def test_SimuLinReg(self):
"""...Test simulation of a Linear Regression
"""
n_samples = 10
n_features = 3
idx = np.arange(n_features)
weights = np.exp(-idx / 10.)
weights[::2] *= -1
seed = 123
simu = SimuLinReg(weights,
None,
n_samples=n_samples,
seed=seed,
verbose=False)
X, y = simu.simulate()
X_truth = np.array([[1.4912667, 0.80881799, 0.26977298],
[1.23227551, 0.50697013, 1.9409132],
[1.8891494, 1.49834791, 2.41445794],
[0.19431319, 0.80245126, 1.02577552],
[-1.61687582, -1.08411865, -0.83438387],
[2.30419894, -0.68987056, -0.39750262],
[-0.28826405, -1.23635074, -0.76124386],
[-1.32869473, -1.8752391, -0.182537],
[0.79464218, 0.65055633, 1.57572506],
[0.71524202, 1.66759831, 0.88679047]])
y_truth = np.array([
-1.23590872, -5.1612244, -4.28171221, -1.00793646, 2.24652287,
-2.7766077, -0.20433269, 0.46957959, -2.37562537, 0.35124802
])
np.testing.assert_array_almost_equal(X_truth, X)
np.testing.assert_array_almost_equal(y_truth, y)
def test_ModelEpsilonInsensitive(self):
"""...Numerical consistency check of loss and gradient for
Epsilon-Insensitive model
"""
np.random.seed(12)
n_samples, n_features = 5000, 10
w0 = np.random.randn(n_features)
c0 = np.random.randn()
# First check with intercept
X, y = SimuLinReg(w0, c0, n_samples=n_samples,
verbose=False).simulate()
X_spars = csr_matrix(X)
model = ModelEpsilonInsensitive(fit_intercept=True,
threshold=1.13).fit(X, y)
model_spars = ModelEpsilonInsensitive(fit_intercept=True,
threshold=1.13).fit(X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-5, 1e-3)
self._test_glm_intercept_vs_hardcoded_intercept(model)
# Then check without intercept
X, y = SimuLinReg(w0,
None,
n_samples=n_samples,
verbose=False,
seed=2038).simulate()
X_spars = csr_matrix(X)
model = ModelEpsilonInsensitive(fit_intercept=False).fit(X, y)
model_spars = ModelEpsilonInsensitive(fit_intercept=False).fit(
X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-5, 1e-3)
def test_ModelLinRegWithIntercepts(self):
"""...Numerical consistency check of loss and gradient for Linear
Regression
"""
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)
X, y = SimuLinReg(w0,
None,
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(X, y)
model_spars = ModelLinRegWithIntercepts().fit(X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-4, 1e-4)
self.assertAlmostEqual(model.get_lip_mean(), 6.324960325598532)
self.assertAlmostEqual(model.get_lip_max(), 30.277118951892113)
self.assertAlmostEqual(model.get_lip_mean(),
model_spars.get_lip_mean())
self.assertAlmostEqual(model.get_lip_max(), model_spars.get_lip_max())
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 test_ModelLinReg(self):
"""...Numerical consistency check of loss and gradient for Linear
Regression
"""
np.random.seed(12)
n_samples, n_features = 5000, 10
w0 = np.random.randn(n_features)
c0 = np.random.randn()
# First check with intercept
X, y = SimuLinReg(w0, c0, n_samples=n_samples,
verbose=False).simulate()
X_spars = csr_matrix(X)
model = ModelLinReg(fit_intercept=True).fit(X, y)
model_spars = ModelLinReg(fit_intercept=True).fit(X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-5, 1e-4)
# Then check without intercept
X, y = SimuLinReg(w0,
None,
n_samples=n_samples,
verbose=False,
seed=2038).simulate()
X_spars = csr_matrix(X)
model = ModelLinReg(fit_intercept=False).fit(X, y)
model_spars = ModelLinReg(fit_intercept=False).fit(X_spars, y)
self.run_test_for_glm(model, model_spars, 1e-5, 1e-4)
# Test for the Lipschitz constants without intercept
self.assertAlmostEqual(model.get_lip_best(), 2.6873683857125981)
self.assertAlmostEqual(model.get_lip_mean(), 9.95845726788432)
self.assertAlmostEqual(model.get_lip_max(), 54.82616964855237)
