def test_sag_multiclass_computed_correctly():
"""tests if the multiclass classifier is computed correctly"""
alpha = .1
n_samples = 20
tol = .00001
max_iter = 40
fit_intercept = True
X, y = make_blobs(n_samples=n_samples,
centers=3,
random_state=0,
cluster_std=0.1)
step_size = get_step_size(X, alpha, fit_intercept, classification=True)
classes = np.unique(y)
clf1 = LogisticRegression(solver='sag',
C=1. / alpha / n_samples,
max_iter=max_iter,
tol=tol,
random_state=77,
fit_intercept=fit_intercept,
multi_class='ovr')
clf2 = clone(clf1)
clf1.fit(X, y)
clf2.fit(sp.csr_matrix(X), y)
coef1 = []
intercept1 = []
coef2 = []
intercept2 = []
for cl in classes:
y_encoded = np.ones(n_samples)
y_encoded[y != cl] = -1
spweights1, spintercept1 = sag_sparse(X,
y_encoded,
step_size,
alpha,
dloss=log_dloss,
n_iter=max_iter,
fit_intercept=fit_intercept)
spweights2, spintercept2 = sag_sparse(X,
y_encoded,
step_size,
alpha,
dloss=log_dloss,
n_iter=max_iter,
sparse=True,
fit_intercept=fit_intercept)
coef1.append(spweights1)
intercept1.append(spintercept1)
coef2.append(spweights2)
intercept2.append(spintercept2)
coef1 = np.vstack(coef1)
intercept1 = np.array(intercept1)
coef2 = np.vstack(coef2)
intercept2 = np.array(intercept2)
for i, cl in enumerate(classes):
assert_array_almost_equal(clf1.coef_[i].ravel(),
coef1[i].ravel(),
decimal=2)
assert_almost_equal(clf1.intercept_[i], intercept1[i], decimal=1)
assert_array_almost_equal(clf2.coef_[i].ravel(),
coef2[i].ravel(),
decimal=2)
assert_almost_equal(clf2.intercept_[i], intercept2[i], decimal=1)
def test_non_consecutive_labels():
# regression tests for labels with gaps
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 2, 2, 2],
[0, 1, 0, 1, 2, 2])
assert_almost_equal(h, 0.67, 2)
assert_almost_equal(c, 0.42, 2)
assert_almost_equal(v, 0.52, 2)
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 1, 1, 1],
[0, 4, 0, 4, 2, 2])
assert_almost_equal(h, 0.67, 2)
assert_almost_equal(c, 0.42, 2)
assert_almost_equal(v, 0.52, 2)
ari_1 = adjusted_rand_score([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2])
ari_2 = adjusted_rand_score([0, 0, 0, 1, 1, 1], [0, 4, 0, 4, 2, 2])
assert_almost_equal(ari_1, 0.24, 2)
assert_almost_equal(ari_2, 0.24, 2)
ri_1 = rand_score([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2])
ri_2 = rand_score([0, 0, 0, 1, 1, 1], [0, 4, 0, 4, 2, 2])
assert_almost_equal(ri_1, 0.66, 2)
assert_almost_equal(ri_2, 0.66, 2)
def test_entropy():
ent = entropy([0, 0, 42.])
assert_almost_equal(ent, 0.6365141, 5)
assert_almost_equal(entropy([]), 1)
def check_randomized_svd_low_rank(dtype):
# Check that extmath.randomized_svd is consistent with linalg.svd
n_samples = 100
n_features = 500
rank = 5
k = 10
decimal = 5 if dtype == np.float32 else 7
dtype = np.dtype(dtype)
# generate a matrix X of approximate effective rank `rank` and no noise
# component (very structured signal):
X = make_low_rank_matrix(n_samples=n_samples,
n_features=n_features,
effective_rank=rank,
tail_strength=0.0,
random_state=0).astype(dtype, copy=False)
assert X.shape == (n_samples, n_features)
# compute the singular values of X using the slow exact method
U, s, Vt = linalg.svd(X, full_matrices=False)
# Convert the singular values to the specific dtype
U = U.astype(dtype, copy=False)
s = s.astype(dtype, copy=False)
Vt = Vt.astype(dtype, copy=False)
for normalizer in ['auto', 'LU', 'QR']: # 'none' would not be stable
# compute the singular values of X using the fast approximate method
Ua, sa, Va = randomized_svd(X,
k,
power_iteration_normalizer=normalizer,
random_state=0)
# If the input dtype is float, then the output dtype is float of the
# same bit size (f32 is not upcast to f64)
# But if the input dtype is int, the output dtype is float64
if dtype.kind == 'f':
assert Ua.dtype == dtype
assert sa.dtype == dtype
assert Va.dtype == dtype
else:
assert Ua.dtype == np.float64
assert sa.dtype == np.float64
assert Va.dtype == np.float64
assert Ua.shape == (n_samples, k)
assert sa.shape == (k, )
assert Va.shape == (k, n_features)
# ensure that the singular values of both methods are equal up to the
# real rank of the matrix
assert_almost_equal(s[:k], sa, decimal=decimal)
# check the singular vectors too (while not checking the sign)
assert_almost_equal(np.dot(U[:, :k], Vt[:k, :]),
np.dot(Ua, Va),
decimal=decimal)
# check the sparse matrix representation
X = sparse.csr_matrix(X)
# compute the singular values of X using the fast approximate method
Ua, sa, Va = \
randomized_svd(X, k, power_iteration_normalizer=normalizer,
random_state=0)
if dtype.kind == 'f':
assert Ua.dtype == dtype
assert sa.dtype == dtype
assert Va.dtype == dtype
else:
assert Ua.dtype.kind == 'f'
assert sa.dtype.kind == 'f'
assert Va.dtype.kind == 'f'
assert_almost_equal(s[:rank], sa[:rank], decimal=decimal)
def test_lml_precomputed(kernel):
# Test that lml of optimized kernel is stored correctly.
gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
assert_almost_equal(gpc.log_marginal_likelihood(gpc.kernel_.theta),
gpc.log_marginal_likelihood(), 7)
def test_ledoit_wolf():
