def get_train_data(fit_intercept=True):
np.random.seed(12)
n_samples = Test.n_samples
n_features = Test.n_features
noise_level = Test.noise_level
nnz_outliers = Test.nnz_outliers
outliers_intensity = Test.outliers_intensity
if fit_intercept:
interc0 = Test.interc0
else:
interc0 = 0.
weights0 = np.sqrt(2 *
np.log(np.linspace(1, 10, n_features) * n_features))
sample_intercepts0 = weights_sparse_gauss(n_weights=n_samples,
nnz=nnz_outliers)
sample_intercepts0[sample_intercepts0 != 0] \
= outliers_intensity \
* np.sqrt(2 * np.log(np.linspace(1, 10, nnz_outliers)
* n_samples)) \
* np.sign(sample_intercepts0[sample_intercepts0 != 0])
X = features_normal_cov_toeplitz(n_samples, n_features, 0.5)
y = X.dot(
weights0) + noise_level * np.random.randn(n_samples) + interc0
y += sample_intercepts0
return X, y, weights0, interc0, sample_intercepts0
def test_ModelLinRegWithInterceptsWithoutGlobalIntercept(self):
"""...Numerical consistency check of loss and gradient for linear
regression with sample intercepts and no global intercept
"""
np.random.seed(12)
n_samples, n_features = 200, 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()
# Add gross outliers to the labels
y += intercept0
X_spars = csr_matrix(X)
model = ModelLinRegWithIntercepts(fit_intercept=True).fit(X, y)
model_spars = ModelLinRegWithIntercepts(fit_intercept=True) \
.fit(X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-4, 1e-4)
self.assertAlmostEqual(model.get_lip_mean(), 7.324960325598536)
self.assertAlmostEqual(model.get_lip_max(), 31.277118951892113)
self.assertAlmostEqual(model.get_lip_mean(),
model_spars.get_lip_mean())
self.assertAlmostEqual(model.get_lip_max(), model_spars.get_lip_max())
self.assertAlmostEqual(model.get_lip_best(), 2.7267793249045438)
def get_train_data(n_features=20, n_samples=3000, nnz=5):
np.random.seed(12)
weights0 = weights_sparse_gauss(n_features, nnz=nnz)
interc0 = 0.1
features, y = SimuLogReg(weights0, interc0, n_samples=n_samples,
verbose=False).simulate()
return features, y
def test_step_type_setting(self):
"""...Test that SVRG step_type parameter behaves correctly
"""
svrg = SVRG()
coeffs0 = weights_sparse_gauss(20, nnz=5, dtype=self.dtype)
interc0 = None
X, y = SimuLogReg(coeffs0,
interc0,
n_samples=3000,
verbose=False,
seed=123,
dtype=self.dtype).simulate()
model = ModelLogReg().fit(X, y)
svrg.set_model(model)
self.assertEqual(svrg.step_type, 'fixed')
self.assertEqual(svrg._solver.get_step_type(), SVRG_StepType_Fixed)
svrg = SVRG(step_type='bb')
svrg.set_model(model)
self.assertEqual(svrg.step_type, 'bb')
self.assertEqual(svrg._solver.get_step_type(),
SVRG_StepType_BarzilaiBorwein)
svrg.step_type = 'fixed'
self.assertEqual(svrg.step_type, 'fixed')
self.assertEqual(svrg._solver.get_step_type(), SVRG_StepType_Fixed)
svrg.step_type = 'bb'
self.assertEqual(svrg.step_type, 'bb')
self.assertEqual(svrg._solver.get_step_type(),
SVRG_StepType_BarzilaiBorwein)
def test_linear_model_serialization(self):
"""...Test serialization of linear models
"""
model_map = {
ModelLinReg: SimuLinReg,
ModelLogReg: SimuLogReg,
ModelPoisReg: SimuPoisReg,
ModelHinge: SimuLogReg,
ModelQuadraticHinge: SimuLogReg,
ModelSmoothedHinge: SimuLogReg,
}
for mod in model_map:
model = mod(fit_intercept=False)
coeffs0 = weights_sparse_gauss(20, nnz=5)
interc0 = None
features, labels = model_map[mod](coeffs0, interc0, n_samples=100,
verbose=False,
seed=123).simulate()
model.fit(features, labels)
pickled = pickle.loads(pickle.dumps(model))
self.assertTrue(model._model.compare(pickled._model))
self.assertEqual(
model.loss(features[0]), pickled.loss(features[0]))
def get_train_data(n_samples=2000, n_features=20, fit_intercept=True):
np.random.seed(12)
weights0 = weights_sparse_gauss(n_features)
if fit_intercept:
intercept0 = -1.
