3RNN/Lib/site-packages/sklearn/mixture/tests/test_gaussian_mixture.py
2024-05-26 19:49:15 +02:00

1423 lines
47 KiB
Python

# Author: Wei Xue <xuewei4d@gmail.com>
# Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause
import copy
import itertools
import re
import sys
import warnings
from io import StringIO
from unittest.mock import Mock
import numpy as np
import pytest
from scipy import linalg, stats
import sklearn
from sklearn.cluster import KMeans
from sklearn.covariance import EmpiricalCovariance
from sklearn.datasets import make_spd_matrix
from sklearn.exceptions import ConvergenceWarning, NotFittedError
from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.mixture import GaussianMixture
from sklearn.mixture._gaussian_mixture import (
_compute_log_det_cholesky,
_compute_precision_cholesky,
_estimate_gaussian_covariances_diag,
_estimate_gaussian_covariances_full,
_estimate_gaussian_covariances_spherical,
_estimate_gaussian_covariances_tied,
_estimate_gaussian_parameters,
)
from sklearn.utils._testing import (
assert_allclose,
assert_almost_equal,
assert_array_almost_equal,
assert_array_equal,
ignore_warnings,
)
from sklearn.utils.extmath import fast_logdet
COVARIANCE_TYPE = ["full", "tied", "diag", "spherical"]
def generate_data(n_samples, n_features, weights, means, precisions, covariance_type):
rng = np.random.RandomState(0)
X = []
if covariance_type == "spherical":
for _, (w, m, c) in enumerate(zip(weights, means, precisions["spherical"])):
X.append(
rng.multivariate_normal(
m, c * np.eye(n_features), int(np.round(w * n_samples))
)
)
if covariance_type == "diag":
for _, (w, m, c) in enumerate(zip(weights, means, precisions["diag"])):
X.append(
rng.multivariate_normal(m, np.diag(c), int(np.round(w * n_samples)))
)
if covariance_type == "tied":
for _, (w, m) in enumerate(zip(weights, means)):
X.append(
rng.multivariate_normal(
m, precisions["tied"], int(np.round(w * n_samples))
)
)
if covariance_type == "full":
for _, (w, m, c) in enumerate(zip(weights, means, precisions["full"])):
X.append(rng.multivariate_normal(m, c, int(np.round(w * n_samples))))
X = np.vstack(X)
return X
class RandomData:
def __init__(self, rng, n_samples=200, n_components=2, n_features=2, scale=50):
self.n_samples = n_samples
self.n_components = n_components
self.n_features = n_features
self.weights = rng.rand(n_components)
self.weights = self.weights / self.weights.sum()
self.means = rng.rand(n_components, n_features) * scale
self.covariances = {
"spherical": 0.5 + rng.rand(n_components),
"diag": (0.5 + rng.rand(n_components, n_features)) ** 2,
"tied": make_spd_matrix(n_features, random_state=rng),
"full": np.array(
[
make_spd_matrix(n_features, random_state=rng) * 0.5
for _ in range(n_components)
]
),
}
self.precisions = {
"spherical": 1.0 / self.covariances["spherical"],
"diag": 1.0 / self.covariances["diag"],
"tied": linalg.inv(self.covariances["tied"]),
"full": np.array(
[linalg.inv(covariance) for covariance in self.covariances["full"]]
),
}
self.X = dict(
zip(
COVARIANCE_TYPE,
[
generate_data(
n_samples,
n_features,
self.weights,
self.means,
self.covariances,
covar_type,
)
for covar_type in COVARIANCE_TYPE
],
)
)
self.Y = np.hstack(
[
np.full(int(np.round(w * n_samples)), k, dtype=int)
for k, w in enumerate(self.weights)
]
)
def test_gaussian_mixture_attributes():
# test bad parameters
rng = np.random.RandomState(0)
X = rng.rand(10, 2)
# 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_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
msg = re.escape(
"The parameter 'weights' should have the shape of "
f"({n_components},), but got {str(weights_bad_shape.shape)}"
)
with pytest.raises(ValueError, match=msg):
g.fit(X)
# Check bad range
weights_bad_range = rng.rand(n_components) + 1
g.weights_init = weights_bad_range
msg = re.escape(
"The parameter 'weights' should be in the range [0, 1], but got"
f" max value {np.min(weights_bad_range):.5f}, "
f"min value {np.max(weights_bad_range):.5f}"
)
with pytest.raises(ValueError, match=msg):
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
msg = re.escape(
"The parameter 'weights' should be normalized, "
f"but got sum(weights) = {np.sum(weights_bad_norm):.5f}"
)
with pytest.raises(ValueError, match=msg):
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_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
msg = "The parameter 'means' should have the shape of "
with pytest.raises(ValueError, match=msg):
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_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] = -1.0
