def test_sdca_identity_poisreg(self):
"""...Test SDCA on specific case of Poisson regression with
indentity link
"""
l_l2sq = 1e-3
n_samples = 10000
n_features = 3
np.random.seed(123)
weight0 = np.random.rand(n_features)
features = np.random.rand(n_samples, n_features)
for intercept in [None, 0.45]:
if intercept is None:
fit_intercept = False
else:
fit_intercept = True
simu = SimuPoisReg(weight0, intercept=intercept, features=features,
n_samples=n_samples, link='identity',
verbose=False)
features, labels = simu.simulate()
model = ModelPoisReg(fit_intercept=fit_intercept, link='identity')
model.fit(features, labels)
sdca = SDCA(l_l2sq=l_l2sq, max_iter=100, verbose=False, tol=1e-14,
seed=Test.sto_seed)
sdca.set_model(model).set_prox(ProxZero())
start_dual = np.sqrt(sdca._rand_max * l_l2sq)
start_dual = start_dual * np.ones(sdca._rand_max)
sdca.solve(start_dual)
# Check that duality gap is 0
self.assertAlmostEqual(
sdca.objective(sdca.solution),
sdca.dual_objective(sdca.dual_solution))
# Check that original vector is approximatively retrieved
if fit_intercept:
original_coeffs = np.hstack((weight0, intercept))
else:
original_coeffs = weight0
np.testing.assert_array_almost_equal(original_coeffs,
sdca.solution, decimal=1)
# Ensure that we solve the same problem as other solvers
svrg = SVRG(max_iter=100, verbose=False, tol=1e-14,
seed=Test.sto_seed)
svrg.set_model(model).set_prox(ProxL2Sq(l_l2sq))
svrg.solve(0.5 * np.ones(model.n_coeffs), step=1e-2)
np.testing.assert_array_almost_equal(svrg.solution, sdca.solution,
decimal=4)
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 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 run_solvers(model, l_l2sq):
try:
svrg_step = 1. / model.get_lip_max()
except AttributeError:
svrg_step = 1e-3
try:
gd_step = 1. / model.get_lip_best()
except AttributeError:
gd_step = 1e-1
bfgs = BFGS(verbose=False, tol=1e-13)
bfgs.set_model(model).set_prox(ProxL2Sq(l_l2sq))
bfgs.solve()
bfgs.history.set_minimizer(bfgs.solution)
bfgs.history.set_minimum(bfgs.objective(bfgs.solution))
bfgs.solve()
svrg = SVRG(step=svrg_step, verbose=False, tol=1e-10, seed=seed)
svrg.set_model(model).set_prox(ProxL2Sq(l_l2sq))
svrg.history.set_minimizer(bfgs.solution)
svrg.history.set_minimum(bfgs.objective(bfgs.solution))
svrg.solve()
sdca = SDCA(l_l2sq, verbose=False, seed=seed, tol=1e-10)
sdca.set_model(model).set_prox(ProxZero())
sdca.history.set_minimizer(bfgs.solution)
sdca.history.set_minimum(bfgs.objective(bfgs.solution))
sdca.solve()
gd = GD(verbose=False, tol=1e-10, step=gd_step, linesearch=False)
gd.set_model(model).set_prox(ProxL2Sq(l_l2sq))
gd.history.set_minimizer(bfgs.solution)
gd.history.set_minimum(bfgs.objective(bfgs.solution))
gd.solve()
agd = AGD(verbose=False, tol=1e-10, step=gd_step, linesearch=False)
agd.set_model(model).set_prox(ProxL2Sq(l_l2sq))
agd.history.set_minimizer(bfgs.solution)
agd.history.set_minimum(bfgs.objective(bfgs.solution))
agd.solve()
return bfgs, svrg, sdca, gd, agd
def test_convergence_with_lags(self):
"""Test longitudinal multinomial model convergence."""
n_intervals = 10
n_lags = 3
n_samples = 1500
n_features = 3
sim = SimuSCCS(n_samples, n_intervals, n_features, n_lags, None,
True, "short", seed=42, verbose=False)
X, y, censoring, coeffs = sim.simulate()
X = LongitudinalFeaturesLagger(n_lags=n_lags) \
.fit_transform(X, censoring)
model = ModelSCCS(n_intervals=n_intervals,
n_lags=n_lags).fit(X, y, censoring)
solver = SVRG(max_iter=15, verbose=False)
solver.set_model(model).set_prox(ProxZero())
coeffs_svrg = solver.solve(step=1 / model.get_lip_max())
np.testing.assert_almost_equal(coeffs, coeffs_svrg, decimal=1)
def test_convergence_with_lags(self):
"""Test longitudinal multinomial model convergence."""
