689 lines
26 KiB
Python
689 lines
26 KiB
Python
import warnings
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from distutils.version import LooseVersion
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import numpy as np
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from scipy import linalg
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import pytest
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from sklearn.model_selection import train_test_split
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from sklearn.utils.testing import assert_equal
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_less
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from sklearn.utils.testing import assert_greater
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from sklearn.utils.testing import assert_raises
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from sklearn.utils.testing import ignore_warnings
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from sklearn.utils.testing import assert_warns
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from sklearn.utils.testing import TempMemmap
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from sklearn.exceptions import ConvergenceWarning
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from sklearn import linear_model, datasets
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from sklearn.linear_model.least_angle import _lars_path_residues
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diabetes = datasets.load_diabetes()
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X, y = diabetes.data, diabetes.target
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# TODO: use another dataset that has multiple drops
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def test_simple():
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# Principle of Lars is to keep covariances tied and decreasing
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# also test verbose output
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from io import StringIO
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import sys
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old_stdout = sys.stdout
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try:
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sys.stdout = StringIO()
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alphas_, active, coef_path_ = linear_model.lars_path(
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diabetes.data, diabetes.target, method="lar", verbose=10)
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sys.stdout = old_stdout
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for (i, coef_) in enumerate(coef_path_.T):
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res = y - np.dot(X, coef_)
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cov = np.dot(X.T, res)
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C = np.max(abs(cov))
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eps = 1e-3
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ocur = len(cov[C - eps < abs(cov)])
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if i < X.shape[1]:
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assert ocur == i + 1
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else:
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# no more than max_pred variables can go into the active set
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assert ocur == X.shape[1]
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finally:
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sys.stdout = old_stdout
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def test_simple_precomputed():
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# The same, with precomputed Gram matrix
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G = np.dot(diabetes.data.T, diabetes.data)
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alphas_, active, coef_path_ = linear_model.lars_path(
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diabetes.data, diabetes.target, Gram=G, method="lar")
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for i, coef_ in enumerate(coef_path_.T):
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res = y - np.dot(X, coef_)
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cov = np.dot(X.T, res)
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C = np.max(abs(cov))
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eps = 1e-3
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ocur = len(cov[C - eps < abs(cov)])
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if i < X.shape[1]:
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assert ocur == i + 1
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else:
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# no more than max_pred variables can go into the active set
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assert ocur == X.shape[1]
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def test_all_precomputed():
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# Test that lars_path with precomputed Gram and Xy gives the right answer
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G = np.dot(X.T, X)
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Xy = np.dot(X.T, y)
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for method in 'lar', 'lasso':
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output = linear_model.lars_path(X, y, method=method)
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output_pre = linear_model.lars_path(X, y, Gram=G, Xy=Xy, method=method)
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for expected, got in zip(output, output_pre):
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assert_array_almost_equal(expected, got)
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@pytest.mark.filterwarnings('ignore: `rcond` parameter will change')
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# numpy deprecation
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def test_lars_lstsq():
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# Test that Lars gives least square solution at the end
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# of the path
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X1 = 3 * diabetes.data # use un-normalized dataset
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clf = linear_model.LassoLars(alpha=0.)
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clf.fit(X1, y)
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# Avoid FutureWarning about default value change when numpy >= 1.14
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rcond = None if LooseVersion(np.__version__) >= '1.14' else -1
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coef_lstsq = np.linalg.lstsq(X1, y, rcond=rcond)[0]
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assert_array_almost_equal(clf.coef_, coef_lstsq)
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@pytest.mark.filterwarnings('ignore:`rcond` parameter will change')
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# numpy deprecation
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def test_lasso_gives_lstsq_solution():
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# Test that Lars Lasso gives least square solution at the end
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# of the path
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alphas_, active, coef_path_ = linear_model.lars_path(X, y, method="lasso")
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coef_lstsq = np.linalg.lstsq(X, y)[0]
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assert_array_almost_equal(coef_lstsq, coef_path_[:, -1])
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def test_collinearity():
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# Check that lars_path is robust to collinearity in input
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X = np.array([[3., 3., 1.],
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[2., 2., 0.],
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[1., 1., 0]])
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y = np.array([1., 0., 0])
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rng = np.random.RandomState(0)
