def test_gaussian_mixture_estimate_log_prob_resp():
# test whether responsibilities are normalized
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=5)
n_samples = rand_data.n_samples
n_features = rand_data.n_features
n_components = rand_data.n_components
X = rng.rand(n_samples, n_features)
for covar_type in COVARIANCE_TYPE:
weights = rand_data.weights
means = rand_data.means
precisions = rand_data.precisions[covar_type]
g = GaussianMixture(n_components=n_components,
random_state=rng,
weights_init=weights,
means_init=means,
precisions_init=precisions,
covariance_type=covar_type)
g.fit(X)
resp = g.predict_proba(X)
assert_array_almost_equal(resp.sum(axis=1), np.ones(n_samples))
assert_array_equal(g.weights_init, weights)
assert_array_equal(g.means_init, means)
assert_array_equal(g.precisions_init, precisions)
def test_gaussian_mixture_fit_predict_n_init():
# Check that fit_predict is equivalent to fit.predict, when n_init > 1
X = np.random.RandomState(0).randn(1000, 5)
gm = GaussianMixture(n_components=5, n_init=5, random_state=0)
y_pred1 = gm.fit_predict(X)
y_pred2 = gm.predict(X)
assert_array_equal(y_pred1, y_pred2)
def test_score():
covar_type = 'full'
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7)
n_components = rand_data.n_components
X = rand_data.X[covar_type]
# Check the error message if we don't call fit
gmm1 = GaussianMixture(n_components=n_components,
n_init=1,
max_iter=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
assert_raise_message(
NotFittedError, "This GaussianMixture instance is not fitted "
"yet. Call 'fit' with appropriate arguments "
"before using this method.", gmm1.score, X)
# Check score value
with warnings.catch_warnings():
warnings.simplefilter("ignore", ConvergenceWarning)
gmm1.fit(X)
gmm_score = gmm1.score(X)
gmm_score_proba = gmm1.score_samples(X).mean()
assert_almost_equal(gmm_score, gmm_score_proba)
# Check if the score increase
gmm2 = GaussianMixture(n_components=n_components,
n_init=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type).fit(X)
assert gmm2.score(X) > gmm1.score(X)
def test_monotonic_likelihood():
# We check that each step of the EM without regularization improve
# monotonically the training set likelihood
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7)
n_components = rand_data.n_components
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
gmm = GaussianMixture(n_components=n_components,
covariance_type=covar_type,
reg_covar=0,
warm_start=True,
max_iter=1,
random_state=rng,
tol=1e-7)
current_log_likelihood = -np.infty
with warnings.catch_warnings():
warnings.simplefilter("ignore", ConvergenceWarning)
# Do one training iteration at a time so we can make sure that the
# training log likelihood increases after each iteration.
for _ in range(600):
prev_log_likelihood = current_log_likelihood
try:
current_log_likelihood = gmm.fit(X).score(X)
except ConvergenceWarning:
pass
assert (current_log_likelihood >= prev_log_likelihood)
if gmm.converged_:
break
assert gmm.converged_
def test_regularisation():