precisions_not_positive = {
"full": precisions_not_pos,
"tied": precisions_not_pos[0],
"diag": np.full((n_components, n_features), -1.0),
"spherical": np.full(n_components, -1.0),
}
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]
msg = f"The parameter '{covar_type} precision' should have the shape of"
with pytest.raises(ValueError, match=msg):
g.fit(X)
# Check not positive precisions
g.precisions_init = precisions_not_positive[covar_type]
msg = f"'{covar_type} precision' should be {not_positive_errors[covar_type]}"
with pytest.raises(ValueError, match=msg):
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_suffstat_sk_full():
# compare the precision matrix compute from the
# EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm="frobenius"), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm="spectral"), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, "full")
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean(axis=0).reshape((1, -1))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm="frobenius"), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm="spectral"), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, "full")
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
def test_suffstat_sk_tied():
# use equation Nk * Sk / N = S_tied
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_full = (
np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full, 0) / n_samples
)
covars_pred_tied = _estimate_gaussian_covariances_tied(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance()
ecov.covariance_ = covars_pred_full
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm="frobenius"), 0)
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm="spectral"), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_tied, "tied")
precs_pred = np.dot(precs_chol_pred, precs_chol_pred.T)
precs_est = linalg.inv(covars_pred_tied)
assert_array_almost_equal(precs_est, precs_pred)
def test_suffstat_sk_diag():
# test against 'full' case
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_diag = _estimate_gaussian_covariances_diag(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance()
for cov_full, cov_diag in zip(covars_pred_full, covars_pred_diag):
ecov.covariance_ = np.diag(np.diag(cov_full))
cov_diag = np.diag(cov_diag)
assert_almost_equal(ecov.error_norm(cov_diag, norm="frobenius"), 0)
assert_almost_equal(ecov.error_norm(cov_diag, norm="spectral"), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_diag, "diag")
assert_almost_equal(covars_pred_diag, 1.0 / precs_chol_pred**2)
def test_gaussian_suffstat_sk_spherical():
# computing spherical covariance equals to the variance of one-dimension
# data after flattening, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
X = rng.rand(n_samples, n_features)
X = X - X.mean()
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean()
covars_pred_spherical = _estimate_gaussian_covariances_spherical(resp, X, nk, xk, 0)
covars_pred_spherical2 = np.dot(X.flatten().T, X.flatten()) / (
n_features * n_samples
)
assert_almost_equal(covars_pred_spherical, covars_pred_spherical2)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_spherical, "spherical")
assert_almost_equal(covars_pred_spherical, 1.0 / precs_chol_pred**2)
def test_compute_log_det_cholesky():
n_features = 2
rand_data = RandomData(np.random.RandomState(0))
for covar_type in COVARIANCE_TYPE:
covariance = rand_data.covariances[covar_type]
if covar_type == "full":
predected_det = np.array([linalg.det(cov) for cov in covariance])
elif covar_type == "tied":
predected_det = linalg.det(covariance)
elif covar_type == "diag":
predected_det = np.array([np.prod(cov) for cov in covariance])
elif covar_type == "spherical":
predected_det = covariance**n_features
# We compute the cholesky decomposition of the covariance matrix
expected_det = _compute_log_det_cholesky(
_compute_precision_cholesky(covariance, covar_type),
covar_type,
n_features=n_features,
)
assert_array_almost_equal(expected_det, -0.5 * np.log(predected_det))
def _naive_lmvnpdf_diag(X, means, covars):
resp = np.empty((len(X), len(means)))
stds = np.sqrt(covars)
for i, (mean, std) in enumerate(zip(means, stds)):
resp[:, i] = stats.norm.logpdf(X, mean, std).sum(axis=1)
return resp
def test_gaussian_mixture_log_probabilities():
from sklearn.mixture._gaussian_mixture import _estimate_log_gaussian_prob
# test against with _naive_lmvnpdf_diag
rng = np.random.RandomState(0)
rand_data = RandomData(rng)
n_samples = 500
n_features = rand_data.n_features
n_components = rand_data.n_components