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f = ignore_warnings
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_, _, coef_path_ = f(linear_model.lars_path)(X, y, alpha_min=0.01)
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assert not np.isnan(coef_path_).any()
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residual = np.dot(X, coef_path_[:, -1]) - y
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assert_less((residual ** 2).sum(), 1.) # just make sure it's bounded
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n_samples = 10
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X = rng.rand(n_samples, 5)
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y = np.zeros(n_samples)
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_, _, coef_path_ = linear_model.lars_path(X, y, Gram='auto', copy_X=False,
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copy_Gram=False, alpha_min=0.,
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method='lasso', verbose=0,
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max_iter=500)
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assert_array_almost_equal(coef_path_, np.zeros_like(coef_path_))
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def test_no_path():
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# Test that the ``return_path=False`` option returns the correct output
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alphas_, active_, coef_path_ = linear_model.lars_path(
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diabetes.data, diabetes.target, method="lar")
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alpha_, active, coef = linear_model.lars_path(
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diabetes.data, diabetes.target, method="lar", return_path=False)
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assert_array_almost_equal(coef, coef_path_[:, -1])
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assert alpha_ == alphas_[-1]
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def test_no_path_precomputed():
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# Test that the ``return_path=False`` option with Gram remains correct
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G = np.dot(diabetes.data.T, diabetes.data)
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alphas_, active_, coef_path_ = linear_model.lars_path(
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diabetes.data, diabetes.target, method="lar", Gram=G)
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alpha_, active, coef = linear_model.lars_path(
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diabetes.data, diabetes.target, method="lar", Gram=G,
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return_path=False)
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assert_array_almost_equal(coef, coef_path_[:, -1])
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assert alpha_ == alphas_[-1]
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def test_no_path_all_precomputed():
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# Test that the ``return_path=False`` option with Gram and Xy remains
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# correct
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X, y = 3 * diabetes.data, diabetes.target
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G = np.dot(X.T, X)
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Xy = np.dot(X.T, y)
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alphas_, active_, coef_path_ = linear_model.lars_path(
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X, y, method="lasso", Gram=G, Xy=Xy, alpha_min=0.9)
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print("---")
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alpha_, active, coef = linear_model.lars_path(
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X, y, method="lasso", Gram=G, Xy=Xy, alpha_min=0.9, return_path=False)
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assert_array_almost_equal(coef, coef_path_[:, -1])
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assert alpha_ == alphas_[-1]
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@pytest.mark.filterwarnings('ignore: You should specify a value') # 0.22
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@pytest.mark.parametrize(
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'classifier',
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[linear_model.Lars, linear_model.LarsCV, linear_model.LassoLarsIC])
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def test_lars_precompute(classifier):
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# Check for different values of precompute
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G = np.dot(X.T, X)
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clf = classifier(precompute=G)
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output_1 = ignore_warnings(clf.fit)(X, y).coef_
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for precompute in [True, False, 'auto', None]:
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clf = classifier(precompute=precompute)
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output_2 = clf.fit(X, y).coef_
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assert_array_almost_equal(output_1, output_2, decimal=8)
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def test_singular_matrix():
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# Test when input is a singular matrix
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X1 = np.array([[1, 1.], [1., 1.]])
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y1 = np.array([1, 1])
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alphas, active, coef_path = linear_model.lars_path(X1, y1)
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assert_array_almost_equal(coef_path.T, [[0, 0], [1, 0]])
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def test_rank_deficient_design():
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# consistency test that checks that LARS Lasso is handling rank
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# deficient input data (with n_features < rank) in the same way
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# as coordinate descent Lasso
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y = [5, 0, 5]
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for X in ([[5, 0],
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[0, 5],
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[10, 10]],
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[[10, 10, 0],
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[1e-32, 0, 0],
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[0, 0, 1]],
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):
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# To be able to use the coefs to compute the objective function,
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# we need to turn off normalization
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lars = linear_model.LassoLars(.1, normalize=False)
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coef_lars_ = lars.fit(X, y).coef_
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obj_lars = (1. / (2. * 3.)
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* linalg.norm(y - np.dot(X, coef_lars_)) ** 2
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+ .1 * linalg.norm(coef_lars_, 1))
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coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
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coef_cd_ = coord_descent.fit(X, y).coef_
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obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
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+ .1 * linalg.norm(coef_cd_, 1))
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assert_less(obj_lars, obj_cd * (1. + 1e-8))
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def test_lasso_lars_vs_lasso_cd(verbose=False):
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# Test that LassoLars and Lasso using coordinate descent give the
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# same results.
