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projektAI/venv/Lib/site-packages/sklearn/linear_model/tests/test_least_angle.py

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2021-06-06 22:13:05 +02:00
import warnings
import numpy as np
import pytest
from scipy import linalg
from sklearn.base import clone
from sklearn.model_selection import train_test_split
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import TempMemmap
from sklearn.utils.fixes import np_version, parse_version
from sklearn.exceptions import ConvergenceWarning
from sklearn import linear_model, datasets
from sklearn.linear_model._least_angle import _lars_path_residues
from sklearn.linear_model import LassoLarsIC, lars_path
from sklearn.linear_model import Lars, LassoLars
# TODO: use another dataset that has multiple drops
diabetes = datasets.load_diabetes()
X, y = diabetes.data, diabetes.target
G = np.dot(X.T, X)
Xy = np.dot(X.T, y)
n_samples = y.size
def test_simple():
# Principle of Lars is to keep covariances tied and decreasing
# also test verbose output
from io import StringIO
import sys
old_stdout = sys.stdout
try:
sys.stdout = StringIO()
_, _, coef_path_ = linear_model.lars_path(
X, y, method="lar", verbose=10
)
sys.stdout = old_stdout
for i, coef_ in enumerate(coef_path_.T):
res = y - np.dot(X, coef_)
cov = np.dot(X.T, res)
C = np.max(abs(cov))
eps = 1e-3
ocur = len(cov[C - eps < abs(cov)])
if i < X.shape[1]:
assert ocur == i + 1
else:
# no more than max_pred variables can go into the active set
assert ocur == X.shape[1]
finally:
sys.stdout = old_stdout
def test_simple_precomputed():
# The same, with precomputed Gram matrix
_, _, coef_path_ = linear_model.lars_path(X, y, Gram=G, method="lar")
for i, coef_ in enumerate(coef_path_.T):
res = y - np.dot(X, coef_)
cov = np.dot(X.T, res)
C = np.max(abs(cov))
eps = 1e-3
ocur = len(cov[C - eps < abs(cov)])
if i < X.shape[1]:
assert ocur == i + 1
else:
# no more than max_pred variables can go into the active set
assert ocur == X.shape[1]
def _assert_same_lars_path_result(output1, output2):
assert len(output1) == len(output2)
for o1, o2 in zip(output1, output2):
assert_allclose(o1, o2)
@pytest.mark.parametrize("method", ["lar", "lasso"])
@pytest.mark.parametrize("return_path", [True, False])
def test_lars_path_gram_equivalent(method, return_path):
_assert_same_lars_path_result(
linear_model.lars_path_gram(
Xy=Xy, Gram=G, n_samples=n_samples, method=method,
return_path=return_path),
linear_model.lars_path(
X, y, Gram=G, method=method,
return_path=return_path))
def test_x_none_gram_none_raises_value_error():
# Test that lars_path with no X and Gram raises exception
Xy = np.dot(X.T, y)
assert_raises(ValueError, linear_model.lars_path, None, y, Gram=None,
Xy=Xy)
def test_all_precomputed():
# Test that lars_path with precomputed Gram and Xy gives the right answer
G = np.dot(X.T, X)
Xy = np.dot(X.T, y)
for method in "lar", "lasso":
output = linear_model.lars_path(X, y, method=method)
output_pre = linear_model.lars_path(X, y, Gram=G, Xy=Xy,
method=method)
for expected, got in zip(output, output_pre):
assert_array_almost_equal(expected, got)
@pytest.mark.filterwarnings('ignore: `rcond` parameter will change')
# numpy deprecation
def test_lars_lstsq():
# Test that Lars gives least square solution at the end
# of the path
X1 = 3 * X # use un-normalized dataset
clf = linear_model.LassoLars(alpha=0.)