self.assertAlmostEqual(model_spars.get_lip_mean(),
model.get_lip_mean())
self.assertAlmostEqual(model_spars.get_lip_max(), model.get_lip_max())
# Test for the Lipschitz constants with intercept
model = ModelLinReg(fit_intercept=True).fit(X, y)
model_spars = ModelLinReg(fit_intercept=True).fit(X_spars, y)
self.assertAlmostEqual(model.get_lip_best(), 2.687568385712598)
self.assertAlmostEqual(model.get_lip_mean(), 10.958457267884327)
self.assertAlmostEqual(model.get_lip_max(), 55.82616964855237)
self.assertAlmostEqual(model_spars.get_lip_mean(),
model.get_lip_mean())
self.assertAlmostEqual(model_spars.get_lip_max(), model.get_lip_max())
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 create_model(model_type, n_samples, n_features, with_intercept=True):
weights = np.random.randn(n_features)
intercept = None
if with_intercept:
intercept = np.random.normal()
if model_type == 'Poisson':
# we need to rescale features to avoid overflows
weights /= n_features
if intercept is not None:
intercept /= n_features
if model_type == 'Linear':
simulator = SimuLinReg(weights,
intercept=intercept,
n_samples=n_samples,
verbose=False)
elif model_type == 'Logistic':
simulator = SimuLogReg(weights,
intercept=intercept,
n_samples=n_samples,
verbose=False)
elif model_type == 'Poisson':
simulator = SimuPoisReg(weights,
intercept=intercept,
n_samples=n_samples,
verbose=False)
labels, features = simulator.simulate()
if model_type == 'Linear':
model = ModelLinReg(fit_intercept=with_intercept)
elif model_type == 'Logistic':
model = ModelLogReg(fit_intercept=with_intercept)
elif model_type == 'Poisson':
model = ModelPoisReg(fit_intercept=with_intercept)
model.fit(labels, features)
return model
def test_ModelHuber_threshold(self):
np.random.seed(12)
n_samples, n_features = 5000, 10
w0 = np.random.randn(n_features)
c0 = np.random.randn()
# First check with intercept
X, y = SimuLinReg(w0, c0, n_samples=n_samples,
verbose=False).simulate()
model = ModelHuber(threshold=1.541).fit(X, y)
self.assertEqual(model._model.get_threshold(), 1.541)
model.threshold = 3.14
self.assertEqual(model._model.get_threshold(), 3.14)
msg = '^threshold must be > 0$'
with self.assertRaisesRegex(RuntimeError, msg):
model = ModelHuber(threshold=-1).fit(X, y)
with self.assertRaisesRegex(RuntimeError, msg):
model.threshold = 0.
def test_set_model_and_set_prox(self):
np.random.seed(12)
n_samples = TestSolver.n_samples
n_features = TestSolver.n_features
weights0 = weights_sparse_gauss(n_features, nnz=5)
interc0 = 2.
model = ModelLinReg()
msg = '^Passed object ModelLinReg has not been fitted. You must call' \
' ``fit`` on it before passing it to ``set_model``$'
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).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_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 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)
=============================
Generates Linear, Logistic and Poisson regression realizations given a
weight vector.
"""
import matplotlib.pyplot as plt
import numpy as np
from tick.simulation import SimuLinReg, SimuLogReg, SimuPoisReg
n_samples, n_features = 150, 2
weights0 = np.array([0.3, 1.2])
intercept0 = 0.5
simu_linreg = SimuLinReg(weights0, intercept0, n_samples=n_samples, seed=123)
X_linreg, y_linreg = simu_linreg.simulate()
simu_logreg = SimuLogReg(weights0, intercept0, n_samples=n_samples, seed=123)
X_logreg, y_logreg = simu_logreg.simulate()
simu_poisreg = SimuPoisReg(weights0,
intercept0,
n_samples=n_samples,
link='exponential',
seed=123)
X_poisreg, y_poisreg = simu_poisreg.simulate()
plt.figure(figsize=(12, 3))
plt.subplot(1, 3, 1)