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X = 3 * diabetes.data
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alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
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lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
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for c, a in zip(lasso_path.T, alphas):
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if a == 0:
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continue
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lasso_cd.alpha = a
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lasso_cd.fit(X, y)
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error = linalg.norm(c - lasso_cd.coef_)
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assert_less(error, 0.01)
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# similar test, with the classifiers
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for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
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clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
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clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
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normalize=False).fit(X, y)
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err = linalg.norm(clf1.coef_ - clf2.coef_)
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assert_less(err, 1e-3)
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# same test, with normalized data
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X = diabetes.data
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alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
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lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
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tol=1e-8)
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for c, a in zip(lasso_path.T, alphas):
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if a == 0:
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continue
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lasso_cd.alpha = a
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lasso_cd.fit(X, y)
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error = linalg.norm(c - lasso_cd.coef_)
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assert_less(error, 0.01)
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def test_lasso_lars_vs_lasso_cd_early_stopping(verbose=False):
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# Test that LassoLars and Lasso using coordinate descent give the
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# same results when early stopping is used.
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# (test : before, in the middle, and in the last part of the path)
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alphas_min = [10, 0.9, 1e-4]
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for alpha_min in alphas_min:
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alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
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alpha_min=alpha_min)
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lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
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lasso_cd.alpha = alphas[-1]
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lasso_cd.fit(X, y)
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error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
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assert_less(error, 0.01)
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# same test, with normalization
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for alpha_min in alphas_min:
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alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
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alpha_min=alpha_min)
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lasso_cd = linear_model.Lasso(fit_intercept=True, normalize=True,
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tol=1e-8)
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lasso_cd.alpha = alphas[-1]
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lasso_cd.fit(X, y)
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error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
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assert_less(error, 0.01)
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def test_lasso_lars_path_length():
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# Test that the path length of the LassoLars is right
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lasso = linear_model.LassoLars()
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lasso.fit(X, y)
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lasso2 = linear_model.LassoLars(alpha=lasso.alphas_[2])
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lasso2.fit(X, y)
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assert_array_almost_equal(lasso.alphas_[:3], lasso2.alphas_)
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# Also check that the sequence of alphas is always decreasing
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assert np.all(np.diff(lasso.alphas_) < 0)
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def test_lasso_lars_vs_lasso_cd_ill_conditioned():
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# Test lasso lars on a very ill-conditioned design, and check that
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# it does not blow up, and stays somewhat close to a solution given
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# by the coordinate descent solver
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# Also test that lasso_path (using lars_path output style) gives
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# the same result as lars_path and previous lasso output style
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# under these conditions.
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rng = np.random.RandomState(42)
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# Generate data
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n, m = 70, 100
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k = 5
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X = rng.randn(n, m)
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w = np.zeros((m, 1))
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i = np.arange(0, m)
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rng.shuffle(i)
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supp = i[:k]
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w[supp] = np.sign(rng.randn(k, 1)) * (rng.rand(k, 1) + 1)
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y = np.dot(X, w)
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sigma = 0.2
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y += sigma * rng.rand(*y.shape)
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y = y.squeeze()
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lars_alphas, _, lars_coef = linear_model.lars_path(X, y, method='lasso')
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_, lasso_coef2, _ = linear_model.lasso_path(X, y,
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alphas=lars_alphas,
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tol=1e-6,
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fit_intercept=False)
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assert_array_almost_equal(lars_coef, lasso_coef2, decimal=1)
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def test_lasso_lars_vs_lasso_cd_ill_conditioned2():
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# Create an ill-conditioned situation in which the LARS has to go
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# far in the path to converge, and check that LARS and coordinate
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# descent give the same answers
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# Note it used to be the case that Lars had to use the drop for good
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# strategy for this but this is no longer the case with the
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# equality_tolerance checks
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X = [[1e20, 1e20, 0],
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[-1e-32, 0, 0],
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[1, 1, 1]]
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y = [10, 10, 1]