clf.fit(X1, y)
# Avoid FutureWarning about default value change when numpy >= 1.14
rcond = None if np_version >= parse_version('1.14') else -1
coef_lstsq = np.linalg.lstsq(X1, y, rcond=rcond)[0]
assert_array_almost_equal(clf.coef_, coef_lstsq)
@pytest.mark.filterwarnings('ignore:`rcond` parameter will change')
# numpy deprecation
def test_lasso_gives_lstsq_solution():
# Test that Lars Lasso gives least square solution at the end
# of the path
_, _, coef_path_ = linear_model.lars_path(X, y, method='lasso')
coef_lstsq = np.linalg.lstsq(X, y)[0]
assert_array_almost_equal(coef_lstsq, coef_path_[:, -1])
def test_collinearity():
# Check that lars_path is robust to collinearity in input
X = np.array([[3., 3., 1.],
[2., 2., 0.],
[1., 1., 0]])
y = np.array([1., 0., 0])
rng = np.random.RandomState(0)
f = ignore_warnings
_, _, coef_path_ = f(linear_model.lars_path)(X, y, alpha_min=0.01)
assert not np.isnan(coef_path_).any()
residual = np.dot(X, coef_path_[:, -1]) - y
assert (residual ** 2).sum() < 1. # just make sure it's bounded
n_samples = 10
X = rng.rand(n_samples, 5)
y = np.zeros(n_samples)
_, _, coef_path_ = linear_model.lars_path(X, y, Gram='auto', copy_X=False,
copy_Gram=False, alpha_min=0.,
method='lasso', verbose=0,
max_iter=500)
assert_array_almost_equal(coef_path_, np.zeros_like(coef_path_))
def test_no_path():
# Test that the ``return_path=False`` option returns the correct output
alphas_, _, coef_path_ = linear_model.lars_path(X, y, method="lar")
alpha_, _, coef = linear_model.lars_path(
X, y, method="lar", return_path=False
)
assert_array_almost_equal(coef, coef_path_[:, -1])
assert alpha_ == alphas_[-1]
def test_no_path_precomputed():
# Test that the ``return_path=False`` option with Gram remains correct
alphas_, _, coef_path_ = linear_model.lars_path(X, y, method="lar", Gram=G)
alpha_, _, coef = linear_model.lars_path(
X, y, method="lar", Gram=G, return_path=False
)
assert_array_almost_equal(coef, coef_path_[:, -1])
assert alpha_ == alphas_[-1]
def test_no_path_all_precomputed():
# Test that the ``return_path=False`` option with Gram and Xy remains
# correct
X, y = 3 * diabetes.data, diabetes.target
G = np.dot(X.T, X)
Xy = np.dot(X.T, y)
alphas_, _, coef_path_ = linear_model.lars_path(
X, y, method='lasso', Xy=Xy, Gram=G, alpha_min=0.9)
alpha_, _, coef = linear_model.lars_path(
X, y, method='lasso', Gram=G, Xy=Xy, alpha_min=0.9, return_path=False)
assert_array_almost_equal(coef, coef_path_[:, -1])
assert alpha_ == alphas_[-1]
@pytest.mark.parametrize(
'classifier',
[linear_model.Lars, linear_model.LarsCV, linear_model.LassoLarsIC])
def test_lars_precompute(classifier):
# Check for different values of precompute
G = np.dot(X.T, X)
clf = classifier(precompute=G)
output_1 = ignore_warnings(clf.fit)(X, y).coef_
for precompute in [True, False, 'auto', None]:
clf = classifier(precompute=precompute)
output_2 = clf.fit(X, y).coef_
assert_array_almost_equal(output_1, output_2, decimal=8)
def test_singular_matrix():
# Test when input is a singular matrix
X1 = np.array([[1, 1.], [1., 1.]])
y1 = np.array([1, 1])
_, _, coef_path = linear_model.lars_path(X1, y1)
assert_array_almost_equal(coef_path.T, [[0, 0], [1, 0]])
def test_rank_deficient_design():
# consistency test that checks that LARS Lasso is handling rank
# deficient input data (with n_features < rank) in the same way
# as coordinate descent Lasso
y = [5, 0, 5]
for X in (
[[5, 0],
[0, 5],
[10, 10]],
[[10, 10, 0],
[1e-32, 0, 0],
[0, 0, 1]]
):
# To be able to use the coefs to compute the objective function,
# we need to turn off normalization
lars = linear_model.LassoLars(.1, normalize=False)
coef_lars_ = lars.fit(X, y).coef_
obj_lars = (1. / (2. * 3.)
