def test_ProxElasticNet(self):
"""...Test of ProxElasticNet
"""
coeffs = self.coeffs.copy()
l_enet = 3e-2
ratio = .3
t = 1.7
prox_enet = ProxElasticNet(l_enet, ratio=ratio)
prox_l1 = ProxL1(ratio * l_enet)
prox_l2 = ProxL2Sq((1 - ratio) * l_enet)
self.assertAlmostEqual(prox_enet.value(coeffs),
prox_l1.value(coeffs) + prox_l2.value(coeffs),
delta=1e-15)
out = coeffs.copy()
prox_l1.call(out, t, out)
prox_l2.call(out, t, out)
assert_almost_equal(prox_enet.call(coeffs, step=t), out, decimal=10)
prox_enet = ProxElasticNet(l_enet, ratio=ratio, positive=True)
prox_l1 = ProxL1(ratio * l_enet, positive=True)
prox_l2 = ProxL2Sq((1 - ratio) * l_enet, positive=True)
self.assertAlmostEqual(prox_enet.value(coeffs),
prox_l1.value(coeffs) + prox_l2.value(coeffs),
delta=1e-15)
out = coeffs.copy()
prox_l1.call(out, t, out)
prox_l2.call(out, t, out)
assert_almost_equal(prox_enet.call(coeffs, step=t), out, decimal=10)
def compare_solver_sdca(self):
"""...Compare SDCA solution with SVRG solution
"""
np.random.seed(12)
n_samples = Test.n_samples
n_features = Test.n_features
for fit_intercept in [True, False]:
y, X, coeffs0, interc0 = TestSolver.generate_logistic_data(
n_features, n_samples)
model = ModelLogReg(fit_intercept=fit_intercept).fit(X, y)
ratio = 0.5
l_enet = 1e-2
# SDCA "elastic-net" formulation is different from elastic-net
# implementation
l_l2_sdca = ratio * l_enet
l_l1_sdca = (1 - ratio) * l_enet
sdca = SDCA(l_l2sq=l_l2_sdca, max_iter=100, verbose=False, tol=0,
seed=Test.sto_seed).set_model(model)
prox_l1 = ProxL1(l_l1_sdca)
sdca.set_prox(prox_l1)
coeffs_sdca = sdca.solve()
# Compare with SVRG
svrg = SVRG(max_iter=100, verbose=False, tol=0,
seed=Test.sto_seed).set_model(model)
prox_enet = ProxElasticNet(l_enet, ratio)
svrg.set_prox(prox_enet)
coeffs_svrg = svrg.solve(step=0.1)
np.testing.assert_allclose(coeffs_sdca, coeffs_svrg)
def test_ProxL1(self):
"""...Test of ProxL1
"""
coeffs = self.coeffs.copy()
l_l1 = 3e-2
t = 1.7
prox = ProxL1(l_l1)
thresh = t * l_l1
out = np.sign(coeffs) * (np.abs(coeffs) - thresh) \
* (np.abs(coeffs) > thresh)
self.assertAlmostEqual(prox.value(coeffs),
l_l1 * np.abs(coeffs).sum(),
delta=1e-15)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=10)
prox = ProxL1(l_l1, (3, 8))
thresh = t * l_l1
sub_coeffs = coeffs[3:8]
out = coeffs.copy()
out[3:8] = np.sign(sub_coeffs) \
* (np.abs(sub_coeffs) - thresh) \
* (np.abs(sub_coeffs) > thresh)
self.assertAlmostEqual(prox.value(coeffs),
l_l1 * np.abs(coeffs[3:8]).sum(),
delta=1e-15)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=10)
prox = ProxL1(l_l1, (3, 8), positive=True)
thresh = t * l_l1
sub_coeffs = coeffs[3:8]
out = coeffs.copy()
out[3:8] = np.sign(sub_coeffs) * (np.abs(sub_coeffs) - thresh) \
* (np.abs(sub_coeffs) > thresh)
idx = out[3:8] < 0
out[3:8][idx] = 0
self.assertAlmostEqual(prox.value(coeffs),
l_l1 * np.abs(coeffs[3:8]).sum(),
delta=1e-15)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=10)
def test_dense_and_sparse_match(self):
"""...Test in SVRG that dense and sparse code matches in all possible
settings
"""
variance_reductions = ['last', 'rand']
rand_types = ['perm', 'unif']
seed = 123
tol = 0.