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alpha = .0001
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def objective_function(coef):
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return (1. / (2. * len(X)) * linalg.norm(y - np.dot(X, coef)) ** 2
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+ alpha * linalg.norm(coef, 1))
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lars = linear_model.LassoLars(alpha=alpha, normalize=False)
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assert_warns(ConvergenceWarning, lars.fit, X, y)
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lars_coef_ = lars.coef_
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lars_obj = objective_function(lars_coef_)
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coord_descent = linear_model.Lasso(alpha=alpha, tol=1e-4, normalize=False)
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cd_coef_ = coord_descent.fit(X, y).coef_
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cd_obj = objective_function(cd_coef_)
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assert_less(lars_obj, cd_obj * (1. + 1e-8))
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def test_lars_add_features():
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# assure that at least some features get added if necessary
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# test for 6d2b4c
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# Hilbert matrix
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n = 5
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H = 1. / (np.arange(1, n + 1) + np.arange(n)[:, np.newaxis])
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clf = linear_model.Lars(fit_intercept=False).fit(
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H, np.arange(n))
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assert np.all(np.isfinite(clf.coef_))
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def test_lars_n_nonzero_coefs(verbose=False):
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lars = linear_model.Lars(n_nonzero_coefs=6, verbose=verbose)
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lars.fit(X, y)
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assert_equal(len(lars.coef_.nonzero()[0]), 6)
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# The path should be of length 6 + 1 in a Lars going down to 6
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# non-zero coefs
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assert_equal(len(lars.alphas_), 7)
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@ignore_warnings
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def test_multitarget():
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# Assure that estimators receiving multidimensional y do the right thing
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X = diabetes.data
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Y = np.vstack([diabetes.target, diabetes.target ** 2]).T
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n_targets = Y.shape[1]
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estimators = [
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linear_model.LassoLars(),
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linear_model.Lars(),
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# regression test for gh-1615
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linear_model.LassoLars(fit_intercept=False),
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linear_model.Lars(fit_intercept=False),
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]
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for estimator in estimators:
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estimator.fit(X, Y)
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Y_pred = estimator.predict(X)
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alphas, active, coef, path = (estimator.alphas_, estimator.active_,
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estimator.coef_, estimator.coef_path_)
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for k in range(n_targets):
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estimator.fit(X, Y[:, k])
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y_pred = estimator.predict(X)
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assert_array_almost_equal(alphas[k], estimator.alphas_)
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assert_array_almost_equal(active[k], estimator.active_)
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assert_array_almost_equal(coef[k], estimator.coef_)
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assert_array_almost_equal(path[k], estimator.coef_path_)
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assert_array_almost_equal(Y_pred[:, k], y_pred)
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@pytest.mark.filterwarnings('ignore: You should specify a value') # 0.22
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def test_lars_cv():
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# Test the LassoLarsCV object by checking that the optimal alpha
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# increases as the number of samples increases.
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# This property is not actually guaranteed in general and is just a
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# property of the given dataset, with the given steps chosen.
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old_alpha = 0
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lars_cv = linear_model.LassoLarsCV()
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for length in (400, 200, 100):
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X = diabetes.data[:length]
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y = diabetes.target[:length]
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lars_cv.fit(X, y)
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np.testing.assert_array_less(old_alpha, lars_cv.alpha_)
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old_alpha = lars_cv.alpha_
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assert not hasattr(lars_cv, 'n_nonzero_coefs')
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@pytest.mark.filterwarnings('ignore::FutureWarning')
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def test_lars_cv_max_iter():
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with warnings.catch_warnings(record=True) as w:
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X = diabetes.data
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y = diabetes.target
|
|
rng = np.random.RandomState(42)
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|
x = rng.randn(len(y))
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|
X = np.c_[X, x, x] # add correlated features
|
|
lars_cv = linear_model.LassoLarsCV(max_iter=5)
|
|
lars_cv.fit(X, y)
|
|
assert len(w) == 0
|
|
|
|
|
|
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], 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_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_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)
|
|
|
|
|
|
@pytest.mark.filterwarnings('ignore: The default of the `iid`') # 0.22
|
|
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
|
|
|
|
# Once deprecation of LAR + positive option is done use these:
|
|
# assert_raises(ValueError, linear_model.lars_path, diabetes['data'],
|
|
# diabetes['target'], method='lar', positive=True)
|
|
|
|
with pytest.warns(DeprecationWarning, match="broken"):
|
|
linear_model.lars_path(diabetes['data'], diabetes['target'],
|
|
return_path=True, method='lar',
|
|
positive=True)
|
|
|
|
method = 'lasso'
|
|
alpha, active, coefs = \
|
|
linear_model.lars_path(diabetes['data'], diabetes['target'],
|
|
return_path=True, method=method,
|
|
positive=False)
|
|
assert coefs.min() < 0
|
|
|
|
alpha, active, coefs = \
|
|
linear_model.lars_path(diabetes['data'], diabetes['target'],
|
|
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': {}}
|
|
|
|
|
|
@pytest.mark.filterwarnings('ignore: You should specify a value') # 0.22
|
|
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 estimator.coef_.min() < 0
|
|
estimator = getattr(linear_model, estname)(positive=True, **params)
|
|
estimator.fit(diabetes['data'], diabetes['target'])
|
|
assert 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)
|
|
|
|
|
|
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, fit_intercept=True,
|
|
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)
|
|
###########################################################################
|