# We train the GaussianMixture on degenerate data by defining two clusters
# of a 0 covariance.
rng = np.random.RandomState(0)
n_samples, n_features = 10, 5
X = np.vstack((np.ones(
(n_samples // 2, n_features)), np.zeros((n_samples // 2, n_features))))
for covar_type in COVARIANCE_TYPE:
gmm = GaussianMixture(n_components=n_samples,
reg_covar=0,
covariance_type=covar_type,
random_state=rng)
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
assert_raise_message(
ValueError, "Fitting the mixture model failed because "
"some components have ill-defined empirical "
"covariance (for instance caused by "
"singleton or collapsed samples). Try to "
"decrease the number of components, or "
"increase reg_covar.", gmm.fit, X)
gmm.set_params(reg_covar=1e-6).fit(X)
def test_gaussian_mixture_n_parameters():
# Test that the right number of parameters is estimated
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 50, 5, 2
X = rng.randn(n_samples, n_features)
n_params = {'spherical': 13, 'diag': 21, 'tied': 26, 'full': 41}
for cv_type in COVARIANCE_TYPE:
g = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=rng).fit(X)
assert g._n_parameters() == n_params[cv_type]
def test_gaussian_mixture_fit():
# recover the ground truth
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_features = rand_data.n_features
n_components = rand_data.n_components
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
g = GaussianMixture(n_components=n_components,
n_init=20,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
g.fit(X)
# needs more data to pass the test with rtol=1e-7
assert_allclose(np.sort(g.weights_),
np.sort(rand_data.weights),
rtol=0.1,
atol=1e-2)
arg_idx1 = g.means_[:, 0].argsort()
arg_idx2 = rand_data.means[:, 0].argsort()
assert_allclose(g.means_[arg_idx1],
rand_data.means[arg_idx2],
rtol=0.1,
atol=1e-2)
if covar_type == 'full':
prec_pred = g.precisions_
prec_test = rand_data.precisions['full']
elif covar_type == 'tied':
prec_pred = np.array([g.precisions_] * n_components)
prec_test = np.array([rand_data.precisions['tied']] * n_components)
elif covar_type == 'spherical':
prec_pred = np.array(
[np.eye(n_features) * c for c in g.precisions_])
prec_test = np.array([
np.eye(n_features) * c
for c in rand_data.precisions['spherical']
])
elif covar_type == 'diag':
prec_pred = np.array([np.diag(d) for d in g.precisions_])
prec_test = np.array(
[np.diag(d) for d in rand_data.precisions['diag']])
arg_idx1 = np.trace(prec_pred, axis1=1, axis2=2).argsort()
arg_idx2 = np.trace(prec_test, axis1=1, axis2=2).argsort()
for k, h in zip(arg_idx1, arg_idx2):
ecov = EmpiricalCovariance()
ecov.covariance_ = prec_test[h]
# the accuracy depends on the number of data and randomness, rng
assert_allclose(ecov.error_norm(prec_pred[k]), 0, atol=0.15)
def test_bic_1d_1component():
# Test all of the covariance_types return the same BIC score for
# 1-dimensional, 1 component fits.
rng = np.random.RandomState(0)
n_samples, n_dim, n_components = 100, 1, 1
X = rng.randn(n_samples, n_dim)
bic_full = GaussianMixture(n_components=n_components,
covariance_type='full',
random_state=rng).fit(X).bic(X)
for covariance_type in ['tied', 'diag', 'spherical']:
bic = GaussianMixture(n_components=n_components,
covariance_type=covariance_type,
random_state=rng).fit(X).bic(X)
assert_almost_equal(bic_full, bic)
def test_gaussian_mixture_verbose():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components = rand_data.n_components
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
g = GaussianMixture(n_components=n_components,
n_init=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type,
verbose=1)
h = GaussianMixture(n_components=n_components,
n_init=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type,
verbose=2)
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
g.fit(X)
h.fit(X)
finally:
sys.stdout = old_stdout
def test_multiple_init():
# Test that multiple inits does not much worse than a single one
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 50, 5, 2
X = rng.randn(n_samples, n_features)
for cv_type in COVARIANCE_TYPE:
train1 = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=0).fit(X).score(X)
train2 = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=0,
n_init=5).fit(X).score(X)