means = rand_data.means
covars_diag = rng.rand(n_components, n_features)
X = rng.rand(n_samples, n_features)
log_prob_naive = _naive_lmvnpdf_diag(X, means, covars_diag)
# full covariances
precs_full = np.array([np.diag(1.0 / np.sqrt(x)) for x in covars_diag])
log_prob = _estimate_log_gaussian_prob(X, means, precs_full, "full")
assert_array_almost_equal(log_prob, log_prob_naive)
# diag covariances
precs_chol_diag = 1.0 / np.sqrt(covars_diag)
log_prob = _estimate_log_gaussian_prob(X, means, precs_chol_diag, "diag")
assert_array_almost_equal(log_prob, log_prob_naive)
# tied
covars_tied = np.array([x for x in covars_diag]).mean(axis=0)
precs_tied = np.diag(np.sqrt(1.0 / covars_tied))
log_prob_naive = _naive_lmvnpdf_diag(X, means, [covars_tied] * n_components)
log_prob = _estimate_log_gaussian_prob(X, means, precs_tied, "tied")
assert_array_almost_equal(log_prob, log_prob_naive)
# spherical
covars_spherical = covars_diag.mean(axis=1)
precs_spherical = 1.0 / np.sqrt(covars_diag.mean(axis=1))
log_prob_naive = _naive_lmvnpdf_diag(
X, means, [[k] * n_features for k in covars_spherical]
)
log_prob = _estimate_log_gaussian_prob(X, means, precs_spherical, "spherical")
assert_array_almost_equal(log_prob, log_prob_naive)
# skip tests on weighted_log_probabilities, log_weights
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_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
msg = (
"This GaussianMixture instance is not fitted yet. Call 'fit' "
"with appropriate arguments before using this estimator."
)
with pytest.raises(NotFittedError, match=msg):
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) > 0.95
@pytest.mark.filterwarnings("ignore:.*did not converge.*")
@pytest.mark.parametrize(
"seed, max_iter, tol",
[
(0, 2, 1e-7), # strict non-convergence
(1, 2, 1e-1), # loose non-convergence
(3, 300, 1e-7), # strict convergence
(4, 300, 1e-1), # loose convergence
],
)
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) > 0.95
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_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_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_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,
)
msg = (
"Best performing initialization did not converge. "
"Try different init parameters, or increase max_iter, "
"tol, or check for degenerate data."
)
with pytest.warns(ConvergenceWarning, match=msg):
g.fit(X)
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_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_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_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_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
@pytest.mark.filterwarnings("ignore:.*did not converge.*")
@pytest.mark.parametrize("seed", (0, 1, 2))
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_
@ignore_warnings(category=ConvergenceWarning)
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_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,
)
msg = (
"This GaussianMixture instance is not fitted yet. Call 'fit' with "
"appropriate arguments before using this estimator."
)
with pytest.raises(NotFittedError, match=msg):
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_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,
)
msg = (
"This GaussianMixture instance is not fitted yet. Call 'fit' with "
"appropriate arguments before using this estimator."
)
with pytest.raises(NotFittedError, match=msg):
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_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.inf
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
current_log_likelihood = gmm.fit(X).score(X)
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)
msg = re.escape(
"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."
)
with pytest.raises(ValueError, match=msg):
gmm.fit(X)
gmm.set_params(reg_covar=1e-6).fit(X)
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_, 1.0 / gmm.covariances_)
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
msg = "This GaussianMixture instance is not fitted"
with pytest.raises(NotFittedError, match=msg):
gmm.sample(0)
gmm.fit(X)
msg = "Invalid value for 'n_samples'"
with pytest.raises(ValueError, match=msg):
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)
@ignore_warnings(category=ConvergenceWarning)
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_gaussian_mixture_setting_best_params():
"""`GaussianMixture`'s best_parameters, `n_iter_` and `lower_bound_`
must be set appropriately in the case of divergence.
