# Author: Alexandre Gramfort # Fabian Pedregosa # # License: BSD 3 clause import numpy as np from scipy import sparse from scipy import linalg from itertools import product from sklearn.utils.testing import assert_array_almost_equal from sklearn.utils.testing import assert_almost_equal from sklearn.utils.testing import assert_equal from sklearn.utils.testing import ignore_warnings from sklearn.linear_model.base import LinearRegression from sklearn.linear_model.base import _preprocess_data from sklearn.linear_model.base import sparse_center_data, center_data from sklearn.linear_model.base import _rescale_data from sklearn.utils import check_random_state from sklearn.utils.testing import assert_greater from sklearn.datasets.samples_generator import make_sparse_uncorrelated from sklearn.datasets.samples_generator import make_regression rng = np.random.RandomState(0) def test_linear_regression(): # Test LinearRegression on a simple dataset. # a simple dataset X = [[1], [2]] Y = [1, 2] reg = LinearRegression() reg.fit(X, Y) assert_array_almost_equal(reg.coef_, [1]) assert_array_almost_equal(reg.intercept_, [0]) assert_array_almost_equal(reg.predict(X), [1, 2]) # test it also for degenerate input X = [[1]] Y = [0] reg = LinearRegression() reg.fit(X, Y) assert_array_almost_equal(reg.coef_, [0]) assert_array_almost_equal(reg.intercept_, [0]) assert_array_almost_equal(reg.predict(X), [0]) def test_linear_regression_sample_weights(): # TODO: loop over sparse data as well rng = np.random.RandomState(0) # It would not work with under-determined systems for n_samples, n_features in ((6, 5), ): y = rng.randn(n_samples) X = rng.randn(n_samples, n_features) sample_weight = 1.0 + rng.rand(n_samples) for intercept in (True, False): # LinearRegression with explicit sample_weight reg = LinearRegression(fit_intercept=intercept) reg.fit(X, y, sample_weight=sample_weight) coefs1 = reg.coef_ inter1 = reg.intercept_ assert_equal(reg.coef_.shape, (X.shape[1], )) # sanity checks assert_greater(reg.score(X, y), 0.5) # Closed form of the weighted least square # theta = (X^T W X)^(-1) * X^T W y W = np.diag(sample_weight) if intercept is False: X_aug = X else: dummy_column = np.ones(shape=(n_samples, 1)) X_aug = np.concatenate((dummy_column, X), axis=1) coefs2 = linalg.solve(X_aug.T.dot(W).dot(X_aug), X_aug.T.dot(W).dot(y)) if intercept is False: assert_array_almost_equal(coefs1, coefs2) else: assert_array_almost_equal(coefs1, coefs2[1:]) assert_almost_equal(inter1, coefs2[0]) def test_raises_value_error_if_sample_weights_greater_than_1d(): # Sample weights must be either scalar or 1D n_sampless = [2, 3] n_featuress = [3, 2] for n_samples, n_features in zip(n_sampless, n_featuress): X = rng.randn(n_samples, n_features) y = rng.randn(n_samples) sample_weights_OK = rng.randn(n_samples) ** 2 + 1 sample_weights_OK_1 = 1. sample_weights_OK_2 = 2. reg = LinearRegression() # make sure the "OK" sample weights actually work reg.fit(X, y, sample_weights_OK) reg.fit(X, y, sample_weights_OK_1) reg.fit(X, y, sample_weights_OK_2) def test_fit_intercept(): # Test assertions on betas shape. X2 = np.array([[0.38349978, 0.61650022], [0.58853682, 0.41146318]]) X3 = np.array([[0.27677969, 0.70693172, 0.01628859], [0.08385139, 0.20692515, 0.70922346]]) y = np.array([1, 1]) lr2_without_intercept = LinearRegression(fit_intercept=False).fit(X2, y) lr2_with_intercept = LinearRegression(fit_intercept=True).fit(X2, y) lr3_without_intercept = LinearRegression(fit_intercept=False).fit(X3, y) lr3_with_intercept = LinearRegression(fit_intercept=True).fit(X3, y) assert_equal(lr2_with_intercept.coef_.shape, lr2_without_intercept.coef_.shape) assert_equal(lr3_with_intercept.coef_.shape, lr3_without_intercept.coef_.shape) assert_equal(lr2_without_intercept.coef_.ndim, lr3_without_intercept.coef_.ndim) def test_linear_regression_sparse(random_state=0): # Test that linear regression also works with sparse data random_state = check_random_state(random_state) for i in range(10): n = 100 X = sparse.eye(n, n) beta = random_state.rand(n) y = X * beta[:, np.newaxis] ols = LinearRegression() ols.fit(X, y.ravel()) assert_array_almost_equal(beta, ols.coef_ + ols.intercept_) assert_array_almost_equal(ols.predict(X) - y.ravel(), 0) def test_linear_regression_multiple_outcome(random_state=0): # Test multiple-outcome linear regressions X, y = make_regression(random_state=random_state) Y = np.vstack((y, y)).T n_features = X.shape[1] reg = LinearRegression(fit_intercept=True) reg.fit((X), Y) assert_equal(reg.coef_.shape, (2, n_features)) Y_pred = reg.predict(X) reg.fit(X, y) y_pred = reg.predict(X) assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3) def test_linear_regression_sparse_multiple_outcome(random_state=0): # Test multiple-outcome linear regressions with sparse data random_state = check_random_state(random_state) X, y = make_sparse_uncorrelated(random_state=random_state) X = sparse.coo_matrix(X) Y = np.vstack((y, y)).T n_features = X.shape[1] ols = LinearRegression() ols.fit(X, Y) assert_equal(ols.coef_.shape, (2, n_features)) Y_pred = ols.predict(X) ols.fit(X, y.ravel()) y_pred = ols.predict(X) assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=3) def test_preprocess_data(): n_samples = 200 n_features = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) expected_X_mean = np.mean(X, axis=0) expected_X_norm = np.std(X, axis=0) * np.sqrt(X.shape[0]) expected_y_mean = np.mean(y, axis=0) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=False, normalize=False) assert_array_almost_equal(X_mean, np.zeros(n_features)) assert_array_almost_equal(y_mean, 0) assert_array_almost_equal(X_norm, np.ones(n_features)) assert_array_almost_equal(Xt, X) assert_array_almost_equal(yt, y) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=False) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_norm, np.ones(n_features)) assert_array_almost_equal(Xt, X - expected_X_mean) assert_array_almost_equal(yt, y - expected_y_mean) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=True) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_norm, expected_X_norm) assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_norm) assert_array_almost_equal(yt, y - expected_y_mean) def test_preprocess_data_multioutput(): n_samples = 200 n_features = 3 n_outputs = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples, n_outputs) expected_y_mean = np.mean(y, axis=0) args = [X, sparse.csc_matrix(X)] for X in args: _, yt, _, y_mean, _ = _preprocess_data(X, y, fit_intercept=False, normalize=False) assert_array_almost_equal(y_mean, np.zeros(n_outputs)) assert_array_almost_equal(yt, y) _, yt, _, y_mean, _ = _preprocess_data(X, y, fit_intercept=True, normalize=False) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(yt, y - y_mean) _, yt, _, y_mean, _ = _preprocess_data(X, y, fit_intercept=True, normalize=True) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(yt, y - y_mean) def test_preprocess_data_weighted(): n_samples = 200 n_features = 2 X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) sample_weight = rng.rand(n_samples) expected_X_mean = np.average(X, axis=0, weights=sample_weight) expected_y_mean = np.average(y, axis=0, weights=sample_weight) # XXX: if normalize=True, should we expect a weighted standard deviation? # Currently not weighted, but calculated with respect to weighted mean expected_X_norm = (np.sqrt(X.shape[0]) * np.mean((X - expected_X_mean) ** 2, axis=0) ** .5) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=False, sample_weight=sample_weight) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_norm, np.ones(n_features)) assert_array_almost_equal(Xt, X - expected_X_mean) assert_array_almost_equal(yt, y - expected_y_mean) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=True, sample_weight=sample_weight) assert_array_almost_equal(X_mean, expected_X_mean) assert_array_almost_equal(y_mean, expected_y_mean) assert_array_almost_equal(X_norm, expected_X_norm) assert_array_almost_equal(Xt, (X - expected_X_mean) / expected_X_norm) assert_array_almost_equal(yt, y - expected_y_mean) def