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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Fabian Pedregosa <fabian.pedregosa@inria.fr>
#
# License: BSD 3 clause
import pytest
import numpy as np
from scipy import sparse
from scipy import linalg
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.linear_model.base import LinearRegression
from sklearn.linear_model.base import _preprocess_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')
@pytest.mark.parametrize('is_sparse', (True, False))
@pytest.mark.parametrize('to_copy', (True, False))
def test_preprocess_copy_data_no_checks(is_sparse, to_copy):
X, y = make_regression()
X[X < 2.5] = 0.0
if is_sparse:
X = sparse.csr_matrix(X)
X_, y_, _, _, _ = _preprocess_data(X, y, True,
copy=to_copy, check_input=False)
if to_copy and is_sparse:
assert not np.may_share_memory(X_.data, X.data)
elif to_copy:
assert not np.may_share_memory(X_, X)
elif is_sparse:
assert np.may_share_memory(X_.data, X.data)
else:
assert np.may_share_memory(X_, X)
def test_dtype_preprocess_data():
n_samples = 200
n_features = 2
X = rng.rand(n_samples, n_features)
y = rng.rand(n_samples)
X_32 = np.asarray(X, dtype=np.float32)
y_32 = np.asarray(y, dtype=np.float32)
X_64 = np.asarray(X, dtype=np.float64)
y_64 = np.asarray(y, dtype=np.float64)
for fit_intercept in [True, False]:
for normalize in [True, False]:
Xt_32, yt_32, X_mean_32, y_mean_32, X_norm_32 = _preprocess_data(
X_32, y_32, fit_intercept=fit_intercept, normalize=normalize,
return_mean=True)
Xt_64, yt_64, X_mean_64, y_mean_64, X_norm_64 = _preprocess_data(
X_64, y_64, fit_intercept=fit_intercept, normalize=normalize,
return_mean=True)
Xt_3264, yt_3264, X_mean_3264, y_mean_3264, X_norm_3264 = (
_preprocess_data(X_32, y_64, fit_intercept=fit_intercept,
normalize=normalize, return_mean=True))
Xt_6432, yt_6432, X_mean_6432, y_mean_6432, X_norm_6432 = (
_preprocess_data(X_64, y_32, fit_intercept=fit_intercept,
normalize=normalize, return_mean=True))
assert_equal(Xt_32.dtype, np.float32)
assert_equal(yt_32.dtype, np.float32)
assert_equal(X_mean_32.dtype, np.float32)
assert_equal(y_mean_32.dtype, np.float32)
assert_equal(X_norm_32.dtype, np.float32)
assert_equal(Xt_64.dtype, np.float64)
assert_equal(yt_64.dtype, np.float64)
assert_equal(X_mean_64.dtype, np.float64)
assert_equal(y_mean_64.dtype, np.float64)
assert_equal(X_norm_64.dtype, np.float64)
assert_equal(Xt_3264.dtype, np.float32)
assert_equal(yt_3264.dtype, np.float32)
assert_equal(X_mean_3264.dtype, np.float32)
assert_equal(y_mean_3264.dtype, np.float32)
assert_equal(X_norm_3264.dtype, np.float32)
assert_equal(Xt_6432.dtype, np.float64)
assert_equal(yt_6432.dtype, np.float64)
assert_equal(X_mean_6432.dtype, np.float64)
assert_equal(y_mean_6432.dtype, np.float64)
assert_equal(X_norm_6432.dtype, np.float64)
assert_equal(X_32.dtype, np.float32)
assert_equal(y_32.dtype, np.float32)
assert_equal(X_64.dtype, np.float64)
assert_equal(y_64.dtype, np.float64)
assert_array_almost_equal(Xt_32, Xt_64)
assert_array_almost_equal(yt_32, yt_64)
assert_array_almost_equal(X_mean_32, X_mean_64)
assert_array_almost_equal(y_mean_32, y_mean_64)
assert_array_almost_equal(X_norm_32, X_norm_64)
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)
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