assert train2 >= train1
def test_convergence_detected_with_warm_start():
# We check that convergence is detected when warm_start=True
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components = rand_data.n_components
X = rand_data.X['full']
for max_iter in (1, 2, 50):
gmm = GaussianMixture(n_components=n_components,
warm_start=True,
max_iter=max_iter,
random_state=rng)
for _ in range(100):
gmm.fit(X)
if gmm.converged_:
break
assert gmm.converged_
assert max_iter >= gmm.n_iter_
def test_init():
# We check that by increasing the n_init number we have a better solution
for random_state in range(15):
rand_data = RandomData(np.random.RandomState(random_state),
n_samples=50,
scale=1)
n_components = rand_data.n_components
X = rand_data.X['full']
gmm1 = GaussianMixture(n_components=n_components,
n_init=1,
max_iter=1,
random_state=random_state).fit(X)
gmm2 = GaussianMixture(n_components=n_components,
n_init=10,
max_iter=1,
random_state=random_state).fit(X)
assert gmm2.lower_bound_ >= gmm1.lower_bound_
def test_score_samples():
covar_type = 'full'
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7)
n_components = rand_data.n_components
X = rand_data.X[covar_type]
# Check the error message if we don't call fit
gmm = GaussianMixture(n_components=n_components,
n_init=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
assert_raise_message(
NotFittedError, "This GaussianMixture instance is not fitted "
"yet. Call 'fit' with appropriate arguments "
"before using this method.", gmm.score_samples, X)
gmm_score_samples = gmm.fit(X).score_samples(X)
assert gmm_score_samples.shape[0] == rand_data.n_samples
def test_gaussian_mixture_fit_predict(seed, max_iter, tol):
rng = np.random.RandomState(seed)
rand_data = RandomData(rng)
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
Y = rand_data.Y
g = GaussianMixture(n_components=rand_data.n_components,
random_state=rng,
weights_init=rand_data.weights,
means_init=rand_data.means,
precisions_init=rand_data.precisions[covar_type],
covariance_type=covar_type,
max_iter=max_iter,
tol=tol)
# check if fit_predict(X) is equivalent to fit(X).predict(X)
f = copy.deepcopy(g)
Y_pred1 = f.fit(X).predict(X)
Y_pred2 = g.fit_predict(X)
assert_array_equal(Y_pred1, Y_pred2)
assert adjusted_rand_score(Y, Y_pred2) > .95
def test_property():
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7)
n_components = rand_data.n_components
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
gmm = GaussianMixture(n_components=n_components,
covariance_type=covar_type,
random_state=rng,
n_init=5)
gmm.fit(X)
if covar_type == 'full':
for prec, covar in zip(gmm.precisions_, gmm.covariances_):
assert_array_almost_equal(linalg.inv(prec), covar)
elif covar_type == 'tied':
assert_array_almost_equal(linalg.inv(gmm.precisions_),
gmm.covariances_)
else:
assert_array_almost_equal(gmm.precisions_, 1. / gmm.covariances_)
def test_check_precisions():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components, n_features = rand_data.n_components, rand_data.n_features
# Define the bad precisions for each covariance_type
precisions_bad_shape = {
'full': np.ones((n_components + 1, n_features, n_features)),
'tied': np.ones((n_features + 1, n_features + 1)),
'diag': np.ones((n_components + 1, n_features)),
'spherical': np.ones((n_components + 1))
}
# Define not positive-definite precisions
precisions_not_pos = np.ones((n_components, n_features, n_features))
precisions_not_pos[0] = np.eye(n_features)
precisions_not_pos[0, 0, 0] = -1.
precisions_not_positive = {
'full': precisions_not_pos,
'tied': precisions_not_pos[0],
'diag': np.full((n_components, n_features), -1.),
'spherical': np.full(n_components, -1.)
}
not_positive_errors = {
'full': 'symmetric, positive-definite',
'tied': 'symmetric, positive-definite',
'diag': 'positive',
'spherical': 'positive'
}
for covar_type in COVARIANCE_TYPE:
X = RandomData(rng).X[covar_type]
g = GaussianMixture(n_components=n_components,
covariance_type=covar_type,
random_state=rng)
# Check precisions with bad shapes
g.precisions_init = precisions_bad_shape[covar_type]
assert_raise_message(
ValueError, "The parameter '%s precision' should have "
"the shape of" % covar_type, g.fit, X)
# Check not positive precisions
g.precisions_init = precisions_not_positive[covar_type]
