/usr/lib/python3/dist-packages/sklearn/linear_model/tests/test_least_angle.py is in python3-sklearn 0.17.0-4.
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import numpy as np
from scipy import linalg
from sklearn.cross_validation import train_test_split
from sklearn.utils.testing import assert_array_almost_equal
from sklearn.utils.testing import assert_true
from sklearn.utils.testing import assert_less
from sklearn.utils.testing import assert_greater
from sklearn.utils.testing import assert_raises
from sklearn.utils.testing import ignore_warnings
from sklearn.utils.testing import assert_no_warnings, assert_warns
from sklearn.utils.testing import TempMemmap
from sklearn.utils import ConvergenceWarning
from sklearn import linear_model, datasets
from sklearn.linear_model.least_angle import _lars_path_residues
diabetes = datasets.load_diabetes()
X, y = diabetes.data, diabetes.target
# TODO: use another dataset that has multiple drops
def test_simple():
# Principle of Lars is to keep covariances tied and decreasing
# also test verbose output
from sklearn.externals.six.moves import cStringIO as StringIO
import sys
old_stdout = sys.stdout
try:
sys.stdout = StringIO()
alphas_, active, coef_path_ = linear_model.lars_path(
diabetes.data, diabetes.target, 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_true(ocur == i + 1)
else:
# no more than max_pred variables can go into the active set
assert_true(ocur == X.shape[1])
finally:
sys.stdout = old_stdout
def test_simple_precomputed():
# The same, with precomputed Gram matrix
G = np.dot(diabetes.data.T, diabetes.data)
alphas_, active, coef_path_ = linear_model.lars_path(
diabetes.data, diabetes.target, 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_true(ocur == i + 1)
else:
# no more than max_pred variables can go into the active set
assert_true(ocur == X.shape[1])
def test_all_precomputed():
# Test that lars_path with precomputed Gram and Xy gives the right answer
X, y = diabetes.data, diabetes.target
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)
def test_lars_lstsq():
# Test that Lars gives least square solution at the end
# of the path
X1 = 3 * diabetes.data # use un-normalized dataset
clf = linear_model.LassoLars(alpha=0.)
clf.fit(X1, y)
coef_lstsq = np.linalg.lstsq(X1, y)[0]
assert_array_almost_equal(clf.coef_, coef_lstsq)
def test_lasso_gives_lstsq_solution():
# Test that Lars Lasso gives least square solution at the end
# of the path
alphas_, active, 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])
f = ignore_warnings
_, _, coef_path_ = f(linear_model.lars_path)(X, y, alpha_min=0.01)
assert_true(not np.isnan(coef_path_).any())
residual = np.dot(X, coef_path_[:, -1]) - y
assert_less((residual ** 2).sum(), 1.) # just make sure it's bounded
n_samples = 10
X = np.random.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_, active_, coef_path_ = linear_model.lars_path(
diabetes.data, diabetes.target, method="lar")
alpha_, active, coef = linear_model.lars_path(
diabetes.data, diabetes.target, method="lar", return_path=False)
assert_array_almost_equal(coef, coef_path_[:, -1])
assert_true(alpha_ == alphas_[-1])
def test_no_path_precomputed():
# Test that the ``return_path=False`` option with Gram remains correct
G = np.dot(diabetes.data.T, diabetes.data)
alphas_, active_, coef_path_ = linear_model.lars_path(
diabetes.data, diabetes.target, method="lar", Gram=G)
alpha_, active, coef = linear_model.lars_path(
diabetes.data, diabetes.target, method="lar", Gram=G,
return_path=False)
assert_array_almost_equal(coef, coef_path_[:, -1])
assert_true(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_, active_, coef_path_ = linear_model.lars_path(
X, y, method="lasso", Gram=G, Xy=Xy, alpha_min=0.9)
print("---")
alpha_, active, 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_true(alpha_ == alphas_[-1])
def test_singular_matrix():
# Test when input is a singular matrix
X1 = np.array([[1, 1.], [1., 1.]])
y1 = np.array([1, 1])
alphas, active, 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_less(obj_lars, obj_cd * (1. + 1e-8))
def test_lasso_lars_vs_lasso_cd(verbose=False):
# 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_less(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_less(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_less(error, 0.01)
def test_lasso_lars_vs_lasso_cd_early_stopping(verbose=False):
# 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 alphas_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=0.9)
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_less(error, 0.01)
alphas_min = [10, 0.9, 1e-4]
# same test, with normalization
for alphas_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=0.9)
lasso_cd = linear_model.Lasso(fit_intercept=True, 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_less(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_true(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_less(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_true(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_equal(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_equal(len(lars.alphas_), 7)
@ignore_warnings
def test_multitarget():
# Assure that estimators receiving multidimensional y do the right thing
X = diabetes.data
Y = np.vstack([diabetes.target, diabetes.target ** 2]).T
n_targets = Y.shape[1]
for estimator in (linear_model.LassoLars(), linear_model.Lars()):
estimator.fit(X, Y)
Y_pred = estimator.predict(X)
Y_dec = assert_warns(DeprecationWarning, estimator.decision_function, X)
assert_array_almost_equal(Y_pred, Y_dec)
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 garantied 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_
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
y = diabetes.target
X = np.c_[X, rng.randn(X.shape[0], 4)] # add 4 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_greater(lars_bic.alpha_, lars_aic.alpha_)
assert_less(len(nonzero_bic), len(nonzero_aic))
assert_less(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_no_warning_for_zero_mse():
# LassoLarsIC should not warn for log of zero MSE.
y = np.arange(10, dtype=float)
X = y.reshape(-1, 1)
lars = linear_model.LassoLarsIC(normalize=False)
assert_no_warnings(lars.fit, X, y)
assert_true(np.any(np.isinf(lars.criterion_)))
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
for method in ['lar', 'lasso']:
alpha, active, coefs = \
linear_model.lars_path(diabetes['data'], diabetes['target'],
return_path=True, method=method,
positive=False)
assert_true(coefs.min() < 0)
alpha, active, coefs = \
linear_model.lars_path(diabetes['data'], diabetes['target'],
return_path=True, method=method,
positive=True)
assert_true(coefs.min() >= 0)
# now we gonna test the positive option for all estimator classes
default_parameter = {'fit_intercept': False}
estimator_parameter_map = {'Lars': {'n_nonzero_coefs': 5},
'LassoLars': {'alpha': 0.1},
'LarsCV': {},
'LassoLarsCV': {},
'LassoLarsIC': {}}
def test_estimatorclasses_positive_constraint():
# testing the transmissibility for the positive option of all estimator
# classes in this same function here
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(diabetes['data'], diabetes['target'])
assert_true(estimator.coef_.min() < 0)
estimator = getattr(linear_model, estname)(positive=True, **params)
estimator.fit(diabetes['data'], diabetes['target'])
assert_true(min(estimator.coef_) >= 0)
def test_lasso_lars_vs_lasso_cd_positive(verbose=False):
# 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_less(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_less(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_less(error, 0.01)
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