Non-regression test for:
https://github.com/scikit-learn/scikit-learn/issues/18216
"""
rnd = np.random.RandomState(0)
n_samples = 30
X = rnd.uniform(size=(n_samples, 3))
# following initialization parameters were found to lead to divergence
means_init = np.array(
[
[0.670637869618158, 0.21038256107384043, 0.12892629765485303],
[0.09394051075844147, 0.5759464955561779, 0.929296197576212],
[0.5033230372781258, 0.9569852381759425, 0.08654043447295741],
[0.18578301420435747, 0.5531158970919143, 0.19388943970532435],
[0.4548589928173794, 0.35182513658825276, 0.568146063202464],
[0.609279894978321, 0.7929063819678847, 0.9620097270828052],
]
)
precisions_init = np.array(
[
999999.999604483,
999999.9990869573,
553.7603944542167,
204.78596008931834,
15.867423501783637,
85.4595728389735,
]
)
weights_init = [
0.03333333333333341,
0.03333333333333341,
0.06666666666666674,
0.06666666666666674,
0.7000000000000001,
0.10000000000000007,
]
gmm = GaussianMixture(
covariance_type="spherical",
reg_covar=0,
means_init=means_init,
weights_init=weights_init,
random_state=rnd,
n_components=len(weights_init),
precisions_init=precisions_init,
max_iter=1,
)
# ensure that no error is thrown during fit
gmm.fit(X)
# check that the fit did not converge
assert not gmm.converged_
# check that parameters are set for gmm
for attr in [
"weights_",
"means_",
"covariances_",
"precisions_cholesky_",
"n_iter_",
"lower_bound_",
]:
assert hasattr(gmm, attr)
@pytest.mark.parametrize(
"init_params", ["random", "random_from_data", "k-means++", "kmeans"]
)
def test_init_means_not_duplicated(init_params, global_random_seed):
# Check that all initialisations provide not duplicated starting means
rng = np.random.RandomState(global_random_seed)
rand_data = RandomData(rng, scale=5)
n_components = rand_data.n_components
X = rand_data.X["full"]
gmm = GaussianMixture(
n_components=n_components, init_params=init_params, random_state=rng, max_iter=0
)
gmm.fit(X)
means = gmm.means_
for i_mean, j_mean in itertools.combinations(means, r=2):
assert not np.allclose(i_mean, j_mean)
@pytest.mark.parametrize(
"init_params", ["random", "random_from_data", "k-means++", "kmeans"]
)
def test_means_for_all_inits(init_params, global_random_seed):
# Check fitted means properties for all initializations
rng = np.random.RandomState(global_random_seed)
rand_data = RandomData(rng, scale=5)
n_components = rand_data.n_components
X = rand_data.X["full"]
gmm = GaussianMixture(
n_components=n_components, init_params=init_params, random_state=rng
)
gmm.fit(X)
assert gmm.means_.shape == (n_components, X.shape[1])
assert np.all(X.min(axis=0) <= gmm.means_)
assert np.all(gmm.means_ <= X.max(axis=0))
assert gmm.converged_
def test_max_iter_zero():
# Check that max_iter=0 returns initialisation as expected
# Pick arbitrary initial means and check equal to max_iter=0
rng = np.random.RandomState(0)
rand_data = RandomData(rng, scale=5)
n_components = rand_data.n_components
X = rand_data.X["full"]
means_init = [[20, 30], [30, 25]]
gmm = GaussianMixture(
n_components=n_components,
random_state=rng,
means_init=means_init,
tol=1e-06,
max_iter=0,
)
gmm.fit(X)
assert_allclose(gmm.means_, means_init)
def test_gaussian_mixture_precisions_init_diag():
"""Check that we properly initialize `precision_cholesky_` when we manually
provide the precision matrix.
In this regard, we check the consistency between estimating the precision
matrix and providing the same precision matrix as initialization. It should
lead to the same results with the same number of iterations.
If the initialization is wrong then the number of iterations will increase.