* linalg.norm(y - np.dot(X, coef_lars_)) ** 2
+ .1 * linalg.norm(coef_lars_, 1))
coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
coef_cd_ = coord_descent.fit(X, y).coef_
obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
+ .1 * linalg.norm(coef_cd_, 1))
assert obj_lars < obj_cd * (1. + 1e-8)
def test_lasso_lars_vs_lasso_cd():
# Test that LassoLars and Lasso using coordinate descent give the
# same results.
X = 3 * diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
for c, a in zip(lasso_path.T, alphas):
if a == 0:
continue
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert error < 0.01
# similar test, with the classifiers
for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
normalize=False).fit(X, y)
err = linalg.norm(clf1.coef_ - clf2.coef_)
assert err < 1e-3
# same test, with normalized data
X = diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
tol=1e-8)
for c, a in zip(lasso_path.T, alphas):
if a == 0:
continue
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert error < 0.01
def test_lasso_lars_vs_lasso_cd_early_stopping():
# Test that LassoLars and Lasso using coordinate descent give the
# same results when early stopping is used.
# (test : before, in the middle, and in the last part of the path)
alphas_min = [10, 0.9, 1e-4]
for alpha_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=alpha_min)
lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
lasso_cd.alpha = alphas[-1]
lasso_cd.fit(X, y)
error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
assert error < 0.01
# same test, with normalization
for alpha_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=alpha_min)
lasso_cd = linear_model.Lasso(normalize=True, tol=1e-8)
lasso_cd.alpha = alphas[-1]
lasso_cd.fit(X, y)
error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
assert error < 0.01
def test_lasso_lars_path_length():
# Test that the path length of the LassoLars is right
lasso = linear_model.LassoLars()
lasso.fit(X, y)
lasso2 = linear_model.LassoLars(alpha=lasso.alphas_[2])
lasso2.fit(X, y)
assert_array_almost_equal(lasso.alphas_[:3], lasso2.alphas_)
# Also check that the sequence of alphas is always decreasing
assert np.all(np.diff(lasso.alphas_) < 0)
def test_lasso_lars_vs_lasso_cd_ill_conditioned():
# Test lasso lars on a very ill-conditioned design, and check that
# it does not blow up, and stays somewhat close to a solution given
# by the coordinate descent solver
# Also test that lasso_path (using lars_path output style) gives
# the same result as lars_path and previous lasso output style
# under these conditions.
rng = np.random.RandomState(42)
# Generate data
n, m = 70, 100
k = 5
X = rng.randn(n, m)
w = np.zeros((m, 1))
i = np.arange(0, m)
rng.shuffle(i)
supp = i[:k]
w[supp] = np.sign(rng.randn(k, 1)) * (rng.rand(k, 1) + 1)
y = np.dot(X, w)
sigma = 0.2
y += sigma * rng.rand(*y.shape)
y = y.squeeze()
lars_alphas, _, lars_coef = linear_model.lars_path(X, y, method='lasso')
_, lasso_coef2, _ = linear_model.lasso_path(X, y,
alphas=lars_alphas,
tol=1e-6,
fit_intercept=False)
assert_array_almost_equal(lars_coef, lasso_coef2, decimal=1)
def test_lasso_lars_vs_lasso_cd_ill_conditioned2():
# Create an ill-conditioned situation in which the LARS has to go
# far in the path to converge, and check that LARS and coordinate
# descent give the same answers
# Note it used to be the case that Lars had to use the drop for good
# strategy for this but this is no longer the case with the
# equality_tolerance checks
X = [[1e20, 1e20, 0],
[-1e-32, 0, 0],
[1, 1, 1]]
y = [10, 10, 1]
alpha = .0001
def objective_function(coef):
return (1. / (2. * len(X)) * linalg.norm(y - np.dot(X, coef)) ** 2
+ alpha * linalg.norm(coef, 1))
lars = linear_model.LassoLars(alpha=alpha, normalize=False)
assert_warns(ConvergenceWarning, lars.fit, X, y)
lars_coef_ = lars.coef_
lars_obj = objective_function(lars_coef_)
coord_descent = linear_model.Lasso(alpha=alpha, tol=1e-4, normalize=False)
cd_coef_ = coord_descent.fit(X, y).coef_
cd_obj = objective_function(cd_coef_)
assert lars_obj < cd_obj * (1. + 1e-8)
def test_lars_add_features():
# assure that at least some features get added if necessary
# test for 6d2b4c
# Hilbert matrix
n = 5
H = 1. / (np.arange(1, n + 1) + np.arange(n)[:, np.newaxis])
clf = linear_model.Lars(fit_intercept=False).fit(
H, np.arange(n))
assert np.all(np.isfinite(clf.coef_))
def test_lars_n_nonzero_coefs(verbose=False):
lars = linear_model.Lars(n_nonzero_coefs=6, verbose=verbose)
lars.fit(X, y)
assert len(lars.coef_.nonzero()[0]) == 6
# The path should be of length 6 + 1 in a Lars going down to 6
# non-zero coefs
assert len(lars.alphas_) == 7
@ignore_warnings
def test_multitarget():
# Assure that estimators receiving multidimensional y do the right thing
Y = np.vstack([y, y ** 2]).T
n_targets = Y.shape[1]
estimators = [
linear_model.LassoLars(),
linear_model.Lars(),
# regression test for gh-1615
linear_model.LassoLars(fit_intercept=False),
linear_model.Lars(fit_intercept=False),
]
for estimator in estimators:
estimator.fit(X, Y)
Y_pred = estimator.predict(X)
alphas, active, coef, path = (estimator.alphas_, estimator.active_,
estimator.coef_, estimator.coef_path_)
for k in range(n_targets):
estimator.fit(X, Y[:, k])
y_pred = estimator.predict(X)
assert_array_almost_equal(alphas[k], estimator.alphas_)
assert_array_almost_equal(active[k], estimator.active_)
assert_array_almost_equal(coef[k], estimator.coef_)
assert_array_almost_equal(path[k], estimator.coef_path_)
assert_array_almost_equal(Y_pred[:, k], y_pred)
def test_lars_cv():