# Tests LedoitWolf module on a simple dataset.
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
lw = LedoitWolf(assume_centered=True)
lw.fit(X_centered)
shrinkage_ = lw.shrinkage_
score_ = lw.score(X_centered)
assert_almost_equal(
ledoit_wolf_shrinkage(X_centered, assume_centered=True), shrinkage_
)
assert_almost_equal(
ledoit_wolf_shrinkage(X_centered, assume_centered=True, block_size=6),
shrinkage_,
)
# compare shrunk covariance obtained from data and from MLE estimate
lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(
X_centered, assume_centered=True
)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_)
# compare estimates given by LW and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=lw.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, lw.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
lw = LedoitWolf(assume_centered=True)
lw.fit(X_1d)
lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X_1d, assume_centered=True)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, lw.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
lw = LedoitWolf(store_precision=False, assume_centered=True)
lw.fit(X_centered)
assert_almost_equal(lw.score(X_centered), score_, 4)
assert lw.precision_ is None
# Same tests without assuming centered data
# test shrinkage coeff on a simple data set
lw = LedoitWolf()
lw.fit(X)
assert_almost_equal(lw.shrinkage_, shrinkage_, 4)
assert_almost_equal(lw.shrinkage_, ledoit_wolf_shrinkage(X))
assert_almost_equal(lw.shrinkage_, ledoit_wolf(X)[1])
assert_almost_equal(lw.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_)
# compare estimates given by LW and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=lw.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, lw.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
lw = LedoitWolf()
lw.fit(X_1d)
lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X_1d)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), lw.covariance_, 4)
# test with one sample
# warning should be raised when using only 1 sample
X_1sample = np.arange(5).reshape(1, 5)
lw = LedoitWolf()
warn_msg = "Only one sample available. You may want to reshape your data array"
with pytest.warns(UserWarning, match=warn_msg):
lw.fit(X_1sample)
assert_array_almost_equal(lw.covariance_, np.zeros(shape=(5, 5), dtype=np.float64))
# test shrinkage coeff on a simple data set (without saving precision)
lw = LedoitWolf(store_precision=False)
lw.fit(X)
assert_almost_equal(lw.score(X), score_, 4)
assert lw.precision_ is None
def test_covariance():
# Tests Covariance module on a simple dataset.
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
emp_cov = empirical_covariance(X)
assert_array_almost_equal(emp_cov, cov.covariance_, 4)
assert_almost_equal(cov.error_norm(emp_cov), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm="spectral"), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm="frobenius"), 0)
assert_almost_equal(cov.error_norm(emp_cov, scaling=False), 0)
assert_almost_equal(cov.error_norm(emp_cov, squared=False), 0)
with pytest.raises(NotImplementedError):
cov.error_norm(emp_cov, norm="foo")
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert np.amin(mahal_dist) > 0
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d), norm="spectral"), 0)
# test with one sample
# Create X with 1 sample and 5 features
X_1sample = np.arange(5).reshape(1, 5)
cov = EmpiricalCovariance()
warn_msg = "Only one sample available. You may want to reshape your data array"
with pytest.warns(UserWarning, match=warn_msg):
cov.fit(X_1sample)
assert_array_almost_equal(cov.covariance_, np.zeros(shape=(5, 5), dtype=np.float64))
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
# test centered case
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
assert_array_equal(cov.location_, np.zeros(X.shape[1]))
def test_calibration_curve():
"""Check calibration_curve function"""
y_true = np.array([0, 0, 0, 1, 1, 1])
y_pred = np.array([0., 0.1, 0.2, 0.8, 0.9, 1.])
prob_true, prob_pred = calibration_curve(y_true, y_pred, n_bins=2)
prob_true_unnormalized, prob_pred_unnormalized = \
calibration_curve(y_true, y_pred * 2, n_bins=2, normalize=True)
assert len(prob_true) == len(prob_pred)
assert len(prob_true) == 2
assert_almost_equal(prob_true, [0, 1])
assert_almost_equal(prob_pred, [0.1, 0.9])
assert_almost_equal(prob_true, prob_true_unnormalized)
assert_almost_equal(prob_pred, prob_pred_unnormalized)
# probabilities outside [0, 1] should not be accepted when normalize
# is set to False
assert_raises(ValueError,
calibration_curve, [1.1], [-0.1],
normalize=False)
# test that quantiles work as expected
y_true2 = np.array([0, 0, 0, 0, 1, 1])
y_pred2 = np.array([0., 0.1, 0.2, 0.5, 0.9, 1.])
prob_true_quantile, prob_pred_quantile = calibration_curve(
y_true2, y_pred2, n_bins=2, strategy='quantile')
assert len(prob_true_quantile) == len(prob_pred_quantile)
assert len(prob_true_quantile) == 2
assert_almost_equal(prob_true_quantile, [0, 2 / 3])
assert_almost_equal(prob_pred_quantile, [0.1, 0.8])
# Check that error is raised when invalid strategy is selected
assert_raises(ValueError,
calibration_curve,
y_true2,
y_pred2,
strategy='percentile')
def test_sparse_random_matrix():
# Check some statical properties of sparse random matrix
n_components = 100
n_features = 500
for density in [0.3, 1.]:
s = 1 / density
A = _sparse_random_matrix(n_components,
n_features,
density=density,
random_state=0)
A = densify(A)
# Check possible values
values = np.unique(A)
assert np.sqrt(s) / np.sqrt(n_components) in values
assert -np.sqrt(s) / np.sqrt(n_components) in values
if density == 1.0:
assert np.size(values) == 2
else:
