295 lines
10 KiB
Python
295 lines
10 KiB
Python
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# 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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from math import log
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import numpy as np
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import pytest
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from sklearn.utils._testing import assert_array_almost_equal
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from sklearn.utils._testing import assert_almost_equal
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from sklearn.utils._testing import assert_array_less
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from sklearn.utils import check_random_state
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from sklearn.linear_model import BayesianRidge, ARDRegression
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from sklearn.linear_model import Ridge
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from sklearn import datasets
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from sklearn.utils.extmath import fast_logdet
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diabetes = datasets.load_diabetes()
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def test_bayesian_ridge_scores():
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"""Check scores attribute shape"""
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X, y = diabetes.data, diabetes.target
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clf = BayesianRidge(compute_score=True)
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clf.fit(X, y)
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assert clf.scores_.shape == (clf.n_iter_ + 1,)
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def test_bayesian_ridge_score_values():
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"""Check value of score on toy example.
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Compute log marginal likelihood with equation (36) in Sparse Bayesian
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Learning and the Relevance Vector Machine (Tipping, 2001):
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- 0.5 * (log |Id/alpha + X.X^T/lambda| +
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y^T.(Id/alpha + X.X^T/lambda).y + n * log(2 * pi))
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+ lambda_1 * log(lambda) - lambda_2 * lambda
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+ alpha_1 * log(alpha) - alpha_2 * alpha
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and check equality with the score computed during training.
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"""
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X, y = diabetes.data, diabetes.target
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n_samples = X.shape[0]
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# check with initial values of alpha and lambda (see code for the values)
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eps = np.finfo(np.float64).eps
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alpha_ = 1.0 / (np.var(y) + eps)
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lambda_ = 1.0
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# value of the parameters of the Gamma hyperpriors
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alpha_1 = 0.1
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alpha_2 = 0.1
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lambda_1 = 0.1
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lambda_2 = 0.1
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# compute score using formula of docstring
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score = lambda_1 * log(lambda_) - lambda_2 * lambda_
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score += alpha_1 * log(alpha_) - alpha_2 * alpha_
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M = 1.0 / alpha_ * np.eye(n_samples) + 1.0 / lambda_ * np.dot(X, X.T)
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M_inv_dot_y = np.linalg.solve(M, y)
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score += -0.5 * (
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fast_logdet(M) + np.dot(y.T, M_inv_dot_y) + n_samples * log(2 * np.pi)
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)
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# compute score with BayesianRidge
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clf = BayesianRidge(
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alpha_1=alpha_1,
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alpha_2=alpha_2,
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lambda_1=lambda_1,
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lambda_2=lambda_2,
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n_iter=1,
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fit_intercept=False,
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compute_score=True,
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)
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clf.fit(X, y)
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assert_almost_equal(clf.scores_[0], score, decimal=9)
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def test_bayesian_ridge_parameter():
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# Test correctness of lambda_ and alpha_ parameters (GitHub issue #8224)
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X = np.array([[1, 1], [3, 4], [5, 7], [4, 1], [2, 6], [3, 10], [3, 2]])
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y = np.array([1, 2, 3, 2, 0, 4, 5]).T
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# A Ridge regression model using an alpha value equal to the ratio of
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# lambda_ and alpha_ from the Bayesian Ridge model must be identical
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br_model = BayesianRidge(compute_score=True).fit(X, y)
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rr_model = Ridge(alpha=br_model.lambda_ / br_model.alpha_).fit(X, y)
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assert_array_almost_equal(rr_model.coef_, br_model.coef_)
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assert_almost_equal(rr_model.intercept_, br_model.intercept_)
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def test_bayesian_sample_weights():