# Test the LassoLarsCV object by checking that the optimal alpha
# increases as the number of samples increases.
# This property is not actually guaranteed in general and is just a
# property of the given dataset, with the given steps chosen.
old_alpha = 0
lars_cv = linear_model.LassoLarsCV()
for length in (400, 200, 100):
X = diabetes.data[:length]
y = diabetes.target[:length]
lars_cv.fit(X, y)
np.testing.assert_array_less(old_alpha, lars_cv.alpha_)
old_alpha = lars_cv.alpha_
assert not hasattr(lars_cv, 'n_nonzero_coefs')
def test_lars_cv_max_iter(recwarn):
warnings.simplefilter('always')
with np.errstate(divide='raise', invalid='raise'):
X = diabetes.data
y = diabetes.target
rng = np.random.RandomState(42)
x = rng.randn(len(y))
X = diabetes.data
X = np.c_[X, x, x] # add correlated features
lars_cv = linear_model.LassoLarsCV(max_iter=5, cv=5)
lars_cv.fit(X, y)
# Check that there is no warning in general and no ConvergenceWarning
# in particular.
# Materialize the string representation of the warning to get a more
# informative error message in case of AssertionError.
recorded_warnings = [str(w) for w in recwarn]
assert recorded_warnings == []
def test_lasso_lars_ic():
# Test the LassoLarsIC object by checking that
# - some good features are selected.
# - alpha_bic > alpha_aic
# - n_nonzero_bic < n_nonzero_aic
lars_bic = linear_model.LassoLarsIC('bic')
lars_aic = linear_model.LassoLarsIC('aic')
rng = np.random.RandomState(42)
X = diabetes.data
X = np.c_[X, rng.randn(X.shape[0], 5)] # add 5 bad features
lars_bic.fit(X, y)
lars_aic.fit(X, y)
nonzero_bic = np.where(lars_bic.coef_)[0]
nonzero_aic = np.where(lars_aic.coef_)[0]
assert lars_bic.alpha_ > lars_aic.alpha_
assert len(nonzero_bic) < len(nonzero_aic)
assert np.max(nonzero_bic) < diabetes.data.shape[1]
# test error on unknown IC
lars_broken = linear_model.LassoLarsIC('<unknown>')
assert_raises(ValueError, lars_broken.fit, X, y)
def test_lars_path_readonly_data():
# When using automated memory mapping on large input, the
# fold data is in read-only mode
# This is a non-regression test for:
# https://github.com/scikit-learn/scikit-learn/issues/4597
splitted_data = train_test_split(X, y, random_state=42)
with TempMemmap(splitted_data) as (X_train, X_test, y_train, y_test):
# The following should not fail despite copy=False
_lars_path_residues(X_train, y_train, X_test, y_test, copy=False)
def test_lars_path_positive_constraint():
# this is the main test for the positive parameter on the lars_path method
# the estimator classes just make use of this function
# we do the test on the diabetes dataset
# ensure that we get negative coefficients when positive=False
# and all positive when positive=True
# for method 'lar' (default) and lasso
err_msg = "Positive constraint not supported for 'lar' coding method."