assert_raise_message(
ValueError, "'%s precision' should be %s" %
(covar_type, not_positive_errors[covar_type]), g.fit, X)
# Check the correct init of precisions_init
g.precisions_init = rand_data.precisions[covar_type]
g.fit(X)
assert_array_equal(rand_data.precisions[covar_type], g.precisions_init)
def test_gaussian_mixture_fit_best_params():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components = rand_data.n_components
n_init = 10
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
g = GaussianMixture(n_components=n_components,
n_init=1,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
ll = []
for _ in range(n_init):
g.fit(X)
ll.append(g.score(X))
ll = np.array(ll)
g_best = GaussianMixture(n_components=n_components,
n_init=n_init,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
g_best.fit(X)
assert_almost_equal(ll.min(), g_best.score(X))
def test_check_weights():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components = rand_data.n_components
X = rand_data.X['full']
g = GaussianMixture(n_components=n_components)
# Check bad shape
weights_bad_shape = rng.rand(n_components, 1)
g.weights_init = weights_bad_shape
assert_raise_message(
ValueError, "The parameter 'weights' should have the shape of "
"(%d,), but got %s" % (n_components, str(weights_bad_shape.shape)),
g.fit, X)
# Check bad range
weights_bad_range = rng.rand(n_components) + 1
g.weights_init = weights_bad_range
assert_raise_message(
ValueError, "The parameter 'weights' should be in the range "
"[0, 1], but got max value %.5f, min value %.5f" %
(np.min(weights_bad_range), np.max(weights_bad_range)), g.fit, X)
# Check bad normalization
weights_bad_norm = rng.rand(n_components)
weights_bad_norm = weights_bad_norm / (weights_bad_norm.sum() + 1)
g.weights_init = weights_bad_norm
assert_raise_message(
ValueError, "The parameter 'weights' should be normalized, "
"but got sum(weights) = %.5f" % np.sum(weights_bad_norm), g.fit, X)
# Check good weights matrix
weights = rand_data.weights
g = GaussianMixture(weights_init=weights, n_components=n_components)
g.fit(X)
assert_array_equal(weights, g.weights_init)
def test_gaussian_mixture_aic_bic():
# Test the aic and bic criteria
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 50, 3, 2
X = rng.randn(n_samples, n_features)
# standard gaussian entropy
sgh = 0.5 * (fast_logdet(np.cov(X.T, bias=1)) + n_features *
(1 + np.log(2 * np.pi)))
for cv_type in COVARIANCE_TYPE:
g = GaussianMixture(n_components=n_components,
covariance_type=cv_type,
random_state=rng,
max_iter=200)
g.fit(X)
aic = 2 * n_samples * sgh + 2 * g._n_parameters()
bic = (2 * n_samples * sgh + np.log(n_samples) * g._n_parameters())
bound = n_features / np.sqrt(n_samples)
assert (g.aic(X) - aic) / n_samples < bound
assert (g.bic(X) - bic) / n_samples < bound
def test_sample():
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=7, n_components=3)
n_features, n_components = rand_data.n_features, rand_data.n_components
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
gmm = GaussianMixture(n_components=n_components,
covariance_type=covar_type,
random_state=rng)
# To sample we need that GaussianMixture is fitted
assert_raise_message(NotFittedError, "This GaussianMixture instance "
"is not fitted", gmm.sample, 0)
gmm.fit(X)
assert_raise_message(ValueError, "Invalid value for 'n_samples",
gmm.sample, 0)
# Just to make sure the class samples correctly
n_samples = 20000
X_s, y_s = gmm.sample(n_samples)
for k in range(n_components):
if covar_type == 'full':
assert_array_almost_equal(gmm.covariances_[k],
np.cov(X_s[y_s == k].T),
decimal=1)
elif covar_type == 'tied':
assert_array_almost_equal(gmm.covariances_,
np.cov(X_s[y_s == k].T),
decimal=1)
elif covar_type == 'diag':
assert_array_almost_equal(gmm.covariances_[k],
np.diag(np.cov(X_s[y_s == k].T)),
decimal=1)
else:
assert_array_almost_equal(gmm.covariances_[k],
np.var(X_s[y_s == k] -
gmm.means_[k]),
decimal=1)
means_s = np.array(
[np.mean(X_s[y_s == k], 0) for k in range(n_components)])
assert_array_almost_equal(gmm.means_, means_s, decimal=1)
# Check shapes of sampled data, see
# https://github.com/scikit-learn/scikit-learn/issues/7701
assert X_s.shape == (n_samples, n_features)
for sample_size in range(1, 100):