else:
intercept0 = None
X, y = SimuLinReg(weights0, intercept0, n_samples=n_samples,
verbose=False).simulate()
return X, y, weights0, intercept0
def test_set_model(self):
"""...Test set_model of saga, should only accept childs of
ModelGeneralizedLinear"""
# We try to pass a ModelCoxRegPartialLik which is not a generalized
# linear model to SAGA to check that the error is raised
msg = '^SAGA accepts only childs of `ModelGeneralizedLinear`$'
with self.assertRaisesRegex(ValueError, msg):
w = weights_sparse_gauss(n_weights=2, nnz=0)
X, T, C = SimuCoxReg(w).simulate()
model = ModelCoxRegPartialLik().fit(X, T, C)
SAGA().set_model(model)
msg = '^SAGA accepts only childs of `ModelGeneralizedLinear`$'
with self.assertRaisesRegex(RuntimeError, msg):
w = weights_sparse_gauss(n_weights=2, nnz=0)
X, T, C = SimuCoxReg(w).simulate()
model = ModelCoxRegPartialLik().fit(X, T, C)
saga = SAGA()
saga._solver.set_model(model._model)
def generate_logistic_data(n_features, n_samples, use_intercept=False):
""" Function to generate labels features y and X that corresponds
to w, c
"""
if n_features <= 5:
raise ValueError("``n_features`` must be larger than 5")
np.random.seed(12)
coeffs0 = weights_sparse_gauss(n_features, nnz=5)
if use_intercept:
interc0 = 2.
else:
interc0 = None
simu = SimuLogReg(coeffs0, interc0, n_samples=n_samples, verbose=False)
X, y = simu.simulate()
return y, X, coeffs0, interc0
def test_variance_reduction_setting(self):
"""...SolverTest SAGA variance_reduction parameter is correctly set"""
svrg = SAGA()
coeffs0 = weights_sparse_gauss(20, nnz=5, dtype=self.dtype)
interc0 = None
X, y = SimuLogReg(coeffs0,
interc0,
n_samples=3000,
verbose=False,
seed=123,
dtype=self.dtype).simulate()
model = ModelLogReg().fit(X, y)
svrg.set_model(model)
svrg.astype(self.dtype)
self.assertEqual(svrg.variance_reduction, 'last')
self.assertEqual(svrg._solver.get_variance_reduction(),
SAGA_VarianceReductionMethod_Last)
svrg = SAGA(variance_reduction='rand')
svrg.set_model(model)
svrg.astype(self.dtype)
self.assertEqual(svrg.variance_reduction, 'rand')
self.assertEqual(svrg._solver.get_variance_reduction(),
SAGA_VarianceReductionMethod_Random)
svrg.variance_reduction = 'avg'
self.assertEqual(svrg.variance_reduction, 'avg')
self.assertEqual(svrg._solver.get_variance_reduction(),
SAGA_VarianceReductionMethod_Average)
svrg.variance_reduction = 'rand'
self.assertEqual(svrg.variance_reduction, 'rand')
self.assertEqual(svrg._solver.get_variance_reduction(),
SAGA_VarianceReductionMethod_Random)
svrg.variance_reduction = 'last'
self.assertEqual(svrg.variance_reduction, 'last')
self.assertEqual(svrg._solver.get_variance_reduction(),
SAGA_VarianceReductionMethod_Last)
with self.assertRaises(ValueError):
svrg.variance_reduction = 'wrong_name'
def test_ModelLinRegWithInterceptsWithGlobalInterceptExtras(self):
"""...Extra tests for linear regression with sample intercepts and
global intercept, check gradient wrt homemade gradient
"""
np.random.seed(12)
n_samples, n_features = 200, 5
w0 = np.random.randn(n_features)
intercept0 = 50 * weights_sparse_gauss(n_weights=n_samples, nnz=30)
c0 = -1.
