e-2
f_parsimony = function.f(beta_parsimony)
f_star = function.f(beta_star)
ferr = abs(f_parsimony - f_star)
# print "ferr:", ferr
assert ferr < 5e-5