assert 0. in values
assert np.size(values) == 3
# Check that the random matrix follow the proper distribution.
# Let's say that each element of a_{ij} of A is taken from
#
# - -sqrt(s) / sqrt(n_components) with probability 1 / 2s
# - 0 with probability 1 - 1 / s
# - +sqrt(s) / sqrt(n_components) with probability 1 / 2s
#
assert_almost_equal(np.mean(A == 0.0), 1 - 1 / s, decimal=2)
assert_almost_equal(np.mean(A == np.sqrt(s) / np.sqrt(n_components)),
1 / (2 * s),
decimal=2)
assert_almost_equal(np.mean(A == -np.sqrt(s) / np.sqrt(n_components)),
1 / (2 * s),
decimal=2)
assert_almost_equal(np.var(A == 0.0, ddof=1), (1 - 1 / s) * 1 / s,
decimal=2)
assert_almost_equal(np.var(A == np.sqrt(s) / np.sqrt(n_components),
ddof=1), (1 - 1 / (2 * s)) * 1 / (2 * s),
decimal=2)
assert_almost_equal(np.var(A == -np.sqrt(s) / np.sqrt(n_components),
ddof=1), (1 - 1 / (2 * s)) * 1 / (2 * s),
decimal=2)
def test_kernel_diag(kernel):
# Test that diag method of kernel returns consistent results.
K_call_diag = np.diag(kernel(X))
K_diag = kernel.diag(X)
assert_almost_equal(K_call_diag, K_diag, 5)
def test_kernel_stationary(kernel):
# Test stationarity of kernels.
K = kernel(X, X + 1)
assert_almost_equal(K[0, 0], np.diag(K))
def test_auto_vs_cross(kernel):
# Auto-correlation and cross-correlation should be consistent.
K_auto = kernel(X)
K_cross = kernel(X, X)
assert_almost_equal(K_auto, K_cross, 5)
def test_warm_start(seed):
random_state = seed
rng = np.random.RandomState(random_state)
n_samples, n_features, n_components = 500, 2, 2
X = rng.rand(n_samples, n_features)
# Assert the warm_start give the same result for the same number of iter
g = GaussianMixture(
n_components=n_components,
n_init=1,
max_iter=2,
reg_covar=0,
random_state=random_state,
warm_start=False,
)
h = GaussianMixture(
n_components=n_components,
n_init=1,
max_iter=1,
reg_covar=0,
random_state=random_state,
warm_start=True,
)
g.fit(X)
score1 = h.fit(X).score(X)
score2 = h.fit(X).score(X)
assert_almost_equal(g.weights_, h.weights_)
assert_almost_equal(g.means_, h.means_)
assert_almost_equal(g.precisions_, h.precisions_)
assert score2 > score1
# Assert that by using warm_start we can converge to a good solution
g = GaussianMixture(
n_components=n_components,
n_init=1,
max_iter=5,
reg_covar=0,
random_state=random_state,
warm_start=False,
tol=1e-6,
)
h = GaussianMixture(
n_components=n_components,
n_init=1,
max_iter=5,
reg_covar=0,
random_state=random_state,
warm_start=True,
tol=1e-6,
)
g.fit(X)
assert not g.converged_
h.fit(X)
# depending on the data there is large variability in the number of
# refit necessary to converge due to the complete randomness of the
# data
for _ in range(1000):
h.fit(X)
if h.converged_:
break
assert h.converged_
def test_multiclass_classifier_class_weight():
"""tests multiclass with classweights for each class"""
alpha = .1
n_samples = 20
tol = .00001
max_iter = 50
class_weight = {0: .45, 1: .55, 2: .75}
fit_intercept = True
X, y = make_blobs(n_samples=n_samples,
centers=3,
random_state=0,
cluster_std=0.1)
step_size = get_step_size(X, alpha, fit_intercept, classification=True)
classes = np.unique(y)
clf1 = LogisticRegression(solver='sag',
C=1. / alpha / n_samples,
max_iter=max_iter,
tol=tol,
random_state=77,
fit_intercept=fit_intercept,
multi_class='ovr',
class_weight=class_weight)
clf2 = clone(clf1)
clf1.fit(X, y)
clf2.fit(sp.csr_matrix(X), y)
le = LabelEncoder()
class_weight_ = compute_class_weight(class_weight, np.unique(y), y)
sample_weight = class_weight_[le.fit_transform(y)]
coef1 = []
intercept1 = []
coef2 = []
intercept2 = []
for cl in classes:
y_encoded = np.ones(n_samples)
y_encoded[y != cl] = -1
spweights1, spintercept1 = sag_sparse(X,
y_encoded,
step_size,
alpha,
n_iter=max_iter,
dloss=log_dloss,
sample_weight=sample_weight)
spweights2, spintercept2 = sag_sparse(X,
y_encoded,
step_size,
alpha,
n_iter=max_iter,
dloss=log_dloss,
sample_weight=sample_weight,
sparse=True)
coef1.append(spweights1)
intercept1.append(spintercept1)
coef2.append(spweights2)
intercept2.append(spintercept2)
coef1 = np.vstack(coef1)
intercept1 = np.array(intercept1)
coef2 = np.vstack(coef2)
intercept2 = np.array(intercept2)
for i, cl in enumerate(classes):
assert_array_almost_equal(clf1.coef_[i].ravel(),
coef1[i].ravel(),
decimal=2)
assert_almost_equal(clf1.intercept_[i], intercept1[i], decimal=1)
assert_array_almost_equal(clf2.coef_[i].ravel(),
coef2[i].ravel(),
decimal=2)
assert_almost_equal(clf2.intercept_[i], intercept2[i], decimal=1)
def test_fastica_simple(add_noise, seed):
