467 lines
17 KiB
Python
467 lines
17 KiB
Python
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# Author: Wei Xue <xuewei4d@gmail.com>
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# Thierry Guillemot <thierry.guillemot.work@gmail.com>
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# License: BSD 3 clause
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import copy
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import numpy as np
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import pytest
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from scipy.special import gammaln
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from sklearn.exceptions import ConvergenceWarning, NotFittedError
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from sklearn.metrics.cluster import adjusted_rand_score
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from sklearn.mixture import BayesianGaussianMixture
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from sklearn.mixture._bayesian_mixture import _log_dirichlet_norm, _log_wishart_norm
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from sklearn.mixture.tests.test_gaussian_mixture import RandomData
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from sklearn.utils._testing import (
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assert_almost_equal,
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assert_array_equal,
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ignore_warnings,
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)
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COVARIANCE_TYPE = ["full", "tied", "diag", "spherical"]
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PRIOR_TYPE = ["dirichlet_process", "dirichlet_distribution"]
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def test_log_dirichlet_norm():
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rng = np.random.RandomState(0)
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weight_concentration = rng.rand(2)
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expected_norm = gammaln(np.sum(weight_concentration)) - np.sum(
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gammaln(weight_concentration)
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)
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predected_norm = _log_dirichlet_norm(weight_concentration)
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assert_almost_equal(expected_norm, predected_norm)
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def test_log_wishart_norm():
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rng = np.random.RandomState(0)
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n_components, n_features = 5, 2
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degrees_of_freedom = np.abs(rng.rand(n_components)) + 1.0
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log_det_precisions_chol = n_features * np.log(range(2, 2 + n_components))
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expected_norm = np.empty(5)
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for k, (degrees_of_freedom_k, log_det_k) in enumerate(
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zip(degrees_of_freedom, log_det_precisions_chol)
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):
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expected_norm[k] = -(
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degrees_of_freedom_k * (log_det_k + 0.5 * n_features * np.log(2.0))
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+ np.sum(
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gammaln(
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0.5
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* (degrees_of_freedom_k - np.arange(0, n_features)[:, np.newaxis])
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),
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0,
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)
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).item()
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predected_norm = _log_wishart_norm(
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degrees_of_freedom, log_det_precisions_chol, n_features
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)
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assert_almost_equal(expected_norm, predected_norm)
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def test_bayesian_mixture_weights_prior_initialisation():
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rng = np.random.RandomState(0)
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n_samples, n_components, n_features = 10, 5, 2
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X = rng.rand(n_samples, n_features)
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# Check correct init for a given value of weight_concentration_prior
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weight_concentration_prior = rng.rand()
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior=weight_concentration_prior, random_state=rng
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).fit(X)
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assert_almost_equal(weight_concentration_prior, bgmm.weight_concentration_prior_)
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# Check correct init for the default value of weight_concentration_prior
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bgmm = BayesianGaussianMixture(n_components=n_components, random_state=rng).fit(X)
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assert_almost_equal(1.0 / n_components, bgmm.weight_concentration_prior_)
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def test_bayesian_mixture_mean_prior_initialisation():
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rng = np.random.RandomState(0)
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n_samples, n_components, n_features = 10, 3, 2
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X = rng.rand(n_samples, n_features)
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# Check correct init for a given value of mean_precision_prior
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mean_precision_prior = rng.rand()
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bgmm = BayesianGaussianMixture(
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mean_precision_prior=mean_precision_prior, random_state=rng
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).fit(X)
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assert_almost_equal(mean_precision_prior, bgmm.mean_precision_prior_)
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# Check correct init for the default value of mean_precision_prior
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bgmm = BayesianGaussianMixture(random_state=rng).fit(X)
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assert_almost_equal(1.0, bgmm.mean_precision_prior_)
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# Check correct init for a given value of mean_prior
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mean_prior = rng.rand(n_features)
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bgmm = BayesianGaussianMixture(
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n_components=n_components, mean_prior=mean_prior, random_state=rng
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).fit(X)
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assert_almost_equal(mean_prior, bgmm.mean_prior_)
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# Check correct init for the default value of bemean_priorta
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bgmm = BayesianGaussianMixture(n_components=n_components, random_state=rng).fit(X)
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assert_almost_equal(X.mean(axis=0), bgmm.mean_prior_)
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def test_bayesian_mixture_precisions_prior_initialisation():
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rng = np.random.RandomState(0)
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n_samples, n_features = 10, 2
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X = rng.rand(n_samples, n_features)
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# Check raise message for a bad value of degrees_of_freedom_prior
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bad_degrees_of_freedom_prior_ = n_features - 1.0
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bgmm = BayesianGaussianMixture(
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degrees_of_freedom_prior=bad_degrees_of_freedom_prior_, random_state=rng
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)
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msg = (
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"The parameter 'degrees_of_freedom_prior' should be greater than"
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f" {n_features -1}, but got {bad_degrees_of_freedom_prior_:.3f}."