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# Test correctness of the sample_weights method
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X = np.array([[1, 1], [3, 4], [5, 7], [4, 1], [2, 6], [3, 10], [3, 2]])
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y = np.array([1, 2, 3, 2, 0, 4, 5]).T
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w = np.array([4, 3, 3, 1, 1, 2, 3]).T
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# A Ridge regression model using an alpha value equal to the ratio of
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# lambda_ and alpha_ from the Bayesian Ridge model must be identical
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br_model = BayesianRidge(compute_score=True).fit(X, y, sample_weight=w)
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rr_model = Ridge(alpha=br_model.lambda_ / br_model.alpha_).fit(
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X, y, sample_weight=w
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)
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assert_array_almost_equal(rr_model.coef_, br_model.coef_)
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assert_almost_equal(rr_model.intercept_, br_model.intercept_)
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def test_toy_bayesian_ridge_object():
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# Test BayesianRidge on toy
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X = np.array([[1], [2], [6], [8], [10]])
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Y = np.array([1, 2, 6, 8, 10])
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clf = BayesianRidge(compute_score=True)
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clf.fit(X, Y)
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# Check that the model could approximately learn the identity function
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test = [[1], [3], [4]]
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assert_array_almost_equal(clf.predict(test), [1, 3, 4], 2)
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def test_bayesian_initial_params():
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# Test BayesianRidge with initial values (alpha_init, lambda_init)
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X = np.vander(np.linspace(0, 4, 5), 4)
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y = np.array([0.0, 1.0, 0.0, -1.0, 0.0]) # y = (x^3 - 6x^2 + 8x) / 3
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# In this case, starting from the default initial values will increase
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# the bias of the fitted curve. So, lambda_init should be small.
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reg = BayesianRidge(alpha_init=1.0, lambda_init=1e-3)
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# Check the R2 score nearly equals to one.
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r2 = reg.fit(X, y).score(X, y)
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assert_almost_equal(r2, 1.0)
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def test_prediction_bayesian_ridge_ard_with_constant_input():
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# Test BayesianRidge and ARDRegression predictions for edge case of
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# constant target vectors
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n_samples = 4
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n_features = 5
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random_state = check_random_state(42)
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constant_value = random_state.rand()
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X = random_state.random_sample((n_samples, n_features))
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y = np.full(n_samples, constant_value, dtype=np.array(constant_value).dtype)
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expected = np.full(n_samples, constant_value, dtype=np.array(constant_value).dtype)
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for clf in [BayesianRidge(), ARDRegression()]:
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y_pred = clf.fit(X, y).predict(X)
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assert_array_almost_equal(y_pred, expected)
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def test_std_bayesian_ridge_ard_with_constant_input():
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# Test BayesianRidge and ARDRegression standard dev. for edge case of
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# constant target vector
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# The standard dev. should be relatively small (< 0.01 is tested here)
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n_samples = 10
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n_features = 5
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random_state = check_random_state(42)
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constant_value = random_state.rand()
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X = random_state.random_sample((n_samples, n_features))
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y = np.full(n_samples, constant_value, dtype=np.array(constant_value).dtype)
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expected_upper_boundary = 0.01
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for clf in [BayesianRidge(), ARDRegression()]:
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_, y_std = clf.fit(X, y).predict(X, return_std=True)
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assert_array_less(y_std, expected_upper_boundary)
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def test_update_of_sigma_in_ard():
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# Checks that `sigma_` is updated correctly after the last iteration
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# of the ARDRegression algorithm. See issue #10128.
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X = np.array([[1, 0], [0, 0]])
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y = np.array([0, 0])
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clf = ARDRegression(n_iter=1)
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clf.fit(X, y)
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# With the inputs above, ARDRegression prunes both of the two coefficients
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# in the first iteration. Hence, the expected shape of `sigma_` is (0, 0).