# Test the FastICA algorithm on very simple data.
rng = np.random.RandomState(seed)
# scipy.stats uses the global RNG:
n_samples = 1000
# Generate two sources:
s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
s2 = stats.t.rvs(1, size=n_samples)
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing angle
phi = 0.6
mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi),
-np.cos(phi)]])
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(2, 1000)
center_and_norm(m)
# function as fun arg
def g_test(x):
return x**3, (3 * x**2).mean(axis=-1)
algos = ["parallel", "deflation"]
nls = ["logcosh", "exp", "cube", g_test]
whitening = [True, False]
for algo, nl, whiten in itertools.product(algos, nls, whitening):
if whiten:
k_, mixing_, s_ = fastica(m.T,
fun=nl,
algorithm=algo,
random_state=rng)
with pytest.raises(ValueError):
fastica(m.T, fun=np.tanh, algorithm=algo)
else:
pca = PCA(n_components=2, whiten=True, random_state=rng)
X = pca.fit_transform(m.T)
k_, mixing_, s_ = fastica(X,
fun=nl,
algorithm=algo,
whiten=False,
random_state=rng)
with pytest.raises(ValueError):
fastica(X, fun=np.tanh, algorithm=algo)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
if whiten:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if not add_noise:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
else:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
# Test FastICA class
_, _, sources_fun = fastica(m.T, fun=nl, algorithm=algo, random_state=seed)
ica = FastICA(fun=nl, algorithm=algo, random_state=seed)
sources = ica.fit_transform(m.T)
assert ica.components_.shape == (2, 2)
assert sources.shape == (1000, 2)
assert_array_almost_equal(sources_fun, sources)
assert_array_almost_equal(sources, ica.transform(m.T))
assert ica.mixing_.shape == (2, 2)
for fn in [np.tanh, "exp(-.5(x^2))"]:
ica = FastICA(fun=fn, algorithm=algo)
with pytest.raises(ValueError):
ica.fit(m.T)
with pytest.raises(TypeError):
FastICA(fun=range(10)).fit(m.T)
def test_regression_metrics_at_limits():
assert_almost_equal(mean_squared_error([0.], [0.]), 0.0)
assert_almost_equal(mean_squared_error([0.], [0.], squared=False), 0.0)
assert_almost_equal(mean_squared_log_error([0.], [0.]), 0.0)
assert_almost_equal(mean_absolute_error([0.], [0.]), 0.0)
assert_almost_equal(mean_pinball_loss([0.], [0.]), 0.0)
assert_almost_equal(mean_absolute_percentage_error([0.], [0.]), 0.0)
assert_almost_equal(median_absolute_error([0.], [0.]), 0.0)
assert_almost_equal(max_error([0.], [0.]), 0.0)
assert_almost_equal(explained_variance_score([0.], [0.]), 1.0)
assert_almost_equal(r2_score([0., 1], [0., 1]), 1.0)
err_msg = ("Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values.")
with pytest.raises(ValueError, match=err_msg):
mean_squared_log_error([-1.], [-1.])
err_msg = ("Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values.")
with pytest.raises(ValueError, match=err_msg):
mean_squared_log_error([1., 2., 3.], [1., -2., 3.])
err_msg = ("Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values.")
with pytest.raises(ValueError, match=err_msg):
mean_squared_log_error([1., -2., 3.], [1., 2., 3.])
# Tweedie deviance error
power = -1.2
assert_allclose(mean_tweedie_deviance([0], [1.], power=power),
2 / (2 - power),
rtol=1e-3)
with pytest.raises(ValueError,
match="can only be used on strictly positive y_pred."):
mean_tweedie_deviance([0.], [0.], power=power)
assert_almost_equal(mean_tweedie_deviance([0.], [0.], power=0), 0.00, 2)
msg = "only be used on non-negative y and strictly positive y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.], [0.], power=1.0)
power = 1.5
assert_allclose(mean_tweedie_deviance([0.], [1.], power=power),
2 / (2 - power))
msg = "only be used on non-negative y and strictly positive y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.], [0.], power=power)
power = 2.
assert_allclose(mean_tweedie_deviance([1.], [1.], power=power),
0.00,
atol=1e-8)
msg = "can only be used on strictly positive y and y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.], [0.], power=power)
power = 3.
assert_allclose(mean_tweedie_deviance([1.], [1.], power=power),
0.00,
atol=1e-8)
msg = "can only be used on strictly positive y and y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.], [0.], power=power)
with pytest.raises(ValueError,
match="is only defined for power<=0 and power>=1"):
mean_tweedie_deviance([0.], [0.], power=0.5)
def _do_bistochastic_test(scaled):
"""Check that rows and columns sum to the same constant."""
_do_scale_test(scaled)
assert_almost_equal(scaled.sum(axis=0).mean(),
scaled.sum(axis=1).mean(),
decimal=1)
def test_regression_custom_weights():
y_true = [[1, 2], [2.5, -1], [4.5, 3], [5, 7]]
y_pred = [[1, 1], [2, -1], [5, 4], [5, 6.5]]
msew = mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6])
rmsew = mean_squared_error(y_true,
y_pred,
multioutput=[0.4, 0.6],
squared=False)
maew = mean_absolute_error(y_true, y_pred, multioutput=[0.4, 0.6])
mapew = mean_absolute_percentage_error(y_true,
y_pred,
multioutput=[0.4, 0.6])
rw = r2_score(y_true, y_pred, multioutput=[0.4, 0.6])
evsw = explained_variance_score(y_true, y_pred, multioutput=[0.4, 0.6])
assert_almost_equal(msew, 0.39, decimal=2)
assert_almost_equal(rmsew, 0.59, decimal=2)
assert_almost_equal(maew, 0.475, decimal=3)
assert_almost_equal(mapew, 0.1668, decimal=2)
assert_almost_equal(rw, 0.94, decimal=2)
assert_almost_equal(evsw, 0.94, decimal=2)
# Handling msle separately as it does not accept negative inputs.
y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
msle = mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7])
msle2 = mean_squared_error(np.log(1 + y_true),
np.log(1 + y_pred),
multioutput=[0.3, 0.7])
assert_almost_equal(msle, msle2, decimal=2)
def test_oas():
# Tests OAS module on a simple dataset.
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_centered, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0:1]
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert oa.precision_ is None
# Same tests without assuming centered data--------------------------------
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
# warning should be raised when using only 1 sample
X_1sample = np.arange(5).reshape(1, 5)
oa = OAS()
warn_msg = "Only one sample available. You may want to reshape your data array"
with pytest.warns(UserWarning, match=warn_msg):
oa.fit(X_1sample)
assert_array_almost_equal(oa.covariance_, np.zeros(shape=(5, 5), dtype=np.float64))
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert oa.precision_ is None
def test_regression_metrics(n_samples=50):
y_true = np.arange(n_samples)
y_pred = y_true + 1
y_pred_2 = y_true - 1
assert_almost_equal(mean_squared_error(y_true, y_pred), 1.)