with pytest.raises(ValueError, match=err_msg):
linear_model.lars_path(
diabetes["data"], diabetes["target"], method="lar", positive=True
)
method = 'lasso'
_, _, coefs = \
linear_model.lars_path(X, y, return_path=True, method=method,
positive=False)
assert coefs.min() < 0
_, _, coefs = \
linear_model.lars_path(X, y, return_path=True, method=method,
positive=True)
assert coefs.min() >= 0
# now we gonna test the positive option for all estimator classes
default_parameter = {'fit_intercept': False}
estimator_parameter_map = {'LassoLars': {'alpha': 0.1},
'LassoLarsCV': {},
'LassoLarsIC': {}}
def test_estimatorclasses_positive_constraint():
# testing the transmissibility for the positive option of all estimator
# classes in this same function here
default_parameter = {'fit_intercept': False}
estimator_parameter_map = {'LassoLars': {'alpha': 0.1},
'LassoLarsCV': {},
'LassoLarsIC': {}}
for estname in estimator_parameter_map:
params = default_parameter.copy()
params.update(estimator_parameter_map[estname])
estimator = getattr(linear_model, estname)(positive=False, **params)
estimator.fit(X, y)
assert estimator.coef_.min() < 0
estimator = getattr(linear_model, estname)(positive=True, **params)
estimator.fit(X, y)
assert min(estimator.coef_) >= 0
def test_lasso_lars_vs_lasso_cd_positive():
# Test that LassoLars and Lasso using coordinate descent give the
# same results when using the positive option
# This test is basically a copy of the above with additional positive
# option. However for the middle part, the comparison of coefficient values
# for a range of alphas, we had to make an adaptations. See below.
# not normalized data
X = 3 * diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
positive=True)
lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8, positive=True)
for c, a in zip(lasso_path.T, alphas):
if a == 0:
continue
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert error < 0.01
# The range of alphas chosen for coefficient comparison here is restricted
# as compared with the above test without the positive option. This is due
# to the circumstance that the Lars-Lasso algorithm does not converge to
# the least-squares-solution for small alphas, see 'Least Angle Regression'
# by Efron et al 2004. The coefficients are typically in congruence up to
# the smallest alpha reached by the Lars-Lasso algorithm and start to
# diverge thereafter. See
# https://gist.github.com/michigraber/7e7d7c75eca694c7a6ff
for alpha in np.linspace(6e-1, 1 - 1e-2, 20):
clf1 = linear_model.LassoLars(fit_intercept=False, alpha=alpha,
normalize=False, positive=True).fit(X, y)
clf2 = linear_model.Lasso(fit_intercept=False, alpha=alpha, tol=1e-8,
normalize=False, positive=True).fit(X, y)
err = linalg.norm(clf1.coef_ - clf2.coef_)
assert err < 1e-3
# normalized data
X = diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
positive=True)
lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
tol=1e-8, positive=True)
for c, a in zip(lasso_path.T[:-1], alphas[:-1]): # don't include alpha=0
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert error < 0.01
def test_lasso_lars_vs_R_implementation():
# Test that sklearn LassoLars implementation agrees with the LassoLars
# implementation available in R (lars library) under the following
# scenarios:
# 1) fit_intercept=False and normalize=False
# 2) fit_intercept=True and normalize=True
# Let's generate the data used in the bug report 7778
y = np.array([-6.45006793, -3.51251449, -8.52445396, 6.12277822,
-19.42109366])
x = np.array([[0.47299829, 0, 0, 0, 0],
[0.08239882, 0.85784863, 0, 0, 0],
[0.30114139, -0.07501577, 0.80895216, 0, 0],
[-0.01460346, -0.1015233, 0.0407278, 0.80338378, 0],
[-0.69363927, 0.06754067, 0.18064514, -0.0803561,
0.40427291]])
X = x.T
###########################################################################
# Scenario 1: Let's compare R vs sklearn when fit_intercept=False and
# normalize=False
###########################################################################
#
# The R result was obtained using the following code:
#
# library(lars)
# model_lasso_lars = lars(X, t(y), type="lasso", intercept=FALSE,
# trace=TRUE, normalize=FALSE)
# r = t(model_lasso_lars$beta)
#
r = np.array([[0, 0, 0, 0, 0, -79.810362809499026, -83.528788732782829,
-83.777653739190711, -83.784156932888934,
-84.033390591756657],
[0, 0, 0, 0, -0.476624256777266, 0, 0, 0, 0,
0.025219751009936],
[0, -3.577397088285891, -4.702795355871871,
-7.016748621359461, -7.614898471899412, -0.336938391359179,
0, 0, 0.001213370600853, 0.048162321585148],
[0, 0, 0, 2.231558436628169, 2.723267514525966,
2.811549786389614, 2.813766976061531, 2.817462468949557,
2.817368178703816, 2.816221090636795],
[0, 0, -1.218422599914637, -3.457726183014808,
-4.021304522060710, -45.827461592423745,
-47.776608869312305,
-47.911561610746404, -47.914845922736234,
-48.039562334265717]])
model_lasso_lars = linear_model.LassoLars(alpha=0, fit_intercept=False,
normalize=False)
model_lasso_lars.fit(X, y)
skl_betas = model_lasso_lars.coef_path_
assert_array_almost_equal(r, skl_betas, decimal=12)