X, y = SimuLinReg(w0, c0, n_samples=n_samples, verbose=False,
seed=2038).simulate()
# Add gross outliers to the labels
y += intercept0
model = ModelLinRegWithIntercepts(fit_intercept=True).fit(X, y)
coeffs = np.random.randn(model.n_coeffs)
grad1 = model.grad(coeffs)
X2 = np.hstack((X, np.ones((n_samples, 1)), np.identity(n_samples)))
grad2 = X2.T.dot(X2.dot(coeffs) - y) / n_samples
np.testing.assert_almost_equal(grad1, grad2, decimal=10)
def test_solver_bfgs(self):
"""...Check BFGS solver for Logistic Regression with Ridge
penalization
"""
# It is the reference solver used in other unittests so we check that
# it's actually close to the true parameter of the simulated dataset
np.random.seed(12)
n_samples = 3000
n_features = 10
coeffs0 = weights_sparse_gauss(n_features, nnz=5)
interc0 = 2.
X, y = SimuLogReg(coeffs0, interc0, n_samples=n_samples,
verbose=False).simulate()
model = ModelLogReg(fit_intercept=True).fit(X, y)
prox = ProxL2Sq(strength=1e-6)
solver = BFGS(max_iter=100, print_every=1, verbose=False,
tol=1e-6).set_model(model).set_prox(prox)
coeffs = solver.solve()
err = Test.evaluate_model(coeffs, coeffs0, interc0)
self.assertAlmostEqual(err, 0., delta=5e-1)
def test_set_model_and_set_prox(self):
np.random.seed(12)
n_samples = TestSolver.n_samples
n_features = TestSolver.n_features
weights0 = weights_sparse_gauss(n_features, nnz=5)
interc0 = 2.
model = ModelLinReg()
msg = '^Passed object ModelLinReg has not been fitted. You must call' \
' ``fit`` on it before passing it to ``set_model``$'
with self.assertRaisesRegex(ValueError, msg):
for solver_class in self.solvers:
if solver_class is SDCA:
solver = solver_class(l_l2sq=1e-1)
else:
solver = solver_class()
solver.set_model(model)
X, y = SimuLinReg(weights0,
interc0,
n_samples=n_samples,
verbose=False,
seed=123,
dtype=self.dtype).simulate()
prox = ProxL2Sq(strength=1e-1)
msg = '^Passed object of class ProxL2Sq is not a Model class$'
with self.assertRaisesRegex(ValueError, msg):
for solver_class in self.solvers:
if solver_class is SDCA:
solver = solver_class(l_l2sq=1e-1)
else:
solver = solver_class()
solver.set_model(prox)
model.fit(X, y)
msg = '^Passed object of class ModelLinReg is not a Prox class$'
with self.assertRaisesRegex(ValueError, msg):
for solver_class in self.solvers:
if solver_class is SDCA:
solver = solver_class(l_l2sq=1e-1)
else:
solver = solver_class()
solver.set_model(model).set_prox(model)
def test_robust_model_serialization(self):
"""...Test serialization of robust models
"""
model_map = {
ModelAbsoluteRegression: SimuLinReg,
ModelEpsilonInsensitive: SimuLinReg,
ModelHuber: SimuLinReg,
ModelLinRegWithIntercepts: SimuLinReg,
ModelModifiedHuber: SimuLogReg
}
for mod in model_map:
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)
pickled = pickle.loads(pickle.dumps(model))
self.assertTrue(model._model.compare(pickled._model))
if mod == ModelLinRegWithIntercepts:
test_vector = np.hstack((X[0], np.ones(n_samples)))
self.assertEqual(model.loss(test_vector),
pickled.loss(test_vector))