assert_almost_equal(
mean_squared_log_error(y_true, y_pred),
mean_squared_error(np.log(1 + y_true), np.log(1 + y_pred)))
assert_almost_equal(mean_absolute_error(y_true, y_pred), 1.)
assert_almost_equal(mean_pinball_loss(y_true, y_pred), 0.5)
assert_almost_equal(mean_pinball_loss(y_true, y_pred_2), 0.5)
assert_almost_equal(mean_pinball_loss(y_true, y_pred, alpha=0.4), 0.6)
assert_almost_equal(mean_pinball_loss(y_true, y_pred_2, alpha=0.4), 0.4)
assert_almost_equal(median_absolute_error(y_true, y_pred), 1.)
mape = mean_absolute_percentage_error(y_true, y_pred)
assert np.isfinite(mape)
assert mape > 1e6
assert_almost_equal(max_error(y_true, y_pred), 1.)
assert_almost_equal(r2_score(y_true, y_pred), 0.995, 2)
assert_almost_equal(explained_variance_score(y_true, y_pred), 1.)
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=0),
mean_squared_error(y_true, y_pred))
# Tweedie deviance needs positive y_pred, except for p=0,
# p>=2 needs positive y_true
# results evaluated by sympy
y_true = np.arange(1, 1 + n_samples)
y_pred = 2 * y_true
n = n_samples
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=-1),
5 / 12 * n * (n**2 + 2 * n + 1))
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=1),
(n + 1) * (1 - np.log(2)))
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=2),
2 * np.log(2) - 1)
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=3 / 2),
((6 * np.sqrt(2) - 8) / n) * np.sqrt(y_true).sum())
assert_almost_equal(mean_tweedie_deviance(y_true, y_pred, power=3),
np.sum(1 / y_true) / (4 * n))
def test_randomized_svd_transpose_consistency():
# Check that transposing the design matrix has limited impact
n_samples = 100
n_features = 500
rank = 4
k = 10
X = make_low_rank_matrix(n_samples=n_samples,
n_features=n_features,
effective_rank=rank,
tail_strength=0.5,
random_state=0)
assert X.shape == (n_samples, n_features)
U1, s1, V1 = randomized_svd(X,
k,
n_iter=3,
transpose=False,
random_state=0)
U2, s2, V2 = randomized_svd(X, k, n_iter=3, transpose=True, random_state=0)
U3, s3, V3 = randomized_svd(X,
k,
n_iter=3,
transpose='auto',
random_state=0)
U4, s4, V4 = linalg.svd(X, full_matrices=False)
assert_almost_equal(s1, s4[:k], decimal=3)
assert_almost_equal(s2, s4[:k], decimal=3)
assert_almost_equal(s3, s4[:k], decimal=3)
assert_almost_equal(np.dot(U1, V1),
np.dot(U4[:, :k], V4[:k, :]),
decimal=2)
assert_almost_equal(np.dot(U2, V2),
np.dot(U4[:, :k], V4[:k, :]),
decimal=2)
# in this case 'auto' is equivalent to transpose
assert_almost_equal(s2, s3)
def test_multioutput_regression():
y_true = np.array([[1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 0, 1]])
y_pred = np.array([[0, 0, 0, 1], [1, 0, 1, 1], [0, 0, 0, 1]])
error = mean_squared_error(y_true, y_pred)
assert_almost_equal(error, (1. / 3 + 2. / 3 + 2. / 3) / 4.)
error = mean_squared_error(y_true, y_pred, squared=False)
assert_almost_equal(error, 0.454, decimal=2)
error = mean_squared_log_error(y_true, y_pred)
assert_almost_equal(error, 0.200, decimal=2)
# mean_absolute_error and mean_squared_error are equal because
# it is a binary problem.
error = mean_absolute_error(y_true, y_pred)
assert_almost_equal(error, (1. + 2. / 3) / 4.)
error = mean_pinball_loss(y_true, y_pred)
assert_almost_equal(error, (1. + 2. / 3) / 8.)
error = np.around(mean_absolute_percentage_error(y_true, y_pred),
decimals=2)
assert np.isfinite(error)
assert error > 1e6
error = median_absolute_error(y_true, y_pred)
assert_almost_equal(error, (1. + 1.) / 4.)
error = r2_score(y_true, y_pred, multioutput='variance_weighted')
assert_almost_equal(error, 1. - 5. / 2)
error = r2_score(y_true, y_pred, multioutput='uniform_average')
assert_almost_equal(error, -.875)
def test_minibatch_update_consistency():
# Check that dense and sparse minibatch update give the same results
rng = np.random.RandomState(42)
old_centers = centers + rng.normal(size=centers.shape)
new_centers = old_centers.copy()
new_centers_csr = old_centers.copy()
weight_sums = np.zeros(new_centers.shape[0], dtype=np.double)
weight_sums_csr = np.zeros(new_centers.shape[0], dtype=np.double)
x_squared_norms = (X**2).sum(axis=1)
x_squared_norms_csr = row_norms(X_csr, squared=True)
buffer = np.zeros(centers.shape[1], dtype=np.double)
buffer_csr = np.zeros(centers.shape[1], dtype=np.double)
# extract a small minibatch
X_mb = X[:10]
X_mb_csr = X_csr[:10]
x_mb_squared_norms = x_squared_norms[:10]
x_mb_squared_norms_csr = x_squared_norms_csr[:10]
sample_weight_mb = np.ones(X_mb.shape[0], dtype=np.double)
# step 1: compute the dense minibatch update
old_inertia, incremental_diff = _mini_batch_step(X_mb,
sample_weight_mb,
x_mb_squared_norms,
new_centers,
weight_sums,
buffer,
1,
None,
random_reassign=False)
assert old_inertia > 0.0
# compute the new inertia on the same batch to check that it decreased
labels, new_inertia = _labels_inertia(X_mb, sample_weight_mb,
x_mb_squared_norms, new_centers)
assert new_inertia > 0.0
assert new_inertia < old_inertia
# check that the incremental difference computation is matching the
# final observed value
effective_diff = np.sum((new_centers - old_centers)**2)
assert_almost_equal(incremental_diff, effective_diff)
# step 2: compute the sparse minibatch update
old_inertia_csr, incremental_diff_csr = _mini_batch_step(
X_mb_csr,
sample_weight_mb,
x_mb_squared_norms_csr,
new_centers_csr,
weight_sums_csr,
buffer_csr,
1,
None,
random_reassign=False)
assert old_inertia_csr > 0.0
# compute the new inertia on the same batch to check that it decreased
labels_csr, new_inertia_csr = _labels_inertia(X_mb_csr, sample_weight_mb,
x_mb_squared_norms_csr,
new_centers_csr)
assert new_inertia_csr > 0.0
assert new_inertia_csr < old_inertia_csr
# check that the incremental difference computation is matching the
# final observed value
effective_diff = np.sum((new_centers_csr - old_centers)**2)
assert_almost_equal(incremental_diff_csr, effective_diff)
# step 3: check that sparse and dense updates lead to the same results
assert_array_equal(labels, labels_csr)
assert_array_almost_equal(new_centers, new_centers_csr)
assert_almost_equal(incremental_diff, incremental_diff_csr)
assert_almost_equal(old_inertia, old_inertia_csr)
assert_almost_equal(new_inertia, new_inertia_csr)
def test_bayesian_mixture_precisions_prior_initialisation():
rng = np.random.RandomState(0)
n_samples, n_features = 10, 2
X = rng.rand(n_samples, n_features)
# Check raise message for a bad value of degrees_of_freedom_prior
bad_degrees_of_freedom_prior_ = n_features - 1.
