def test_ProxTV(self):
"""...Test of ProxTV
"""
coeffs = self.coeffs.copy().astype(self.dtype)
l_tv = 0.5
t = 1.7
out = np.array([
-0.40102846, -0.40102846, -0.40102846, -0.31364696, -0.31364696,
1.03937619, 1.03937619, 1.03937619, -0.21598253, -0.21598253
])
prox = ProxTV(l_tv).astype(self.dtype)
val = l_tv * np.abs(coeffs[1:] - coeffs[:-1]).sum()
self.assertAlmostEqual(prox.value(coeffs), val, delta=self.delta)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=7)
coeffs = self.coeffs.copy().astype(self.dtype)
out = np.array([
-0.86017247, -0.58127151, -0.6116414, 0.11135304, 0.11135304,
1.32270952, 1.32270952, 1.32270952, -0.27576309, -1.00620197
])
prox = ProxTV(l_tv, (3, 8)).astype(self.dtype)
val = l_tv * np.abs(coeffs[3:8][1:] - coeffs[3:8][:-1]).sum()
self.assertAlmostEqual(prox.value(coeffs), val, delta=self.delta)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=7)
coeffs = self.coeffs.copy().astype(self.dtype)
out = np.array([
-0.86017247, -0.58127151, -0.6116414, 0.11135304, 0.11135304,
1.32270952, 1.32270952, 1.32270952, -0.27576309, -1.00620197
])
prox = ProxTV(l_tv, (3, 8), positive=True).astype(self.dtype)
prox.call(coeffs, step=t)
val = l_tv * np.abs(coeffs[3:8][1:] - coeffs[3:8][:-1]).sum()
self.assertAlmostEqual(prox.value(coeffs), val, delta=self.delta)
assert_almost_equal(prox.call(coeffs, step=t), out, decimal=7)
def test_prox_multi(self):
"""...Test of ProxMulti
"""
coeffs = self.coeffs.copy().astype(self.dtype)
double_coeffs = np.concatenate([coeffs, coeffs]).astype(self.dtype)
half_size = coeffs.shape[0]
full_size = double_coeffs.shape[0]
l_tv = 0.5
t = 1.7
prox_tv = ProxTV(strength=l_tv).astype(self.dtype)
prox_tv_multi = ProxTV(strength=l_tv,
range=(0, half_size)).astype(self.dtype)
l_enet = 3e-2
ratio = .3
prox_enet = ProxElasticNet(l_enet, ratio=ratio).astype(self.dtype)
prox_enet_multi = ProxElasticNet(l_enet,
ratio=ratio,
range=(half_size,
full_size)).astype(self.dtype)
prox_multi = ProxMulti((prox_tv_multi, prox_enet_multi))
# Test that the value of the prox is correct
val_multi = prox_multi.value(double_coeffs)
val_correct = prox_enet.value(coeffs) + prox_tv.value(coeffs)
self.assertAlmostEqual(val_multi,
val_correct,
places=self.decimal_places)
# Test that the prox is correct
out1 = prox_tv.call(coeffs, step=t)
out2 = prox_enet.call(coeffs, step=t)
out_correct = np.concatenate([out1, out2])
out_multi = prox_multi.call(double_coeffs, step=t)
np.testing.assert_almost_equal(out_multi, out_correct)
# An example with overlapping coefficients
start1 = 5
end1 = 13
start2 = 10
end2 = 17
prox_tv = ProxTV(strength=l_tv,
range=(start1, end1)).astype(self.dtype)
prox_enet = ProxElasticNet(strength=l_enet,
ratio=ratio,
range=(start2, end2)).astype(self.dtype)
prox_multi = ProxMulti((prox_tv, prox_enet))
val_correct = prox_tv.value(double_coeffs)
val_correct += prox_enet.value(double_coeffs)
val_multi = prox_multi.value(double_coeffs)
self.assertAlmostEqual(val_multi, val_correct)
out_correct = prox_tv.call(double_coeffs)
out_correct = prox_enet.call(out_correct)
out_multi = prox_multi.call(double_coeffs)
np.testing.assert_almost_equal(out_multi, out_correct)
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).astype(self.dtype),
ProxElasticNet(strength=1e-2, ratio=0.9).astype(self.dtype),
ProxEquality(range=(0, n_features)).astype(self.dtype),
ProxL1(strength=1e-3, range=(5, 17)).astype(self.dtype),
ProxL1w(strength=1e-3, weights=np.arange(5, 17, dtype=np.double),
range=(5, 17)).astype(self.dtype),
]
for intercept in [-1, None]:
X, y = self.simu_linreg_data(dtype=self.dtype, 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, dtype=self.dtype, 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)
solver_sparse.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)
solver_dense.set_model(model_dense).set_prox(prox)
solver_sparse.solve()
solver_dense.solve()
places = 7
if self.dtype is "float32":
places = 3
np.testing.assert_array_almost_equal(solver_sparse.solution,
solver_dense.solution,
decimal=places)
def _construct_prox_obj(self, coeffs=None, project=False):
n_penalized_features = len(self.penalized_features) \
if self.penalized_features is not None else 0
if project:
# project future _coeffs on the support of given _coeffs
if all(self.n_lags == 0):
proxs = [ProxZero()]
elif coeffs is not None:
prox_ranges = self._detect_support(coeffs)
proxs = [ProxEquality(0, range=r) for r in prox_ranges]
else:
raise ValueError("Coeffs are None. " +
"Equality penalty cannot infer the "
"coefficients support.")