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assert clf.sigma_.shape == (0, 0)
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# Ensure that no error is thrown at prediction stage
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clf.predict(X, return_std=True)
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def test_toy_ard_object():
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# Test BayesianRegression ARD classifier
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X = np.array([[1], [2], [3]])
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Y = np.array([1, 2, 3])
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clf = ARDRegression(compute_score=True)
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clf.fit(X, Y)
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# Check that the model could approximately learn the identity function
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test = [[1], [3], [4]]
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assert_array_almost_equal(clf.predict(test), [1, 3, 4], 2)
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@pytest.mark.parametrize("n_samples, n_features", ((10, 100), (100, 10)))
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def test_ard_accuracy_on_easy_problem(global_random_seed, n_samples, n_features):
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# Check that ARD converges with reasonable accuracy on an easy problem
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# (Github issue #14055)
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X = np.random.RandomState(global_random_seed).normal(size=(250, 3))
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y = X[:, 1]
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regressor = ARDRegression()
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regressor.fit(X, y)
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abs_coef_error = np.abs(1 - regressor.coef_[1])
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assert abs_coef_error < 1e-10
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def test_return_std():
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# Test return_std option for both Bayesian regressors
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def f(X):
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return np.dot(X, w) + b
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def f_noise(X, noise_mult):
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return f(X) + np.random.randn(X.shape[0]) * noise_mult
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d = 5
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n_train = 50
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n_test = 10
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w = np.array([1.0, 0.0, 1.0, -1.0, 0.0])
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b = 1.0
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X = np.random.random((n_train, d))
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X_test = np.random.random((n_test, d))
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for decimal, noise_mult in enumerate([1, 0.1, 0.01]):
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y = f_noise(X, noise_mult)
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m1 = BayesianRidge()
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m1.fit(X, y)
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y_mean1, y_std1 = m1.predict(X_test, return_std=True)
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assert_array_almost_equal(y_std1, noise_mult, decimal=decimal)
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m2 = ARDRegression()
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m2.fit(X, y)
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y_mean2, y_std2 = m2.predict(X_test, return_std=True)
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assert_array_almost_equal(y_std2, noise_mult, decimal=decimal)
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def test_update_sigma(global_random_seed):
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# make sure the two update_sigma() helpers are equivalent. The woodbury
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# formula is used when n_samples < n_features, and the other one is used
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# otherwise.
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rng = np.random.RandomState(global_random_seed)
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# set n_samples == n_features to avoid instability issues when inverting
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# the matrices. Using the woodbury formula would be unstable when
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# n_samples > n_features
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n_samples = n_features = 10
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X = rng.randn(n_samples, n_features)
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alpha = 1
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lmbda = np.arange(1, n_features + 1)
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keep_lambda = np.array([True] * n_features)
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reg = ARDRegression()
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sigma = reg._update_sigma(X, alpha, lmbda, keep_lambda)
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sigma_woodbury = reg._update_sigma_woodbury(X, alpha, lmbda, keep_lambda)
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np.testing.assert_allclose(sigma, sigma_woodbury)
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@pytest.mark.parametrize("dtype", [np.float32, np.float64])
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@pytest.mark.parametrize("Estimator", [BayesianRidge, ARDRegression])
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def test_dtype_match(dtype, Estimator):
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# Test that np.float32 input data is not cast to np.float64 when possible
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X = np.array([[1, 1], [3, 4], [5, 7], [4, 1], [2, 6], [3, 10], [3, 2]], dtype=dtype)
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y = np.array([1, 2, 3, 2, 0, 4, 5]).T
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model = Estimator()
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# check type consistency
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model.fit(X, y)
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attributes = ["coef_", "sigma_"]
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for attribute in attributes:
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assert getattr(model, attribute).dtype == X.dtype
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y_mean, y_std = model.predict(X, return_std=True)
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assert y_mean.dtype == X.dtype
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assert y_std.dtype == X.dtype
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@pytest.mark.parametrize("Estimator", [BayesianRidge, ARDRegression])
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def test_dtype_correctness(Estimator):
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X = np.array([[1, 1], [3, 4], [5, 7], [4, 1], [2, 6], [3, 10], [3, 2]])
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y = np.array([1, 2, 3, 2, 0, 4, 5]).T
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model = Estimator()
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coef_32 = model.fit(X.astype(np.float32), y).coef_
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coef_64 = model.fit(X.astype(np.float64), y).coef_
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np.testing.assert_allclose(coef_32, coef_64, rtol=1e-4)
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