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)
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with pytest.raises(ValueError, match=msg):
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bgmm.fit(X)
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# Check correct init for a given value of degrees_of_freedom_prior
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degrees_of_freedom_prior = rng.rand() + n_features - 1.0
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bgmm = BayesianGaussianMixture(
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degrees_of_freedom_prior=degrees_of_freedom_prior, random_state=rng
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).fit(X)
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assert_almost_equal(degrees_of_freedom_prior, bgmm.degrees_of_freedom_prior_)
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# Check correct init for the default value of degrees_of_freedom_prior
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degrees_of_freedom_prior_default = n_features
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bgmm = BayesianGaussianMixture(
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degrees_of_freedom_prior=degrees_of_freedom_prior_default, random_state=rng
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).fit(X)
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assert_almost_equal(
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degrees_of_freedom_prior_default, bgmm.degrees_of_freedom_prior_
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)
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# Check correct init for a given value of covariance_prior
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covariance_prior = {
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"full": np.cov(X.T, bias=1) + 10,
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"tied": np.cov(X.T, bias=1) + 5,
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"diag": np.diag(np.atleast_2d(np.cov(X.T, bias=1))) + 3,
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"spherical": rng.rand(),
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}
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bgmm = BayesianGaussianMixture(random_state=rng)
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for cov_type in ["full", "tied", "diag", "spherical"]:
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bgmm.covariance_type = cov_type
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bgmm.covariance_prior = covariance_prior[cov_type]
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bgmm.fit(X)
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assert_almost_equal(covariance_prior[cov_type], bgmm.covariance_prior_)
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# Check correct init for the default value of covariance_prior
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covariance_prior_default = {
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"full": np.atleast_2d(np.cov(X.T)),
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"tied": np.atleast_2d(np.cov(X.T)),
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"diag": np.var(X, axis=0, ddof=1),
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"spherical": np.var(X, axis=0, ddof=1).mean(),
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}
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bgmm = BayesianGaussianMixture(random_state=0)
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for cov_type in ["full", "tied", "diag", "spherical"]:
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bgmm.covariance_type = cov_type
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bgmm.fit(X)
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assert_almost_equal(covariance_prior_default[cov_type], bgmm.covariance_prior_)
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def test_bayesian_mixture_check_is_fitted():
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rng = np.random.RandomState(0)
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n_samples, n_features = 10, 2
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# Check raise message
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bgmm = BayesianGaussianMixture(random_state=rng)
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X = rng.rand(n_samples, n_features)
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msg = "This BayesianGaussianMixture instance is not fitted yet."
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with pytest.raises(ValueError, match=msg):
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bgmm.score(X)
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def test_bayesian_mixture_weights():
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rng = np.random.RandomState(0)
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n_samples, n_features = 10, 2
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X = rng.rand(n_samples, n_features)
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# Case Dirichlet distribution for the weight concentration prior type
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type="dirichlet_distribution",
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n_components=3,
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random_state=rng,
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).fit(X)
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expected_weights = bgmm.weight_concentration_ / np.sum(bgmm.weight_concentration_)
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assert_almost_equal(expected_weights, bgmm.weights_)
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assert_almost_equal(np.sum(bgmm.weights_), 1.0)
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# Case Dirichlet process for the weight concentration prior type
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dpgmm = BayesianGaussianMixture(
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weight_concentration_prior_type="dirichlet_process",
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n_components=3,
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random_state=rng,
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).fit(X)
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weight_dirichlet_sum = (
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dpgmm.weight_concentration_[0] + dpgmm.weight_concentration_[1]
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)
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tmp = dpgmm.weight_concentration_[1] / weight_dirichlet_sum
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expected_weights = (
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dpgmm.weight_concentration_[0]
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/ weight_dirichlet_sum
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* np.hstack((1, np.cumprod(tmp[:-1])))
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)
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expected_weights /= np.sum(expected_weights)
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assert_almost_equal(expected_weights, dpgmm.weights_)
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assert_almost_equal(np.sum(dpgmm.weights_), 1.0)
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@ignore_warnings(category=ConvergenceWarning)
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def test_monotonic_likelihood():
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# We check that each step of the each step of variational inference without
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# regularization improve monotonically the training set of the bound
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rng = np.random.RandomState(0)
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rand_data = RandomData(rng, scale=20)
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n_components = rand_data.n_components
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for prior_type in PRIOR_TYPE:
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for covar_type in COVARIANCE_TYPE:
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X = rand_data.X[covar_type]
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type=prior_type,
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n_components=2 * n_components,
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covariance_type=covar_type,
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warm_start=True,
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max_iter=1,
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random_state=rng,
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tol=1e-3,
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)
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current_lower_bound = -np.inf
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# Do one training iteration at a time so we can make sure that the
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# training log likelihood increases after each iteration.