X_s, _ = gmm.sample(sample_size)
assert X_s.shape == (sample_size, n_features)
def test_gaussian_mixture_fit_convergence_warning():
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=1)
n_components = rand_data.n_components
max_iter = 1
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
g = GaussianMixture(n_components=n_components,
n_init=1,
max_iter=max_iter,
reg_covar=0,
random_state=rng,
covariance_type=covar_type)
assert_warns_message(
ConvergenceWarning, 'Initialization %d did not converge. '
'Try different init parameters, '
'or increase max_iter, tol '
'or check for degenerate data.' % max_iter, g.fit, X)
def test_check_means():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_components, n_features = rand_data.n_components, rand_data.n_features
X = rand_data.X['full']
g = GaussianMixture(n_components=n_components)
# Check means bad shape
means_bad_shape = rng.rand(n_components + 1, n_features)
g.means_init = means_bad_shape
assert_raise_message(ValueError,
"The parameter 'means' should have the shape of ",
g.fit, X)
# Check good means matrix
means = rand_data.means
g.means_init = means
g.fit(X)
assert_array_equal(means, g.means_init)
def test_gaussian_mixture_predict_predict_proba():
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
for covar_type in COVARIANCE_TYPE:
X = rand_data.X[covar_type]
Y = rand_data.Y
g = GaussianMixture(n_components=rand_data.n_components,
random_state=rng,
weights_init=rand_data.weights,
means_init=rand_data.means,
precisions_init=rand_data.precisions[covar_type],
covariance_type=covar_type)
# Check a warning message arrive if we don't do fit
assert_raise_message(
NotFittedError, "This GaussianMixture instance is not fitted "
"yet. Call 'fit' with appropriate arguments "
"before using this method.", g.predict, X)
g.fit(X)
Y_pred = g.predict(X)
Y_pred_proba = g.predict_proba(X).argmax(axis=1)
assert_array_equal(Y_pred, Y_pred_proba)
assert adjusted_rand_score(Y, Y_pred) > .95
def test_gaussian_mixture_attributes():
# test bad parameters
rng = np.random.RandomState(0)
X = rng.rand(10, 2)
n_components_bad = 0
gmm = GaussianMixture(n_components=n_components_bad)
assert_raise_message(
ValueError, "Invalid value for 'n_components': %d "
"Estimation requires at least one component" % n_components_bad,
gmm.fit, X)
# covariance_type should be in [spherical, diag, tied, full]
covariance_type_bad = 'bad_covariance_type'
gmm = GaussianMixture(covariance_type=covariance_type_bad)
assert_raise_message(
ValueError, "Invalid value for 'covariance_type': %s "
"'covariance_type' should be in "
"['spherical', 'tied', 'diag', 'full']" % covariance_type_bad, gmm.fit,
X)
tol_bad = -1
gmm = GaussianMixture(tol=tol_bad)
assert_raise_message(
ValueError, "Invalid value for 'tol': %.5f "
"Tolerance used by the EM must be non-negative" % tol_bad, gmm.fit, X)
reg_covar_bad = -1
gmm = GaussianMixture(reg_covar=reg_covar_bad)
assert_raise_message(
ValueError, "Invalid value for 'reg_covar': %.5f "
"regularization on covariance must be "
"non-negative" % reg_covar_bad, gmm.fit, X)
max_iter_bad = 0
gmm = GaussianMixture(max_iter=max_iter_bad)
assert_raise_message(
ValueError, "Invalid value for 'max_iter': %d "
"Estimation requires at least one iteration" % max_iter_bad, gmm.fit,
X)
n_init_bad = 0
gmm = GaussianMixture(n_init=n_init_bad)
assert_raise_message(
ValueError, "Invalid value for 'n_init': %d "
"Estimation requires at least one run" % n_init_bad, gmm.fit, X)
init_params_bad = 'bad_method'
gmm = GaussianMixture(init_params=init_params_bad)
assert_raise_message(
ValueError,
"Unimplemented initialization method '%s'" % init_params_bad, gmm.fit,
X)
# test good parameters
n_components, tol, n_init, max_iter, reg_covar = 2, 1e-4, 3, 30, 1e-1
covariance_type, init_params = 'full', 'random'
gmm = GaussianMixture(n_components=n_components,
tol=tol,
n_init=n_init,
max_iter=max_iter,
reg_covar=reg_covar,
covariance_type=covariance_type,
init_params=init_params).fit(X)
assert gmm.n_components == n_components
assert gmm.covariance_type == covariance_type
assert gmm.tol == tol
assert gmm.reg_covar == reg_covar
assert gmm.max_iter == max_iter
assert gmm.n_init == n_init
assert gmm.init_params == init_params
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_