else:
self.assertEqual(model.loss(X[0]), pickled.loss(X[0]))
def test_asaga_solver(self):
"""...Check ASAGA solver for a Logistic Regression with Elastic net
penalization
"""
seed = 1398
np.random.seed(seed)
n_samples = 4000
n_features = 30
weights = weights_sparse_gauss(n_features, nnz=3).astype(self.dtype)
intercept = 0.2
penalty_strength = 1e-3
sparsity = 1e-4
features = sparse.rand(n_samples, n_features, density=sparsity,
format='csr', random_state=8).astype(self.dtype)
simulator = SimuLogReg(weights, n_samples=n_samples, features=features,
verbose=False, intercept=intercept,
dtype=self.dtype)
features, labels = simulator.simulate()
model = ModelLogReg(fit_intercept=True)
model.fit(features, labels)
prox = ProxElasticNet(penalty_strength, ratio=0.1, range=(0,
n_features))
solver_step = 1. / model.get_lip_max()
saga = SAGA(step=solver_step, max_iter=100, tol=1e-10, verbose=False,
n_threads=1, record_every=10, seed=seed)
saga.set_model(model).set_prox(prox)
saga.solve()
asaga = SAGA(step=solver_step, max_iter=100, tol=1e-10, verbose=False,
n_threads=2, record_every=10, seed=seed)
asaga.set_model(model).set_prox(prox)
asaga.solve()
np.testing.assert_array_almost_equal(saga.solution, asaga.solution,
decimal=4)
self.assertGreater(np.linalg.norm(saga.solution[:-1]), 0)
.. _In Advances in Neural Information Processing Systems: http://papers.nips.cc/paper/6286-barzilai-borwein-step-size-for-stochastic-gradient-descent
"""
import numpy as np
import matplotlib.pyplot as plt
from cycler import cycler
from tick.simulation import SimuLogReg, weights_sparse_gauss
from tick.optim.solver import SVRG
from tick.optim.model import ModelLogReg
from tick.optim.prox import ProxElasticNet
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))
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 = []
def get_train_data(n_features=10, n_samples=10000, nnz=3, seed=12):
np.random.seed(seed)
coeffs0 = weights_sparse_gauss(n_features, nnz=nnz)
features, times, censoring = SimuCoxReg(coeffs0,
verbose=False).simulate()
return features, times, censoring
def test_serializing_solvers(self):
"""...Test serialization of solvers
"""
ratio = 0.5
l_enet = 1e-2
sd = ratio * l_enet
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:
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 = ProxL1(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]))
def check_solver(self,
solver,
fit_intercept=True,
model='logreg',
decimal=1):
"""Check solver instance finds same parameters as scipy BFGS
Parameters
----------
solver : `Solver`
Instance of a solver to be tested
fit_intercept : `bool`, default=True
Model uses intercept is `True`
model : 'linreg' | 'logreg' | 'poisreg', default='logreg'
Name of the model used to test the solver
decimal : `int`, default=1
Number of decimals required for the test
"""
# Set seed for data simulation
np.random.seed(12)
n_samples = TestSolver.n_samples
n_features = TestSolver.n_features
coeffs0 = weights_sparse_gauss(n_features, nnz=5)
if fit_intercept:
interc0 = 2.