max_iter = 50
n_samples = 500
n_features = 20
# Crazy prox examples
proxs = [
ProxTV(strength=1e-2, range=(5, 13), positive=True),
ProxElasticNet(strength=1e-2, ratio=0.9),
ProxEquality(range=(0, n_features)),
ProxL1(strength=1e-3, range=(5, 17)),
ProxL1w(strength=1e-3, weights=np.arange(5, 17, dtype=np.double),
range=(5, 17)),
]
for intercept in [-1, None]:
X, y = self.simu_linreg_data(interc=intercept,
n_features=n_features,
n_samples=n_samples)
fit_intercept = intercept is not None
model_dense, model_spars = self.get_dense_and_sparse_linreg_model(
X, y, fit_intercept=fit_intercept)
step = 1 / model_spars.get_lip_max()
for variance_reduction, rand_type, prox in product(
variance_reductions, rand_types, proxs):
solver_sparse = SVRG(step=step, tol=tol, max_iter=max_iter,
verbose=False,
variance_reduction=variance_reduction,
rand_type=rand_type, seed=seed) \
.set_model(model_spars) \
.set_prox(prox)
solver_dense = SVRG(step=step, tol=tol, max_iter=max_iter,
verbose=False,
variance_reduction=variance_reduction,
rand_type=rand_type, seed=seed) \
.set_model(model_dense) \
.set_prox(prox)
solver_sparse.solve()
solver_dense.solve()
np.testing.assert_array_almost_equal(solver_sparse.solution,
solver_dense.solution, 7)
def test_solver_sdca(self):
"""...Check SDCA solver for a Logistic regression with Ridge
penalization and L1 penalization
"""
solver = SDCA(l_l2sq=1e-5, max_iter=100, verbose=False, tol=0)
self.check_solver(solver,
fit_intercept=False,
model="logreg",
decimal=1)
# Now a specific test with a real prox for SDCA
np.random.seed(12)
n_samples = Test.n_samples
n_features = Test.n_features
for fit_intercept in [True, False]:
y, X, coeffs0, interc0 = TestSolver.generate_logistic_data(
n_features, n_samples)
model = ModelLogReg(fit_intercept=fit_intercept).fit(X, y)
ratio = 0.5
l_enet = 1e-2
# SDCA "elastic-net" formulation is different from elastic-net
# implementation
l_l2_sdca = ratio * l_enet
l_l1_sdca = (1 - ratio) * l_enet
sdca = SDCA(l_l2sq=l_l2_sdca,
max_iter=100,
verbose=False,
tol=0,
seed=Test.sto_seed).set_model(model)
prox_l1 = ProxL1(l_l1_sdca)
sdca.set_prox(prox_l1)
coeffs_sdca = sdca.solve()
# Compare with SVRG
svrg = SVRG(max_iter=100, verbose=False, tol=0,
seed=Test.sto_seed).set_model(model)
prox_enet = ProxElasticNet(l_enet, ratio)
svrg.set_prox(prox_enet)
coeffs_svrg = svrg.solve(step=0.1)
np.testing.assert_allclose(coeffs_sdca, coeffs_svrg)
def test_solver_gfb(self):
"""...Check GFB's solver for a Logistic Regression with ElasticNet
penalization
Notes
-----
Using GFB solver with l1 and l2 penalizations is obviously a bad
idea as ElasticNet prox is meant to do this, but it allows us to
compare with another algorithm.
