325 lines
12 KiB
Python
325 lines
12 KiB
Python
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Fabian Pedregosa <fabian.pedregosa@inria.fr>
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#
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# License: BSD 3 clause
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import numpy as np
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from scipy import sparse
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_equal
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from sklearn.linear_model.base import LinearRegression
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from sklearn.linear_model.base import center_data, sparse_center_data, _rescale_data
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from sklearn.utils import check_random_state
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from sklearn.utils.testing import assert_raise_message
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from sklearn.utils.testing import assert_greater
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from sklearn.datasets.samples_generator import make_sparse_uncorrelated
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from sklearn.datasets.samples_generator import make_regression
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def test_linear_regression():
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# Test LinearRegression on a simple dataset.
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# a simple dataset
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X = [[1], [2]]
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Y = [1, 2]
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clf = LinearRegression()
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clf.fit(X, Y)
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assert_array_almost_equal(clf.coef_, [1])
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assert_array_almost_equal(clf.intercept_, [0])
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assert_array_almost_equal(clf.predict(X), [1, 2])
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# test it also for degenerate input
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X = [[1]]
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Y = [0]
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clf = LinearRegression()
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clf.fit(X, Y)
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assert_array_almost_equal(clf.coef_, [0])
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assert_array_almost_equal(clf.intercept_, [0])
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assert_array_almost_equal(clf.predict(X), [0])
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def test_linear_regression_sample_weights():
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rng = np.random.RandomState(0)
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for n_samples, n_features in ((6, 5), (5, 10)):
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y = rng.randn(n_samples)
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X = rng.randn(n_samples, n_features)
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sample_weight = 1.0 + rng.rand(n_samples)
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clf = LinearRegression()
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clf.fit(X, y, sample_weight)
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coefs1 = clf.coef_
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assert_equal(clf.coef_.shape, (X.shape[1], ))
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assert_greater(clf.score(X, y), 0.9)
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assert_array_almost_equal(clf.predict(X), y)
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# Sample weight can be implemented via a simple rescaling
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# for the square loss.
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scaled_y = y * np.sqrt(sample_weight)
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scaled_X = X * np.sqrt(sample_weight)[:, np.newaxis]
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clf.fit(X, y)
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coefs2 = clf.coef_
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assert_array_almost_equal(coefs1, coefs2)
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def test_raises_value_error_if_sample_weights_greater_than_1d():
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# Sample weights must be either scalar or 1D
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n_sampless = [2, 3]
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n_featuress = [3, 2]
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rng = np.random.RandomState(42)
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for n_samples, n_features in zip(n_sampless, n_featuress):
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X = rng.randn(n_samples, n_features)
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y = rng.randn(n_samples)
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sample_weights_OK = rng.randn(n_samples) ** 2 + 1
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sample_weights_OK_1 = 1.
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sample_weights_OK_2 = 2.
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clf = LinearRegression()
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# make sure the "OK" sample weights actually work
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clf.fit(X, y, sample_weights_OK)
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clf.fit(X, y, sample_weights_OK_1)
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clf.fit(X, y, sample_weights_OK_2)
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def test_fit_intercept():
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# Test assertions on betas shape.