test_sparse_preprocess_data_with_return_mean(): n_samples = 200 n_features = 2 # random_state not supported yet in sparse.rand X = sparse.rand(n_samples, n_features, density=.5) # , random_state=rng X = X.tolil() y = rng.rand(n_samples) XA = X.toarray() expected_X_norm = np.std(XA, axis=0) * np.sqrt(X.shape[0]) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=False, normalize=False, return_mean=True) assert_array_almost_equal(X_mean, np.zeros(n_features)) assert_array_almost_equal(y_mean, 0) assert_array_almost_equal(X_norm, np.ones(n_features)) assert_array_almost_equal(Xt.A, XA) assert_array_almost_equal(yt, y) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=False, return_mean=True) assert_array_almost_equal(X_mean, np.mean(XA, axis=0)) assert_array_almost_equal(y_mean, np.mean(y, axis=0)) assert_array_almost_equal(X_norm, np.ones(n_features)) assert_array_almost_equal(Xt.A, XA) assert_array_almost_equal(yt, y - np.mean(y, axis=0)) Xt, yt, X_mean, y_mean, X_norm = \ _preprocess_data(X, y, fit_intercept=True, normalize=True, return_mean=True) assert_array_almost_equal(X_mean, np.mean(XA, axis=0)) assert_array_almost_equal(y_mean, np.mean(y, axis=0)) assert_array_almost_equal(X_norm, expected_X_norm) assert_array_almost_equal(Xt.A, XA / expected_X_norm) assert_array_almost_equal(yt, y - np.mean(y, axis=0)) def test_csr_preprocess_data(): # Test output format of _preprocess_data, when input is csr X, y = make_regression() X[X < 2.5] = 0.0 csr = sparse.csr_matrix(X) csr_, y, _, _, _ = _preprocess_data(csr, y, True) assert_equal(csr_.getformat(), 'csr') def test_rescale_data(): n_samples = 200 n_features = 2 sample_weight = 1.0 + rng.rand(n_samples) X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) rescaled_X, rescaled_y = _rescale_data(X, y, sample_weight) rescaled_X2 = X * np.sqrt(sample_weight)[:, np.newaxis] rescaled_y2 = y * np.sqrt(sample_weight) assert_array_almost_equal(rescaled_X, rescaled_X2) assert_array_almost_equal(rescaled_y, rescaled_y2) @ignore_warnings # all deprecation warnings def test_deprecation_center_data(): n_samples = 200 n_features = 2 w = 1.0 + rng.rand(n_samples) X = rng.rand(n_samples, n_features) y = rng.rand(n_samples) param_grid = product([True, False], [True, False], [True, False], [None, w]) for (fit_intercept, normalize, copy, sample_weight) in param_grid: XX = X.copy() # such that we can try copy=False as well X1, y1, X1_mean, X1_var, y1_mean = \ center_data(XX, y, fit_intercept=fit_intercept, normalize=normalize, copy=copy, sample_weight=sample_weight) XX = X.copy() X2, y2, X2_mean, X2_var, y2_mean = \ _preprocess_data(XX, y, fit_intercept=fit_intercept, normalize=normalize, copy=copy, sample_weight=sample_weight) assert_array_almost_equal(X1, X2) assert_array_almost_equal(y1, y2) assert_array_almost_equal(X1_mean, X2_mean) assert_array_almost_equal(X1_var, X2_var) assert_array_almost_equal(y1_mean, y2_mean) # Sparse cases X = sparse.csr_matrix(X) for (fit_intercept, normalize, copy, sample_weight) in param_grid: X1, y1, X1_mean, X1_var, y1_mean = \ center_data(X, y, fit_intercept=fit_intercept, normalize=normalize, copy=copy, sample_weight=sample_weight) X2, y2, X2_mean, X2_var, y2_mean = \ _preprocess_data(X, y, fit_intercept=fit_intercept, normalize=normalize, copy=copy, sample_weight=sample_weight, return_mean=False) assert_array_almost_equal(X1.toarray(), X2.toarray()) assert_array_almost_equal(y1, y2) assert_array_almost_equal(X1_mean, X2_mean) assert_array_almost_equal(X1_var, X2_var) assert_array_almost_equal(y1_mean, y2_mean) for (fit_intercept, normalize) in product([True, False], [True, False]): X1, y1, X1_mean, X1_var, y1_mean = \ sparse_center_data(X, y, fit_intercept=fit_intercept, normalize=normalize) X2, y2, X2_mean, X2_var, y2_mean = \ _preprocess_data(X, y, fit_intercept=fit_intercept, normalize=normalize, return_mean=True) assert_array_almost_equal(X1.toarray(), X2.toarray()) assert_array_almost_equal(y1, y2) assert_array_almost_equal(X1_mean, X2_mean) assert_array_almost_equal(X1_var, X2_var) assert_array_almost_equal(y1_mean, y2_mean)