"""
n_samples = 200
n_features = 10
y, X, w, c = Test.generate_logistic_data(n_features=n_features,
n_samples=n_samples)
strength = 1e-3
ratio = 0.3
prox_elasticnet = ProxElasticNet(strength, ratio)
prox_l1 = ProxL1(strength * ratio)
prox_l2 = ProxL2Sq(strength * (1 - ratio))
# First we get GFB solution with prox l1 and prox l2
gfb = GFB(tol=1e-13, max_iter=1000, verbose=False, step=1)
Test.prepare_solver(gfb, X, y, prox=None)
gfb.set_prox([prox_l1, prox_l2])
gfb_solution = gfb.solve()
# Then we get AGD solution with prox ElasticNet
agd = AGD(tol=1e-13,
max_iter=1000,
verbose=False,
step=0.5,
linesearch=False)
Test.prepare_solver(agd, X, y, prox=prox_elasticnet)
agd_solution = agd.solve()
# Finally we assert that both algorithms lead to the same solution
np.testing.assert_almost_equal(gfb_solution, agd_solution, decimal=1)
import numpy as np
import matplotlib.pyplot as plt
from tick.optim.prox import ProxL1
x = 0.5 * np.random.randn(50)
a, b = x.min() - 1e-1, x.max() + 1e-1
proxs = [
ProxL1(strength=0.),
ProxL1(strength=3e-1),
ProxL1(strength=3e-1, range=(10, 40)),
ProxL1(strength=3e-1, positive=True),
ProxL1(strength=3e-1, range=(10, 40), positive=True),
]
names = [
"original vector",
"prox",
"prox with range=(10, 40)",
"prox with positive=True",
"range=(10, 40) and positive=True",
]
_, ax_list = plt.subplots(1, 5, figsize=(20, 4), sharey=True)
for prox, name, ax in zip(proxs, names, ax_list):
ax.stem(prox.call(x))
ax.set_title(name)
ax.set_xlim((-1, 51))
ax.set_ylim((a, b))
"""
import numpy as np
import matplotlib.pyplot as plt
from tick.optim.prox import ProxL1, ProxElasticNet, ProxL2Sq, \
ProxPositive, ProxSlope, ProxTV, ProxZero
x = np.random.randn(50)
a, b = x.min() - 1e-1, x.max() + 1e-1
s = 0.4
proxs = [
ProxZero(),
ProxPositive(),
ProxL2Sq(strength=s),
ProxL1(strength=s),
ProxElasticNet(strength=s, ratio=0.5),
ProxSlope(strength=s),
ProxTV(strength=s)
]
fig, _ = plt.subplots(2, 4, figsize=(16, 8), sharey=True, sharex=True)
fig.axes[0].stem(x)
fig.axes[0].set_title("original vector", fontsize=16)
fig.axes[0].set_xlim((-1, 51))
fig.axes[0].set_ylim((a, b))
for i, prox in enumerate(proxs):
fig.axes[i + 1].stem(prox.call(x))
fig.axes[i + 1].set_title(prox.name, fontsize=16)
fig.axes[i + 1].set_xlim((-1, 51))
import numpy as np
import matplotlib.pyplot as plt
from tick.optim.prox import ProxL1, ProxTV, ProxMulti
s = 0.4
prox = ProxMulti(proxs=(ProxTV(strength=s, range=(0, 20)),
ProxL1(strength=2 * s, range=(20, 50))))
x = np.random.randn(50)
a, b = x.min() - 1e-1, x.max() + 1e-1
plt.figure(figsize=(8, 4))
plt.subplot(1, 2, 1)
plt.stem(x)
plt.title("original vector", fontsize=16)
plt.xlim((-1, 51))
plt.ylim((a, b))
plt.subplot(1, 2, 2)
plt.stem(prox.call(x))
plt.title("ProxMulti: TV and L1", fontsize=16)
plt.xlim((-1, 51))
plt.ylim((a, b))
plt.vlines(20, a, b, linestyles='dashed')
plt.tight_layout()
plt.show()