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X2 = np.array([[0.38349978, 0.61650022],
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[0.58853682, 0.41146318]])
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X3 = np.array([[0.27677969, 0.70693172, 0.01628859],
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[0.08385139, 0.20692515, 0.70922346]])
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y = np.array([1, 1])
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lr2_without_intercept = LinearRegression(fit_intercept=False).fit(X2, y)
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lr2_with_intercept = LinearRegression(fit_intercept=True).fit(X2, y)
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lr3_without_intercept = LinearRegression(fit_intercept=False).fit(X3, y)
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lr3_with_intercept = LinearRegression(fit_intercept=True).fit(X3, y)
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assert_equal(lr2_with_intercept.coef_.shape,
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lr2_without_intercept.coef_.shape)
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assert_equal(lr3_with_intercept.coef_.shape,
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lr3_without_intercept.coef_.shape)
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assert_equal(lr2_without_intercept.coef_.ndim,
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lr3_without_intercept.coef_.ndim)
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def test_linear_regression_sparse(random_state=0):
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"Test that linear regression also works with sparse data"
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random_state = check_random_state(random_state)
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for i in range(10):
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n = 100
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X = sparse.eye(n, n)
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beta = random_state.rand(n)
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y = X * beta[:, np.newaxis]
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ols = LinearRegression()
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ols.fit(X, y.ravel())
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assert_array_almost_equal(beta, ols.coef_ + ols.intercept_)
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assert_array_almost_equal(ols.residues_, 0)
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def test_linear_regression_multiple_outcome(random_state=0):
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"Test multiple-outcome linear regressions"
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X, y = make_regression(random_state=random_state)
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Y = np.vstack((y, y)).T
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n_features = X.shape[1]
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clf = LinearRegression(fit_intercept=True)
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clf.fit((X), Y)
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assert_equal(clf.coef_.shape, (2, n_features))
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Y_pred = clf.predict(X)
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clf.fit(X, y)
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y_pred = clf.predict(X)
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assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3)
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def test_linear_regression_sparse_multiple_outcome(random_state=0):
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"Test multiple-outcome linear regressions with sparse data"
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random_state = check_random_state(random_state)
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X, y = make_sparse_uncorrelated(random_state=random_state)
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X = sparse.coo_matrix(X)
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Y = np.vstack((y, y)).T
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n_features = X.shape[1]
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ols = LinearRegression()
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ols.fit(X, Y)
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assert_equal(ols.coef_.shape, (2, n_features))
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Y_pred = ols.predict(X)
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ols.fit(X, y.ravel())
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y_pred = ols.predict(X)
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assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3)
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def test_center_data():
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n_samples = 200
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n_features = 2
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rng = check_random_state(0)
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X = rng.rand(n_samples, n_features)
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y = rng.rand(n_samples)
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expected_X_mean = np.mean(X, axis=0)
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# XXX: currently scaled to variance=n_samples
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expected_X_std = np.std(X, axis=0) * np.sqrt(X.shape[0])
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expected_y_mean = np.mean(y, axis=0)
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Xt, yt, X_mean, y_mean, X_std = center_data(X, y, fit_intercept=False,
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normalize=False)
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assert_array_almost_equal(X_mean, np.zeros(n_features))
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assert_array_almost_equal(y_mean, 0)
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assert_array_almost_equal(X_std, np.ones(n_features))
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assert_array_almost_equal(Xt, X)
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assert_array_almost_equal(yt, y)
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Xt, yt, X_mean, y_mean, X_std = center_data(X, y, fit_intercept=True,
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normalize=False)
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assert_array_almost_equal(X_mean, expected_X_mean)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(X_std, np.ones(n_features))
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assert_array_almost_equal(Xt, X - expected_X_mean)
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assert_array_almost_equal(yt, y - expected_y_mean)
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Xt, yt, X_mean, y_mean, X_std = center_data(X, y, fit_intercept=True,
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normalize=True)
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assert_array_almost_equal(X_mean, expected_X_mean)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(X_std, expected_X_std)
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assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_std)
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assert_array_almost_equal(yt, y - expected_y_mean)
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def test_center_data_multioutput():
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n_samples = 200
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n_features = 3
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n_outputs = 2
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rng = check_random_state(0)
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X = rng.rand(n_samples, n_features)
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y = rng.rand(n_samples, n_outputs)
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expected_y_mean = np.mean(y, axis=0)
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args = [(center_data, X), (sparse_center_data, sparse.csc_matrix(X))]
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for center, X in args:
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_, yt, _, y_mean, _ = center(X, y, fit_intercept=False,
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normalize=False)
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assert_array_almost_equal(y_mean, np.zeros(n_outputs))
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assert_array_almost_equal(yt, y)
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_, yt, _, y_mean, _ = center(X, y, fit_intercept=True,
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normalize=False)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(yt, y - y_mean)
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_, yt, _, y_mean, _ = center(X, y, fit_intercept=True,
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normalize=True)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(yt, y - y_mean)
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def test_center_data_weighted():
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n_samples = 200
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n_features = 2
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rng = check_random_state(0)
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X = rng.rand(n_samples, n_features)
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y = rng.rand(n_samples)
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sample_weight = rng.rand(n_samples)
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expected_X_mean = np.average(X, axis=0, weights=sample_weight)
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expected_y_mean = np.average(y, axis=0, weights=sample_weight)
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# XXX: if normalize=True, should we expect a weighted standard deviation?