n_intervals = 10
n_samples = 800
n_features = 2
n_lags = np.repeat(2, n_features).astype(dtype="uint64")
sim = SimuSCCS(n_samples,
n_intervals,
n_features,
n_lags,
None,
"multiple_exposures",
seed=42)
_, X, y, censoring, coeffs = sim.simulate()
coeffs = np.hstack(coeffs)
X, _, _ = LongitudinalFeaturesLagger(n_lags=n_lags) \
.fit_transform(X, censoring)
model = ModelSCCS(n_intervals=n_intervals,
n_lags=n_lags).fit(X, y, censoring)
solver = SVRG(max_iter=15, verbose=False)
solver.set_model(model).set_prox(ProxZero())
coeffs_svrg = solver.solve(step=1 / model.get_lip_max())
np.testing.assert_almost_equal(coeffs, coeffs_svrg, decimal=1)
n_samples=n_samples, seed=123, verbose=False).simulate()
model = ModelLogReg(fit_intercept=True).fit(X, y)
prox = ProxElasticNet(strength=1e-3, ratio=0.5, range=(0, n_features))
x0 = np.zeros(model.n_coeffs)
optimal_step = 1 / model.get_lip_max()
tested_steps = [optimal_step, 1e-2 * optimal_step, 10 * optimal_step]
solvers = []
solver_labels = []
for step in tested_steps:
svrg = SVRG(max_iter=30, tol=1e-10, verbose=False)
svrg.set_model(model).set_prox(prox)
svrg.solve(step=step)
svrg_bb = SVRG(max_iter=30, tol=1e-10, verbose=False, step_type='bb')
svrg_bb.set_model(model).set_prox(prox)
svrg_bb.solve(step=step)
solvers += [svrg, svrg_bb]
optimal_factor = step / optimal_step
if optimal_factor != 1:
solver_labels += ['SVRG {:.2g} * optimal step'.format(optimal_factor),
'SVRG BB {:.2g} * optimal step'.format(optimal_factor)]
else:
solver_labels += ['SVRG optimal step'.format(optimal_factor),
'SVRG BB optimal step'.format(optimal_factor)]
model = ModelLogReg(fit_intercept=True)
model.fit(features, labels)
prox = ProxElasticNet(penalty_strength, ratio=0.5, range=(0, n_features))
svrg_step = 1. / model.get_lip_max()
test_n_threads = [1, 2, 4]
svrg_list = []
svrg_labels = []
for n_threads in test_n_threads:
svrg = SVRG(step=svrg_step, seed=seed, max_iter=30, verbose=False,
n_threads=n_threads)
svrg.set_model(model).set_prox(prox)
svrg.solve()
svrg_list += [svrg]
if n_threads == 1:
svrg_labels += ['SVRG']
else:
svrg_labels += ['ASVRG {}'.format(n_threads)]
plot_history(svrg_list, x="time", dist_min=True, log_scale=True,
labels=svrg_labels, show=False)
plt.ylim([3e-3, 0.3])
plt.ylabel('log distance to optimal objective', fontsize=14)
plt.tight_layout()
plt.show()
from tick.prox import ProxElasticNet, ProxL1
from tick.plot import plot_history
n_samples, n_features, = 5000, 50
weights0 = weights_sparse_gauss(n_features, nnz=10)
intercept0 = 0.2
X, y = SimuLogReg(weights=weights0,
intercept=intercept0,
n_samples=n_samples,
seed=123,
verbose=False).simulate()
model = ModelLogReg(fit_intercept=True).fit(X, y)
prox = ProxElasticNet(strength=1e-3, ratio=0.5, range=(0, n_features))
solver_params = {'max_iter': 100, 'tol': 0., 'verbose': False}
x0 = np.zeros(model.n_coeffs)
gd = GD(linesearch=False, **solver_params).set_model(model).set_prox(prox)
gd.solve(x0, step=1 / model.get_lip_best())
agd = AGD(linesearch=False, **solver_params).set_model(model).set_prox(prox)
agd.solve(x0, step=1 / model.get_lip_best())
sgd = SGD(**solver_params).set_model(model).set_prox(prox)
sgd.solve(x0, step=500.)
svrg = SVRG(**solver_params).set_model(model).set_prox(prox)
svrg.solve(x0, step=1 / model.get_lip_max())
plot_history([gd, agd, sgd, svrg], log_scale=True, dist_min=True)