bgmm = BayesianGaussianMixture(
degrees_of_freedom_prior=bad_degrees_of_freedom_prior_,
random_state=rng)
assert_raise_message(ValueError,
"The parameter 'degrees_of_freedom_prior' should be "
"greater than %d, but got %.3f."
% (n_features - 1, bad_degrees_of_freedom_prior_),
bgmm.fit, X)
# Check correct init for a given value of degrees_of_freedom_prior
degrees_of_freedom_prior = rng.rand() + n_features - 1.
bgmm = BayesianGaussianMixture(
degrees_of_freedom_prior=degrees_of_freedom_prior,
random_state=rng).fit(X)
assert_almost_equal(degrees_of_freedom_prior,
bgmm.degrees_of_freedom_prior_)
# Check correct init for the default value of degrees_of_freedom_prior
degrees_of_freedom_prior_default = n_features
bgmm = BayesianGaussianMixture(
degrees_of_freedom_prior=degrees_of_freedom_prior_default,
random_state=rng).fit(X)
assert_almost_equal(degrees_of_freedom_prior_default,
bgmm.degrees_of_freedom_prior_)
# Check correct init for a given value of covariance_prior
covariance_prior = {
'full': np.cov(X.T, bias=1) + 10,
'tied': np.cov(X.T, bias=1) + 5,
'diag': np.diag(np.atleast_2d(np.cov(X.T, bias=1))) + 3,
'spherical': rng.rand()}
bgmm = BayesianGaussianMixture(random_state=rng)
for cov_type in ['full', 'tied', 'diag', 'spherical']:
bgmm.covariance_type = cov_type
bgmm.covariance_prior = covariance_prior[cov_type]
bgmm.fit(X)
assert_almost_equal(covariance_prior[cov_type],
bgmm.covariance_prior_)
# Check raise message for a bad spherical value of covariance_prior
bad_covariance_prior_ = -1.
bgmm = BayesianGaussianMixture(covariance_type='spherical',
covariance_prior=bad_covariance_prior_,
random_state=rng)
assert_raise_message(ValueError,
"The parameter 'spherical covariance_prior' "
"should be greater than 0., but got %.3f."
% bad_covariance_prior_,
bgmm.fit, X)
# Check correct init for the default value of covariance_prior
covariance_prior_default = {
'full': np.atleast_2d(np.cov(X.T)),
'tied': np.atleast_2d(np.cov(X.T)),
'diag': np.var(X, axis=0, ddof=1),
'spherical': np.var(X, axis=0, ddof=1).mean()}
bgmm = BayesianGaussianMixture(random_state=0)
for cov_type in ['full', 'tied', 'diag', 'spherical']:
bgmm.covariance_type = cov_type
bgmm.fit(X)
assert_almost_equal(covariance_prior_default[cov_type],
bgmm.covariance_prior_)
def test_agglomerative_clustering():