else:
interc0 = None
if model == 'linreg':
X, y = SimuLinReg(coeffs0,
interc0,
n_samples=n_samples,
verbose=False,
seed=123).simulate()
model = ModelLinReg(fit_intercept=fit_intercept).fit(X, y)
elif model == 'logreg':
X, y = SimuLogReg(coeffs0,
interc0,
n_samples=n_samples,
verbose=False,
seed=123).simulate()
model = ModelLogReg(fit_intercept=fit_intercept).fit(X, y)
elif model == 'poisreg':
X, y = SimuPoisReg(coeffs0,
interc0,
n_samples=n_samples,
verbose=False,
seed=123).simulate()
# Rescale features to avoid overflows in Poisson simulations
X /= np.linalg.norm(X, axis=1).reshape(n_samples, 1)
model = ModelPoisReg(fit_intercept=fit_intercept).fit(X, y)
else:
raise ValueError("``model`` must be either 'linreg', 'logreg' or"
" 'poisreg'")
solver.set_model(model)
strength = 1e-2
prox = ProxL2Sq(strength, (0, model.n_features))
if type(solver) is not SDCA:
solver.set_prox(prox)
else:
solver.set_prox(ProxZero())
solver.l_l2sq = strength
coeffs_solver = solver.solve()
# Compare with BFGS
bfgs = BFGS(max_iter=100,
verbose=False).set_model(model).set_prox(prox)
coeffs_bfgs = bfgs.solve()
np.testing.assert_almost_equal(coeffs_solver,
coeffs_bfgs,
decimal=decimal)
# We ensure that reached coeffs are not equal to zero
self.assertGreater(norm(coeffs_solver), 0)
self.assertAlmostEqual(solver.objective(coeffs_bfgs),
solver.objective(coeffs_solver),
delta=1e-2)
def test_variance_reduction_setting(self):
"""...Test that SVRG variance_reduction parameter behaves correctly
"""
svrg = SVRG()
coeffs0 = weights_sparse_gauss(20, nnz=5, dtype=self.dtype)
interc0 = None
X, y = SimuLogReg(coeffs0,
interc0,
n_samples=3000,
verbose=False,
seed=123,
dtype=self.dtype).simulate()
model = ModelLogReg().fit(X, y)
svrg.set_model(model)
self.assertEqual(svrg.variance_reduction, 'last')
self.assertEqual(svrg._solver.get_variance_reduction(),
SVRG_VarianceReductionMethod_Last)
svrg = SVRG(variance_reduction='rand')
svrg.set_model(model)
self.assertEqual(svrg.variance_reduction, 'rand')
self.assertEqual(svrg._solver.get_variance_reduction(),
SVRG_VarianceReductionMethod_Random)
svrg.variance_reduction = 'avg'
self.assertEqual(svrg.variance_reduction, 'avg')
self.assertEqual(svrg._solver.get_variance_reduction(),
SVRG_VarianceReductionMethod_Average)
svrg.variance_reduction = 'rand'
self.assertEqual(svrg.variance_reduction, 'rand')
self.assertEqual(svrg._solver.get_variance_reduction(),
SVRG_VarianceReductionMethod_Random)
svrg.variance_reduction = 'last'
self.assertEqual(svrg.variance_reduction, 'last')
self.assertEqual(svrg._solver.get_variance_reduction(),
SVRG_VarianceReductionMethod_Last)
msg = '^variance_reduction should be one of "avg, last, rand", ' \
'got "stuff"$'
with self.assertRaisesRegex(ValueError, msg):
svrg = SVRG(variance_reduction='stuff')
svrg.set_model(model)
with self.assertRaisesRegex(ValueError, msg):
svrg.variance_reduction = 'stuff'
X, y = self.simu_linreg_data(dtype=self.dtype)
model_dense, model_spars = self.get_dense_and_sparse_linreg_model(
X, y, dtype=self.dtype)
try:
svrg.set_model(model_dense)
svrg.variance_reduction = 'avg'
svrg.variance_reduction = 'last'
svrg.variance_reduction = 'rand'
svrg.set_model(model_spars)
svrg.variance_reduction = 'last'
svrg.variance_reduction = 'rand'
except Exception:
self.fail('Setting variance_reduction in these cases should have '
'been ok')
msg = "'avg' variance reduction cannot be used with sparse datasets"
with catch_warnings(record=True) as w:
simplefilter('always')
svrg.set_model(model_spars)
svrg.variance_reduction = 'avg'
self.assertEqual(len(w), 1)
self.assertTrue(issubclass(w[0].category, UserWarning))
self.assertEqual(str(w[0].message), msg)
def _test_solver_sparse_and_dense_consistency(
self,
create_solver,
model_classes=list([ModelLinReg, ModelLogReg, ModelPoisReg]),
proxs_classes=list([ProxL2Sq, ProxL1]),
fit_intercepts=list([False, True])):
"""...Test that solvers can run all glm models and are consistent
with sparsity
"""
n_samples = 50
n_features = 10
coeffs0 = weights_sparse_gauss(n_features, nnz=5)
interc0 = 2.