elif n_penalized_features > 0 and self._C_tv is not None or \
self._C_group_l1 is not None:
# TV and GroupLasso penalties
blocks_start = np.zeros(n_penalized_features)
blocks_end = np.zeros(n_penalized_features)
proxs = []
for i in self.penalized_features:
start = int(self._features_offset[i])
blocks_start[i] = start
end = int(blocks_start[i] + self._n_lags[i] + 1)
blocks_end[i] = end
if self._C_tv is not None:
proxs.append(ProxTV(1 / self._C_tv, range=(start, end)))
if self._C_group_l1 is not None:
blocks_size = blocks_end - blocks_start
proxs.append(
ProxGroupL1(1 / self._C_group_l1, blocks_start.tolist(),
blocks_size.tolist()))
else:
# Default prox: does nothing
proxs = [ProxZero()]
prox_obj = ProxMulti(tuple(proxs))
return prox_obj
import numpy as np
import matplotlib.pyplot as plt
from tick.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()
ProxPositive, ProxSlope, ProxTV, ProxZero, ProxBinarsity, ProxGroupL1, \
ProxEquality, ProxL1w
np.random.seed(12)
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),
ProxEquality(range=(25, 40)),
ProxL1w(strength=s, weights=0.1 * np.arange(50, dtype=np.double)),
ProxGroupL1(strength=2 * s,
blocks_start=np.arange(0, 50, 10),
blocks_length=10 * np.ones((5, ))),
ProxBinarsity(strength=s,
blocks_start=np.arange(0, 50, 10),
blocks_length=10 * np.ones((5, )))
]
fig, _ = plt.subplots(3, 4, figsize=(16, 12), 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))
def test_serializing_solvers(self):
"""...Test serialization of solvers
"""
ratio = 0.5
l_enet = 1e-2
sd = ratio * l_enet
proxes = [
ProxZero(),
ProxTV(2),
ProxL1(2),
ProxGroupL1(strength=1, blocks_start=[0, 3, 8],
blocks_length=[3, 5, 2])
]
solvers = [
AdaGrad(step=1e-3, max_iter=100, verbose=False, tol=0),
SGD(step=1e-3, max_iter=100, verbose=False, tol=0),
SDCA(l_l2sq=sd, max_iter=100, verbose=False, tol=0),
SAGA(step=1e-3, max_iter=100, verbose=False, tol=0),
SVRG(step=1e-3, max_iter=100, verbose=False, tol=0)
]
model_map = {
ModelLinReg: SimuLinReg,
ModelLogReg: SimuLogReg,
ModelPoisReg: SimuPoisReg,
ModelHinge: SimuLogReg,
ModelQuadraticHinge: SimuLogReg,
ModelSmoothedHinge: SimuLogReg,
ModelAbsoluteRegression: SimuLinReg,
ModelEpsilonInsensitive: SimuLinReg,
ModelHuber: SimuLinReg,
ModelLinRegWithIntercepts: SimuLinReg,
ModelModifiedHuber: SimuLogReg
}
for solver in solvers:
for mod in model_map:
for prox in proxes:
np.random.seed(12)
n_samples, n_features = 100, 5
w0 = np.random.randn(n_features)
intercept0 = 50 * weights_sparse_gauss(n_weights=n_samples,
nnz=30)
c0 = None
X, y = SimuLinReg(w0, c0, n_samples=n_samples, verbose=False,
seed=2038).simulate()
if mod == ModelLinRegWithIntercepts:
y += intercept0
model = mod(fit_intercept=False).fit(X, y)
# prox = ProxZero() #(2.)
solver.set_model(model)
solver.set_prox(prox)
pickled = pickle.loads(pickle.dumps(solver))
self.assertTrue(solver._solver.compare(pickled._solver))
self.assertTrue(
solver.model._model.compare(pickled.model._model))
self.assertTrue(solver.prox._prox.compare(pickled.prox._prox))
if mod == ModelLinRegWithIntercepts:
test_vector = np.hstack((X[0], np.ones(n_samples)))
self.assertEqual(
model.loss(test_vector),
solver.model.loss(test_vector))
else:
self.assertEqual(model.loss(X[0]), solver.model.loss(X[0]))