# Check that we obtain the correct number of clusters with
# agglomerative clustering.
rng = np.random.RandomState(0)
mask = np.ones([10, 10], dtype=bool)
n_samples = 100
X = rng.randn(n_samples, 50)
connectivity = grid_to_graph(*mask.shape)
for linkage in ("ward", "complete", "average", "single"):
clustering = AgglomerativeClustering(n_clusters=10,
connectivity=connectivity,
linkage=linkage)
clustering.fit(X)
# test caching
try:
tempdir = mkdtemp()
clustering = AgglomerativeClustering(
n_clusters=10, connectivity=connectivity,
memory=tempdir,
linkage=linkage)
clustering.fit(X)
labels = clustering.labels_
assert np.size(np.unique(labels)) == 10
finally:
shutil.rmtree(tempdir)
# Turn caching off now
clustering = AgglomerativeClustering(
n_clusters=10, connectivity=connectivity, linkage=linkage)
# Check that we obtain the same solution with early-stopping of the
# tree building
clustering.compute_full_tree = False
clustering.fit(X)
assert_almost_equal(normalized_mutual_info_score(clustering.labels_,
labels), 1)
clustering.connectivity = None
clustering.fit(X)
assert np.size(np.unique(clustering.labels_)) == 10
# Check that we raise a TypeError on dense matrices
clustering = AgglomerativeClustering(
n_clusters=10,
connectivity=sparse.lil_matrix(
connectivity.toarray()[:10, :10]),
linkage=linkage)
with pytest.raises(ValueError):
clustering.fit(X)
# Test that using ward with another metric than euclidean raises an
# exception
clustering = AgglomerativeClustering(
n_clusters=10,
connectivity=connectivity.toarray(),
affinity="manhattan",
linkage="ward")
with pytest.raises(ValueError):
clustering.fit(X)
# Test using another metric than euclidean works with linkage complete
for affinity in PAIRED_DISTANCES.keys():
# Compare our (structured) implementation to scipy
clustering = AgglomerativeClustering(
n_clusters=10,
connectivity=np.ones((n_samples, n_samples)),
affinity=affinity,
linkage="complete")
clustering.fit(X)
clustering2 = AgglomerativeClustering(
n_clusters=10,
connectivity=None,
affinity=affinity,
linkage="complete")
clustering2.fit(X)
assert_almost_equal(normalized_mutual_info_score(clustering2.labels_,
clustering.labels_),
1)
# Test that using a distance matrix (affinity = 'precomputed') has same
# results (with connectivity constraints)
clustering = AgglomerativeClustering(n_clusters=10,
connectivity=connectivity,
linkage="complete")
clustering.fit(X)
X_dist = pairwise_distances(X)
clustering2 = AgglomerativeClustering(n_clusters=10,
connectivity=connectivity,
affinity='precomputed',
linkage="complete")
clustering2.fit(X_dist)
assert_array_equal(clustering.labels_, clustering2.labels_)
def test_y_multioutput():
# Test that GPR can deal with multi-dimensional target values
y_2d = np.vstack((y, y * 2)).T
# Test for fixed kernel that first dimension of 2d GP equals the output
# of 1d GP and that second dimension is twice as large
kernel = RBF(length_scale=1.0)
gpr = GaussianProcessRegressor(kernel=kernel,
optimizer=None,
normalize_y=False)
gpr.fit(X, y)
gpr_2d = GaussianProcessRegressor(kernel=kernel,
optimizer=None,
normalize_y=False)
gpr_2d.fit(X, y_2d)
y_pred_1d, y_std_1d = gpr.predict(X2, return_std=True)
y_pred_2d, y_std_2d = gpr_2d.predict(X2, return_std=True)
_, y_cov_1d = gpr.predict(X2, return_cov=True)
_, y_cov_2d = gpr_2d.predict(X2, return_cov=True)
assert_almost_equal(y_pred_1d, y_pred_2d[:, 0])
assert_almost_equal(y_pred_1d, y_pred_2d[:, 1] / 2)
# Standard deviation and covariance do not depend on output
assert_almost_equal(y_std_1d, y_std_2d)
assert_almost_equal(y_cov_1d, y_cov_2d)
y_sample_1d = gpr.sample_y(X2, n_samples=10)
y_sample_2d = gpr_2d.sample_y(X2, n_samples=10)
assert_almost_equal(y_sample_1d, y_sample_2d[:, 0])
# Test hyperparameter optimization
for kernel in kernels:
gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
gpr.fit(X, y)
gpr_2d = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
gpr_2d.fit(X, np.vstack((y, y)).T)
assert_almost_equal(gpr.kernel_.theta, gpr_2d.kernel_.theta, 4)
def test_adjusted_mutual_info_score():
# Compute the Adjusted Mutual Information and test against known values
labels_a = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])
labels_b = np.array([1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 3, 2, 2])
# Mutual information
mi = mutual_info_score(labels_a, labels_b)
assert_almost_equal(mi, 0.41022, 5)
# with provided sparse contingency
C = contingency_matrix(labels_a, labels_b, sparse=True)
mi = mutual_info_score(labels_a, labels_b, contingency=C)
assert_almost_equal(mi, 0.41022, 5)
# with provided dense contingency
C = contingency_matrix(labels_a, labels_b)
mi = mutual_info_score(labels_a, labels_b, contingency=C)
assert_almost_equal(mi, 0.41022, 5)
# Expected mutual information
n_samples = C.sum()
emi = expected_mutual_information(C, n_samples)
assert_almost_equal(emi, 0.15042, 5)
# Adjusted mutual information
ami = adjusted_mutual_info_score(labels_a, labels_b)
assert_almost_equal(ami, 0.27821, 5)
ami = adjusted_mutual_info_score([1, 1, 2, 2], [2, 2, 3, 3])
assert ami == pytest.approx(1.0)
# Test with a very large array
a110 = np.array([list(labels_a) * 110]).flatten()
b110 = np.array([list(labels_b) * 110]).flatten()
ami = adjusted_mutual_info_score(a110, b110)
assert_almost_equal(ami, 0.38, 2)
def test_enet_path():
# We use a large number of samples and of informative features so that
# the l1_ratio selected is more toward ridge than lasso
X, y, X_test, y_test = build_dataset(n_samples=200,
n_features=100,
n_informative_features=100)
max_iter = 150
# Here we have a small number of iterations, and thus the
# ElasticNet might not converge. This is to speed up tests
clf = ElasticNetCV(alphas=[0.01, 0.05, 0.1],
eps=2e-3,
l1_ratio=[0.5, 0.7],
cv=3,
max_iter=max_iter)
ignore_warnings(clf.fit)(X, y)
# Well-conditioned settings, we should have selected our
# smallest penalty
assert_almost_equal(clf.alpha_, min(clf.alphas_))
# Non-sparse ground truth: we should have selected an elastic-net
# that is closer to ridge than to lasso
assert clf.l1_ratio_ == min(clf.l1_ratio)
clf = ElasticNetCV(alphas=[0.01, 0.05, 0.1],
eps=2e-3,
l1_ratio=[0.5, 0.7],
cv=3,
max_iter=max_iter,
precompute=True)
ignore_warnings(clf.fit)(X, y)
# Well-conditioned settings, we should have selected our
# smallest penalty
assert_almost_equal(clf.alpha_, min(clf.alphas_))
# Non-sparse ground truth: we should have selected an elastic-net
# that is closer to ridge than to lasso
assert clf.l1_ratio_ == min(clf.l1_ratio)
# We are in well-conditioned settings with low noise: we should
# have a good test-set performance
assert clf.score(X_test, y_test) > 0.99
# Multi-output/target case
X, y, X_test, y_test = build_dataset(n_features=10, n_targets=3)
clf = MultiTaskElasticNetCV(n_alphas=5,
eps=2e-3,
l1_ratio=[0.5, 0.7],
cv=3,
max_iter=max_iter)
ignore_warnings(clf.fit)(X, y)
# We are in well-conditioned settings with low noise: we should
# have a good test-set performance
assert clf.score(X_test, y_test) > 0.99
assert clf.coef_.shape == (3, 10)
