324 lines
11 KiB
Python
324 lines
11 KiB
Python
import numpy as np
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_true
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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 import linear_model, datasets
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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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"""
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Principle of Lars is to keep covariances tied and decreasing
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"""
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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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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_true(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_true(ocur == X.shape[1])
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def test_simple_precomputed():
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"""
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The same, with precomputed Gram matrix
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"""
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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_true(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_true(ocur == X.shape[1])
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def test_all_precomputed():
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"""
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Test that lars_path with precomputed Gram and Xy gives the right answer
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"""
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X, y = 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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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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def test_lars_lstsq():
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"""
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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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"""
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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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coef_lstsq = np.linalg.lstsq(X1, y)[0]
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assert_array_almost_equal(clf.coef_, coef_lstsq)
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def test_lasso_gives_lstsq_solution():
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"""
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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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"""
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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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_, _, coef_path_ = linear_model.lars_path(X, y, alpha_min=0.01)
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assert_true(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 = np.random.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., 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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"""
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Test that the ``return_path=False`` option returns the correct output
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"""
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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_true(alpha_ == alphas_[-1])
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def test_no_path_precomputed():
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"""
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Test that the ``return_path=False`` option with Gram remains correct
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"""
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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_true(alpha_ == alphas_[-1])
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def test_no_path_all_precomputed():
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"""
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Test that the ``return_path=False`` option with Gram and Xy remains correct
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"""
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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_true(alpha_ == alphas_[-1])
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def test_singular_matrix():
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"""
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Test when input is a singular matrix
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"""
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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], [1, 0]])
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def test_lasso_lars_vs_lasso_cd(verbose=False):
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"""
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Test that LassoLars and Lasso using coordinate descent give the
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same results
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"""
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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 = np.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):
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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 = np.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 = np.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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"""
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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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"""
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alphas_min = [10, 0.9, 1e-4]
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for alphas_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=0.9)
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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 = np.linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
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assert_less(error, 0.01)
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alphas_min = [10, 0.9, 1e-4]
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# same test, with normalization
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for alphas_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=0.9)
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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 = np.linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
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assert_less(error, 0.01)
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def test_lars_add_features():
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"""
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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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"""
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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_true(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_true(len(lars.coef_.nonzero()[0]) == 6)
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def test_multitarget():
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"""
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Assure that estimators receiving multidimensional y do the right thing
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"""
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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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for estimator in (linear_model.LassoLars(), linear_model.Lars()):
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estimator.fit(X, Y)
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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 xrange(n_targets):
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estimator.fit(X, Y[:, k])
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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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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 actualy garantied in general and is just a
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property of the given dataset, with the given steps chosen.
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"""
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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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def test_lasso_lars_ic():
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""" Test the LassoLarsIC object by checking that
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- some good features are selected.
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- alpha_bic > alpha_aic
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- n_nonzero_bic < n_nonzero_aic
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"""
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lars_bic = linear_model.LassoLarsIC('bic')
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lars_aic = linear_model.LassoLarsIC('aic')
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rng = np.random.RandomState(42)
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X = diabetes.data
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y = diabetes.target
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X = np.c_[X, rng.randn(X.shape[0], 4)] # add 4 bad features
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lars_bic.fit(X, y)
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lars_aic.fit(X, y)
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nonzero_bic = np.where(lars_bic.coef_)[0]
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nonzero_aic = np.where(lars_aic.coef_)[0]
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assert_greater(lars_bic.alpha_, lars_aic.alpha_)
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assert_less(len(nonzero_bic), len(nonzero_aic))
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assert_less(np.max(nonzero_bic), diabetes.data.shape[1])
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if __name__ == '__main__':
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import nose
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nose.runmodule()
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