###########################################################################
###########################################################################
# Scenario 2: Let's compare R vs sklearn when fit_intercept=True and
# normalize=True
#
# Note: When normalize is equal to True, R returns the coefficients in
# their original units, that is, they are rescaled back, whereas sklearn
# does not do that, therefore, we need to do this step before comparing
# their results.
###########################################################################
#
# The R result was obtained using the following code:
#
# library(lars)
# model_lasso_lars2 = lars(X, t(y), type="lasso", intercept=TRUE,
# trace=TRUE, normalize=TRUE)
# r2 = t(model_lasso_lars2$beta)
r2 = np.array([[0, 0, 0, 0, 0],
[0, 0, 0, 8.371887668009453, 19.463768371044026],
[0, 0, 0, 0, 9.901611055290553],
[0, 7.495923132833733, 9.245133544334507,
17.389369207545062, 26.971656815643499],
[0, 0, -1.569380717440311, -5.924804108067312,
-7.996385265061972]])
model_lasso_lars2 = linear_model.LassoLars(alpha=0, normalize=True)
model_lasso_lars2.fit(X, y)
skl_betas2 = model_lasso_lars2.coef_path_
# Let's rescale back the coefficients returned by sklearn before comparing
# against the R result (read the note above)
temp = X - np.mean(X, axis=0)
normx = np.sqrt(np.sum(temp ** 2, axis=0))
skl_betas2 /= normx[:, np.newaxis]
assert_array_almost_equal(r2, skl_betas2, decimal=12)
###########################################################################
@pytest.mark.parametrize('copy_X', [True, False])
def test_lasso_lars_copyX_behaviour(copy_X):
"""
Test that user input regarding copy_X is not being overridden (it was until
at least version 0.21)
"""
lasso_lars = LassoLarsIC(copy_X=copy_X, precompute=False)
rng = np.random.RandomState(0)
X = rng.normal(0, 1, (100, 5))
X_copy = X.copy()
y = X[:, 2]
lasso_lars.fit(X, y)
assert copy_X == np.array_equal(X, X_copy)
@pytest.mark.parametrize('copy_X', [True, False])
def test_lasso_lars_fit_copyX_behaviour(copy_X):
"""
Test that user input to .fit for copy_X overrides default __init__ value
"""
lasso_lars = LassoLarsIC(precompute=False)
rng = np.random.RandomState(0)
X = rng.normal(0, 1, (100, 5))
X_copy = X.copy()
y = X[:, 2]
lasso_lars.fit(X, y, copy_X=copy_X)
assert copy_X == np.array_equal(X, X_copy)
@pytest.mark.parametrize('est', (LassoLars(alpha=1e-3), Lars()))
def test_lars_with_jitter(est):
# Test that a small amount of jitter helps stability,
# using example provided in issue #2746
X = np.array([[0.0, 0.0, 0.0, -1.0, 0.0],
[0.0, -1.0, 0.0, 0.0, 0.0]])
y = [-2.5, -2.5]
expected_coef = [0, 2.5, 0, 2.5, 0]
# set to fit_intercept to False since target is constant and we want check
# the value of coef. coef would be all zeros otherwise.
est.set_params(fit_intercept=False)
est_jitter = clone(est).set_params(jitter=10e-8, random_state=0)
est.fit(X, y)
est_jitter.fit(X, y)
assert np.mean((est.coef_ - est_jitter.coef_)**2) > .1
np.testing.assert_allclose(est_jitter.coef_, expected_coef, rtol=1e-3)
def test_X_none_gram_not_none():
with pytest.raises(ValueError,
match="X cannot be None if Gram is not None"):
lars_path(X=None, y=[1], Gram='not None')
def test_copy_X_with_auto_gram():
# Non-regression test for #17789, `copy_X=True` and Gram='auto' does not
# overwrite X
rng = np.random.RandomState(42)
X = rng.rand(6, 6)
y = rng.rand(6)
X_before = X.copy()
linear_model.lars_path(X, y, Gram='auto', copy_X=True, method='lasso')
# X did not change
assert_allclose(X, X_before)
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