# Mono-output should have same cross-validated alpha_ and l1_ratio_
# in both cases.
X, y, _, _ = build_dataset(n_features=10)
clf1 = ElasticNetCV(n_alphas=5, eps=2e-3, l1_ratio=[0.5, 0.7])
clf1.fit(X, y)
clf2 = MultiTaskElasticNetCV(n_alphas=5, eps=2e-3, l1_ratio=[0.5, 0.7])
clf2.fit(X, y[:, np.newaxis])
assert_almost_equal(clf1.l1_ratio_, clf2.l1_ratio_)
assert_almost_equal(clf1.alpha_, clf2.alpha_)
def test_importances_asymptotic():
# Check whether variable importances of totally randomized trees
# converge towards their theoretical values (See Louppe et al,
# Understanding variable importances in forests of randomized trees, 2013).
def binomial(k, n):
return 0 if k < 0 or k > n else comb(int(n), int(k), exact=True)
def entropy(samples):
n_samples = len(samples)
entropy = 0.
for count in np.bincount(samples):
p = 1. * count / n_samples
if p > 0:
entropy -= p * np.log2(p)
return entropy
def mdi_importance(X_m, X, y):
n_samples, n_features = X.shape
features = list(range(n_features))
features.pop(X_m)
values = [np.unique(X[:, i]) for i in range(n_features)]
imp = 0.
for k in range(n_features):
# Weight of each B of size k
coef = 1. / (binomial(k, n_features) * (n_features - k))
# For all B of size k
for B in combinations(features, k):
# For all values B=b
for b in product(*[values[B[j]] for j in range(k)]):
mask_b = np.ones(n_samples, dtype=np.bool)
for j in range(k):
mask_b &= X[:, B[j]] == b[j]
X_, y_ = X[mask_b, :], y[mask_b]
n_samples_b = len(X_)
if n_samples_b > 0:
children = []
for xi in values[X_m]:
mask_xi = X_[:, X_m] == xi
children.append(y_[mask_xi])
imp += (
coef * (1. * n_samples_b / n_samples) # P(B=b)
* (entropy(y_) - sum([
entropy(c) * len(c) / n_samples_b
for c in children
])))
return imp
data = np.array([[0, 0, 1, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1, 2],
[1, 0, 1, 1, 0, 1, 1, 3], [0, 1, 1, 1, 0, 1, 0, 4],
[1, 1, 0, 1, 0, 1, 1, 5], [1, 1, 0, 1, 1, 1, 1, 6],
[1, 0, 1, 0, 0, 1, 0, 7], [1, 1, 1, 1, 1, 1, 1, 8],
[1, 1, 1, 1, 0, 1, 1, 9], [1, 1, 1, 0, 1, 1, 1, 0]])
X, y = np.array(data[:, :7], dtype=np.bool), data[:, 7]
n_features = X.shape[1]
# Compute true importances
true_importances = np.zeros(n_features)
for i in range(n_features):
true_importances[i] = mdi_importance(i, X, y)
# Estimate importances with totally randomized trees
clf = ExtraTreesClassifier(n_estimators=500,
max_features=1,
criterion="entropy",
random_state=0).fit(X, y)
importances = sum(
tree.tree_.compute_feature_importances(normalize=False)
for tree in clf.estimators_) / clf.n_estimators
# Check correctness
assert_almost_equal(entropy(y), sum(importances))
assert np.abs(true_importances - importances).mean() < 0.01
def test_compare_covar_type():
# We can compare the 'full' precision with the other cov_type if we apply
# 1 iter of the M-step (done during _initialize_parameters).
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7)
X = rand_data.X['full']
n_components = rand_data.n_components
for prior_type in PRIOR_TYPE:
# Computation of the full_covariance
bgmm = BayesianGaussianMixture(
weight_concentration_prior_type=prior_type,
n_components=2 * n_components,
covariance_type='full',
max_iter=1,
random_state=0,
tol=1e-7)
bgmm._check_initial_parameters(X)
bgmm._initialize_parameters(X, np.random.RandomState(0))
full_covariances = (
bgmm.covariances_ *
bgmm.degrees_of_freedom_[:, np.newaxis, np.newaxis])
# Check tied_covariance = mean(full_covariances, 0)
bgmm = BayesianGaussianMixture(
weight_concentration_prior_type=prior_type,
n_components=2 * n_components,
covariance_type='tied',
max_iter=1,
random_state=0,
tol=1e-7)
bgmm._check_initial_parameters(X)
bgmm._initialize_parameters(X, np.random.RandomState(0))
tied_covariance = bgmm.covariances_ * bgmm.degrees_of_freedom_
assert_almost_equal(tied_covariance, np.mean(full_covariances, 0))
# Check diag_covariance = diag(full_covariances)
bgmm = BayesianGaussianMixture(
weight_concentration_prior_type=prior_type,
n_components=2 * n_components,
covariance_type='diag',
max_iter=1,
random_state=0,
tol=1e-7)
bgmm._check_initial_parameters(X)
bgmm._initialize_parameters(X, np.random.RandomState(0))
diag_covariances = (bgmm.covariances_ *
bgmm.degrees_of_freedom_[:, np.newaxis])
assert_almost_equal(
diag_covariances,
np.array([np.diag(cov) for cov in full_covariances]))
# Check spherical_covariance = np.mean(diag_covariances, 0)
bgmm = BayesianGaussianMixture(
weight_concentration_prior_type=prior_type,
n_components=2 * n_components,
covariance_type='spherical',
max_iter=1,
random_state=0,
tol=1e-7)
bgmm._check_initial_parameters(X)
bgmm._initialize_parameters(X, np.random.RandomState(0))
spherical_covariances = bgmm.covariances_ * bgmm.degrees_of_freedom_
assert_almost_equal(spherical_covariances,
np.mean(diag_covariances, 1))