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for _ in range(600):
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prev_lower_bound = current_lower_bound
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current_lower_bound = bgmm.fit(X).lower_bound_
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assert current_lower_bound >= prev_lower_bound
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if bgmm.converged_:
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break
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assert bgmm.converged_
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def test_compare_covar_type():
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# We can compare the 'full' precision with the other cov_type if we apply
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# 1 iter of the M-step (done during _initialize_parameters).
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rng = np.random.RandomState(0)
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rand_data = RandomData(rng, scale=7)
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X = rand_data.X["full"]
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n_components = rand_data.n_components
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for prior_type in PRIOR_TYPE:
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# Computation of the full_covariance
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type=prior_type,
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n_components=2 * n_components,
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covariance_type="full",
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max_iter=1,
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random_state=0,
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tol=1e-7,
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)
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bgmm._check_parameters(X)
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bgmm._initialize_parameters(X, np.random.RandomState(0))
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full_covariances = (
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bgmm.covariances_ * bgmm.degrees_of_freedom_[:, np.newaxis, np.newaxis]
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)
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# Check tied_covariance = mean(full_covariances, 0)
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type=prior_type,
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n_components=2 * n_components,
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covariance_type="tied",
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max_iter=1,
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random_state=0,
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tol=1e-7,
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)
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bgmm._check_parameters(X)
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bgmm._initialize_parameters(X, np.random.RandomState(0))
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tied_covariance = bgmm.covariances_ * bgmm.degrees_of_freedom_
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assert_almost_equal(tied_covariance, np.mean(full_covariances, 0))
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# Check diag_covariance = diag(full_covariances)
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type=prior_type,
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n_components=2 * n_components,
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covariance_type="diag",
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max_iter=1,
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random_state=0,
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tol=1e-7,
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)
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bgmm._check_parameters(X)
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bgmm._initialize_parameters(X, np.random.RandomState(0))
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diag_covariances = bgmm.covariances_ * bgmm.degrees_of_freedom_[:, np.newaxis]
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assert_almost_equal(
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diag_covariances, np.array([np.diag(cov) for cov in full_covariances])
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)
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# Check spherical_covariance = np.mean(diag_covariances, 0)
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bgmm = BayesianGaussianMixture(
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weight_concentration_prior_type=prior_type,
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n_components=2 * n_components,
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covariance_type="spherical",
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max_iter=1,
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random_state=0,
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tol=1e-7,
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)
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bgmm._check_parameters(X)
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bgmm._initialize_parameters(X, np.random.RandomState(0))
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spherical_covariances = bgmm.covariances_ * bgmm.degrees_of_freedom_