Non-regression test for:
https://github.com/scikit-learn/scikit-learn/issues/16944
"""
# generate a toy dataset
n_samples = 300
rng = np.random.RandomState(0)
shifted_gaussian = rng.randn(n_samples, 2) + np.array([20, 20])
C = np.array([[0.0, -0.7], [3.5, 0.7]])
stretched_gaussian = np.dot(rng.randn(n_samples, 2), C)
X = np.vstack([shifted_gaussian, stretched_gaussian])
# common parameters to check the consistency of precision initialization
n_components, covariance_type, reg_covar, random_state = 2, "diag", 1e-6, 0
# execute the manual initialization to compute the precision matrix:
# - run KMeans to have an initial guess
# - estimate the covariance
# - compute the precision matrix from the estimated covariance
resp = np.zeros((X.shape[0], n_components))
label = (
KMeans(n_clusters=n_components, n_init=1, random_state=random_state)
.fit(X)
.labels_
)
resp[np.arange(X.shape[0]), label] = 1
_, _, covariance = _estimate_gaussian_parameters(
X, resp, reg_covar=reg_covar, covariance_type=covariance_type
)
precisions_init = 1 / covariance
gm_with_init = GaussianMixture(
n_components=n_components,
covariance_type=covariance_type,
reg_covar=reg_covar,
precisions_init=precisions_init,
random_state=random_state,
).fit(X)
gm_without_init = GaussianMixture(
n_components=n_components,
covariance_type=covariance_type,
reg_covar=reg_covar,
random_state=random_state,
).fit(X)
assert gm_without_init.n_iter_ == gm_with_init.n_iter_
assert_allclose(
gm_with_init.precisions_cholesky_, gm_without_init.precisions_cholesky_
)
def _generate_data(seed, n_samples, n_features, n_components):
"""Randomly generate samples and responsibilities."""
rs = np.random.RandomState(seed)
X = rs.random_sample((n_samples, n_features))
resp = rs.random_sample((n_samples, n_components))
resp /= resp.sum(axis=1)[:, np.newaxis]
return X, resp
def _calculate_precisions(X, resp, covariance_type):
"""Calculate precision matrix of X and its Cholesky decomposition
for the given covariance type.
"""
reg_covar = 1e-6
weights, means, covariances = _estimate_gaussian_parameters(
X, resp, reg_covar, covariance_type
)
precisions_cholesky = _compute_precision_cholesky(covariances, covariance_type)
_, n_components = resp.shape
# Instantiate a `GaussianMixture` model in order to use its
# `_set_parameters` method to return the `precisions_` and
# `precisions_cholesky_` from matching the `covariance_type`
# provided.
gmm = GaussianMixture(n_components=n_components, covariance_type=covariance_type)
params = (weights, means, covariances, precisions_cholesky)
gmm._set_parameters(params)
return gmm.precisions_, gmm.precisions_cholesky_
@pytest.mark.parametrize("covariance_type", COVARIANCE_TYPE)
def test_gaussian_mixture_precisions_init(covariance_type, global_random_seed):
"""Non-regression test for #26415."""
X, resp = _generate_data(
seed=global_random_seed,
n_samples=100,
n_features=3,
n_components=4,
)
precisions_init, desired_precisions_cholesky = _calculate_precisions(
X, resp, covariance_type
)
gmm = GaussianMixture(
covariance_type=covariance_type, precisions_init=precisions_init
)
gmm._initialize(X, resp)
actual_precisions_cholesky = gmm.precisions_cholesky_
assert_allclose(actual_precisions_cholesky, desired_precisions_cholesky)
def test_gaussian_mixture_single_component_stable():
"""
Non-regression test for #23032 ensuring 1-component GM works on only a
few samples.
"""
rng = np.random.RandomState(0)
X = rng.multivariate_normal(np.zeros(2), np.identity(2), size=3)
gm = GaussianMixture(n_components=1)
gm.fit(X).sample()
def test_gaussian_mixture_all_init_does_not_estimate_gaussian_parameters(
monkeypatch,
global_random_seed,
):
"""When all init parameters are provided, the Gaussian parameters
are not estimated.
Non-regression test for gh-26015.
"""
mock = Mock(side_effect=_estimate_gaussian_parameters)
monkeypatch.setattr(
sklearn.mixture._gaussian_mixture, "_estimate_gaussian_parameters", mock
)
rng = np.random.RandomState(global_random_seed)
rand_data = RandomData(rng)
gm = GaussianMixture(
n_components=rand_data.n_components,
weights_init=rand_data.weights,
means_init=rand_data.means,
precisions_init=rand_data.precisions["full"],
random_state=rng,
)
gm.fit(rand_data.X["full"])
# The initial gaussian parameters are not estimated. They are estimated for every
# m_step.
assert mock.call_count == gm.n_iter_