seed = 123
prox_strength = 1e-3
model_simu_map = {
ModelLinReg: SimuLinReg,
ModelPoisReg: SimuPoisReg,
ModelLogReg: SimuLogReg,
}
cases = itertools.product(model_classes, proxs_classes, fit_intercepts)
for Model, Prox, fit_intercept in cases:
if fit_intercept:
interc = interc0
else:
interc = None
Simu = model_simu_map[Model]
simu = Simu(coeffs0,
interc,
n_samples=n_samples,
seed=seed,
verbose=False)
X, y = simu.simulate()
X_sparse = csr_matrix(X)
for sparse in [True, False]:
model = Model(fit_intercept=fit_intercept)
if sparse:
model.fit(X_sparse, y)
else:
model.fit(X, y)
prox = Prox(prox_strength, (0, n_features))
solver = create_solver()
solver.set_model(model).set_prox(prox)
if sparse:
iterate_sparse = solver.solve()
else:
iterate_dense = solver.solve()
error_msg = 'Failed for %s and %s solved with %s' % (
model.name, prox.name, solver.name)
if fit_intercept:
error_msg += ' with intercept'
else:
error_msg += ' without intercept'
self.assertEqual(np.isfinite(iterate_dense).all(), True, error_msg)
np.testing.assert_almost_equal(iterate_dense,
iterate_sparse,
err_msg=error_msg)
from tick.inference import RobustLinearRegression, std_iqr
from tick.metrics import support_fdp, support_recall
np.random.seed(1)
n_samples = 1000
n_features = 5
noise_level = 1.
n_outliers = 50
outliers_intensity = 5.
intercept0 = -3.
log_linspace = np.log(n_features * np.linspace(1, 10, n_features))
weights0 = np.sqrt(2 * log_linspace)
sample_intercepts0 = weights_sparse_gauss(n_weights=n_samples, nnz=n_outliers)
idx_nnz = sample_intercepts0 != 0
log_linspace = np.log(n_samples * np.linspace(1, 10, n_outliers))
sample_intercepts0[idx_nnz] = outliers_intensity * np.sqrt(2 * log_linspace) \
* np.sign(sample_intercepts0[idx_nnz])
X = features_normal_cov_toeplitz(n_samples, n_features, 0.5)
y = X.dot(weights0) + noise_level * np.random.randn(n_samples) \
+ intercept0 + sample_intercepts0
target_fdr = 0.1
noise_level = std_iqr(y)
learner = RobustLinearRegression(C_sample_intercepts=2 * n_samples /
noise_level,
penalty='none',
The plot given below compares the distance to the minimum of each solver along
iterations, on a logarithmic scale.
"""
import numpy as np
import matplotlib.pyplot as plt
from tick.simulation import SimuPoisReg, weights_sparse_gauss
from tick.inference import PoissonRegression
from tick.plot import plot_history
n_samples = 50000
n_features = 100
np.random.seed(123)
weight0 = weights_sparse_gauss(n_features, nnz=int(n_features-1)) / 20.
intercept0 = -0.1
X, y = SimuPoisReg(weight0, intercept0, n_samples=n_samples,
verbose=False, seed=123).simulate()
opts = {'verbose': False, 'record_every': 1, 'tol': 1e-8, 'max_iter': 40}
poisson_regressions = [
PoissonRegression(solver='gd', **opts),
PoissonRegression(solver='agd', **opts),
PoissonRegression(solver='svrg', random_state=1234, **opts),
PoissonRegression(solver='bfgs', **opts)
]
for poisson_regression in poisson_regressions:
poisson_regression.fit(X, y)