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assert_almost_equal(spherical_covariances, np.mean(diag_covariances, 1))
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@ignore_warnings(category=ConvergenceWarning)
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def test_check_covariance_precision():
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# We check that the dot product of the covariance and the precision
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# matrices is identity.
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rng = np.random.RandomState(0)
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rand_data = RandomData(rng, scale=7)
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n_components, n_features = 2 * rand_data.n_components, 2
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# Computation of the full_covariance
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bgmm = BayesianGaussianMixture(
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n_components=n_components, max_iter=100, random_state=rng, tol=1e-3, reg_covar=0
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)
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for covar_type in COVARIANCE_TYPE:
|
||
|
|
bgmm.covariance_type = covar_type
|
||
|
|
bgmm.fit(rand_data.X[covar_type])
|
||
|
|
|
||
|
|
if covar_type == "full":
|
||
|
|
for covar, precision in zip(bgmm.covariances_, bgmm.precisions_):
|
||
|
|
assert_almost_equal(np.dot(covar, precision), np.eye(n_features))
|
||
|
|
elif covar_type == "tied":
|
||
|
|
assert_almost_equal(
|
||
|
|
np.dot(bgmm.covariances_, bgmm.precisions_), np.eye(n_features)
|
||
|
|
)
|
||
|
|
|
||
|
|
elif covar_type == "diag":
|
||
|
|
assert_almost_equal(
|
||
|
|
bgmm.covariances_ * bgmm.precisions_,
|
||
|
|
np.ones((n_components, n_features)),
|
||
|
|
)
|
||
|
|
|
||
|
|
else:
|
||
|
|
assert_almost_equal(
|
||
|
|
bgmm.covariances_ * bgmm.precisions_, np.ones(n_components)
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
@ignore_warnings(category=ConvergenceWarning)
|
||
|
|
def test_invariant_translation():
|
||
|
|
# We check here that adding a constant in the data change correctly the
|
||
|
|
# parameters of the mixture
|
||
|
|
rng = np.random.RandomState(0)
|
||
|
|
rand_data = RandomData(rng, scale=100)
|
||
|
|
n_components = 2 * rand_data.n_components
|
||
|
|
|
||
|
|
for prior_type in PRIOR_TYPE:
|
||
|
|
for covar_type in COVARIANCE_TYPE:
|
||
|
|
X = rand_data.X[covar_type]
|
||
|
|
bgmm1 = BayesianGaussianMixture(
|
||
|
|
weight_concentration_prior_type=prior_type,
|
||
|
|
n_components=n_components,
|
||
|
|
max_iter=100,
|
||
|
|
random_state=0,
|
||
|
|
tol=1e-3,
|
||
|
|
reg_covar=0,
|
||
|
|
).fit(X)
|
||
|
|
bgmm2 = BayesianGaussianMixture(
|
||
|
|
weight_concentration_prior_type=prior_type,
|
||
|
|
n_components=n_components,
|
||
|
|
max_iter=100,
|
||
|
|
random_state=0,
|
||
|
|
tol=1e-3,
|
||
|
|
reg_covar=0,
|
||
|
|
).fit(X + 100)
|
||
|
|
|
||
|
|
assert_almost_equal(bgmm1.means_, bgmm2.means_ - 100)
|
||
|
|
assert_almost_equal(bgmm1.weights_, bgmm2.weights_)
|
||
|
|
assert_almost_equal(bgmm1.covariances_, bgmm2.covariances_)
|
||
|
|
|
||
|
|
|
||
|
|
@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_bayesian_mixture_fit_predict(seed, max_iter, tol):
|
||
|
|
rng = np.random.RandomState(seed)
|
||
|
|
rand_data = RandomData(rng, n_samples=50, scale=7)
|
||
|
|
n_components = 2 * rand_data.n_components
|
||
|
|
|
||
|
|
for covar_type in COVARIANCE_TYPE:
|
||
|
|
bgmm1 = BayesianGaussianMixture(
|
||
|
|
n_components=n_components,
|
||
|
|
max_iter=max_iter,
|
||
|
|
random_state=rng,
|
||
|
|
tol=tol,
|
||
|
|
reg_covar=0,
|
||
|
|
)
|
||
|
|
bgmm1.covariance_type = covar_type
|
||
|
|
bgmm2 = copy.deepcopy(bgmm1)
|
||
|
|
X = rand_data.X[covar_type]
|
||
|
|
|
||
|
|
Y_pred1 = bgmm1.fit(X).predict(X)
|
||
|
|
Y_pred2 = bgmm2.fit_predict(X)
|
||
|
|
assert_array_equal(Y_pred1, Y_pred2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_bayesian_mixture_fit_predict_n_init():
|
||
|
|
# Check that fit_predict is equivalent to fit.predict, when n_init > 1
|
||
|
|
X = np.random.RandomState(0).randn(50, 5)
|
||
|
|
gm = BayesianGaussianMixture(n_components=5, n_init=10, random_state=0)
|
||
|
|
y_pred1 = gm.fit_predict(X)
|
||
|
|
y_pred2 = gm.predict(X)
|
||
|
|
assert_array_equal(y_pred1, y_pred2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_bayesian_mixture_predict_predict_proba():
|
||
|
|
# this is the same test as test_gaussian_mixture_predict_predict_proba()
|
||
|
|
rng = np.random.RandomState(0)
|
||
|
|
rand_data = RandomData(rng)
|
||
|
|
for prior_type in PRIOR_TYPE:
|
||
|
|
for covar_type in COVARIANCE_TYPE:
|
||
|
|
X = rand_data.X[covar_type]
|
||
|
|
Y = rand_data.Y
|
||
|
|
bgmm = BayesianGaussianMixture(
|
||
|
|
n_components=rand_data.n_components,
|
||
|
|
random_state=rng,
|
||
|
|
weight_concentration_prior_type=prior_type,
|
||
|
|
covariance_type=covar_type,
|
||
|
|
)
|
||
|
|
|
||
|
|
# Check a warning message arrive if we don't do fit
|
||
|
|
msg = (
|
||
|
|
"This BayesianGaussianMixture instance is not fitted yet. "
|
||
|
|
"Call 'fit' with appropriate arguments before using this "
|
||
|
|
"estimator."
|
||
|
|
)
|
||
|
|
with pytest.raises(NotFittedError, match=msg):
|
||
|
|
bgmm.predict(X)
|
||
|
|
|
||
|
|
bgmm.fit(X)
|
||
|
|
Y_pred = bgmm.predict(X)
|
||
|
|
Y_pred_proba = bgmm.predict_proba(X).argmax(axis=1)
|
||
|
|
assert_array_equal(Y_pred, Y_pred_proba)
|
||
|
|
assert adjusted_rand_score(Y, Y_pred) >= 0.95
|