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# Currently not weighted, but calculated with respect to weighted mean
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# XXX: currently scaled to variance=n_samples
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expected_X_std = (np.sqrt(X.shape[0]) *
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np.mean((X - expected_X_mean) ** 2, axis=0) ** .5)
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Xt, yt, X_mean, y_mean, X_std = center_data(X, y, fit_intercept=True,
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normalize=False,
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sample_weight=sample_weight)
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assert_array_almost_equal(X_mean, expected_X_mean)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(X_std, np.ones(n_features))
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assert_array_almost_equal(Xt, X - expected_X_mean)
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assert_array_almost_equal(yt, y - expected_y_mean)
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Xt, yt, X_mean, y_mean, X_std = center_data(X, y, fit_intercept=True,
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normalize=True,
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sample_weight=sample_weight)
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assert_array_almost_equal(X_mean, expected_X_mean)
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assert_array_almost_equal(y_mean, expected_y_mean)
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assert_array_almost_equal(X_std, expected_X_std)
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assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_std)
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assert_array_almost_equal(yt, y - expected_y_mean)
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def test_sparse_center_data():
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n_samples = 200
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n_features = 2
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rng = check_random_state(0)
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# random_state not supported yet in sparse.rand
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X = sparse.rand(n_samples, n_features, density=.5) # , random_state=rng
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X = X.tolil()
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y = rng.rand(n_samples)
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XA = X.toarray()
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# XXX: currently scaled to variance=n_samples
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expected_X_std = np.std(XA, axis=0) * np.sqrt(X.shape[0])
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Xt, yt, X_mean, y_mean, X_std = sparse_center_data(X, y,
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fit_intercept=False,
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normalize=False)
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assert_array_almost_equal(X_mean, np.zeros(n_features))
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assert_array_almost_equal(y_mean, 0)
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assert_array_almost_equal(X_std, np.ones(n_features))
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assert_array_almost_equal(Xt.A, XA)
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assert_array_almost_equal(yt, y)
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Xt, yt, X_mean, y_mean, X_std = sparse_center_data(X, y,
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fit_intercept=True,
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normalize=False)
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assert_array_almost_equal(X_mean, np.mean(XA, axis=0))
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assert_array_almost_equal(y_mean, np.mean(y, axis=0))
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assert_array_almost_equal(X_std, np.ones(n_features))
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assert_array_almost_equal(Xt.A, XA)
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assert_array_almost_equal(yt, y - np.mean(y, axis=0))
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Xt, yt, X_mean, y_mean, X_std = sparse_center_data(X, y,
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fit_intercept=True,
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normalize=True)
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assert_array_almost_equal(X_mean, np.mean(XA, axis=0))
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assert_array_almost_equal(y_mean, np.mean(y, axis=0))
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assert_array_almost_equal(X_std, expected_X_std)
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assert_array_almost_equal(Xt.A, XA / expected_X_std)
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assert_array_almost_equal(yt, y - np.mean(y, axis=0))
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def test_csr_sparse_center_data():
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# Test output format of sparse_center_data, when input is csr
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X, y = make_regression()
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X[X < 2.5] = 0.0
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csr = sparse.csr_matrix(X)
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csr_, y, _, _, _ = sparse_center_data(csr, y, True)
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assert_equal(csr_.getformat(), 'csr')
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def test_rescale_data():
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n_samples = 200
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n_features = 2
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rng = np.random.RandomState(0)
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sample_weight = 1.0 + rng.rand(n_samples)
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X = rng.rand(n_samples, n_features)
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y = rng.rand(n_samples)
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rescaled_X, rescaled_y = _rescale_data(X, y, sample_weight)
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rescaled_X2 = X * np.sqrt(sample_weight)[:, np.newaxis]
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rescaled_y2 = y * np.sqrt(sample_weight)
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assert_array_almost_equal(rescaled_X, rescaled_X2)
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assert_array_almost_equal(rescaled_y, rescaled_y2)
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