287 lines
10 KiB
Python
287 lines
10 KiB
Python
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""" Test the graphical_lasso module.
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"""
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import sys
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from io import StringIO
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import numpy as np
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import pytest
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from numpy.testing import assert_allclose
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from scipy import linalg
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from sklearn import datasets
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from sklearn.covariance import (
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GraphicalLasso,
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GraphicalLassoCV,
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empirical_covariance,
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graphical_lasso,
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)
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from sklearn.datasets import make_sparse_spd_matrix
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from sklearn.utils import check_random_state
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from sklearn.utils._testing import (
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_convert_container,
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assert_array_almost_equal,
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assert_array_less,
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)
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def test_graphical_lassos(random_state=1):
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"""Test the graphical lasso solvers.
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This checks is unstable for some random seeds where the covariance found with "cd"
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and "lars" solvers are different (4 cases / 100 tries).
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"""
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# Sample data from a sparse multivariate normal
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dim = 20
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n_samples = 100
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random_state = check_random_state(random_state)
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prec = make_sparse_spd_matrix(dim, alpha=0.95, random_state=random_state)
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cov = linalg.inv(prec)
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X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
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emp_cov = empirical_covariance(X)
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for alpha in (0.0, 0.1, 0.25):
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covs = dict()
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icovs = dict()
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for method in ("cd", "lars"):
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cov_, icov_, costs = graphical_lasso(
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emp_cov, return_costs=True, alpha=alpha, mode=method
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)
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covs[method] = cov_
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icovs[method] = icov_
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costs, dual_gap = np.array(costs).T
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# Check that the costs always decrease (doesn't hold if alpha == 0)
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if not alpha == 0:
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# use 1e-12 since the cost can be exactly 0
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assert_array_less(np.diff(costs), 1e-12)
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# Check that the 2 approaches give similar results
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assert_allclose(covs["cd"], covs["lars"], atol=5e-4)
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assert_allclose(icovs["cd"], icovs["lars"], atol=5e-4)
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# Smoke test the estimator
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model = GraphicalLasso(alpha=0.25).fit(X)
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model.score(X)
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assert_array_almost_equal(model.covariance_, covs["cd"], decimal=4)
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assert_array_almost_equal(model.covariance_, covs["lars"], decimal=4)
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# For a centered matrix, assume_centered could be chosen True or False
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# Check that this returns indeed the same result for centered data
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Z = X - X.mean(0)
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precs = list()
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for assume_centered in (False, True):
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prec_ = GraphicalLasso(assume_centered=assume_centered).fit(Z).precision_
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precs.append(prec_)
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assert_array_almost_equal(precs[0], precs[1])
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def test_graphical_lasso_when_alpha_equals_0():
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"""Test graphical_lasso's early return condition when alpha=0."""
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X = np.random.randn(100, 10)
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emp_cov = empirical_covariance(X, assume_centered=True)
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model = GraphicalLasso(alpha=0, covariance="precomputed").fit(emp_cov)
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assert_allclose(model.precision_, np.linalg.inv(emp_cov))
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_, precision = graphical_lasso(emp_cov, alpha=0)
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assert_allclose(precision, np.linalg.inv(emp_cov))
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@pytest.mark.parametrize("mode", ["cd", "lars"])
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def test_graphical_lasso_n_iter(mode):
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X, _ = datasets.make_classification(n_samples=5_000, n_features=20, random_state=0)
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emp_cov = empirical_covariance(X)
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_, _, n_iter = graphical_lasso(
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emp_cov, 0.2, mode=mode, max_iter=2, return_n_iter=True
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)
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assert n_iter == 2
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def test_graphical_lasso_iris():
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# Hard-coded solution from R glasso package for alpha=1.0
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# (need to set penalize.diagonal to FALSE)
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cov_R = np.array(
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[
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[0.68112222, 0.0000000, 0.265820, 0.02464314],
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[0.00000000, 0.1887129, 0.000000, 0.00000000],
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[0.26582000, 0.0000000, 3.095503, 0.28697200],
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[0.02464314, 0.0000000, 0.286972, 0.57713289],
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]
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)
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icov_R = np.array(
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[
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[1.5190747, 0.000000, -0.1304475, 0.0000000],
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[0.0000000, 5.299055, 0.0000000, 0.0000000],
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[-0.1304475, 0.000000, 0.3498624, -0.1683946],
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[0.0000000, 0.000000, -0.1683946, 1.8164353],
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]
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)
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X = datasets.load_iris().data
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emp_cov = empirical_covariance(X)
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for method in ("cd", "lars"):
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cov, icov = graphical_lasso(emp_cov, alpha=1.0, return_costs=False, mode=method)
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assert_array_almost_equal(cov, cov_R)
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assert_array_almost_equal(icov, icov_R)
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def test_graph_lasso_2D():
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# Hard-coded solution from Python skggm package
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# obtained by calling `quic(emp_cov, lam=.1, tol=1e-8)`
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cov_skggm = np.array([[3.09550269, 1.186972], [1.186972, 0.57713289]])
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icov_skggm = np.array([[1.52836773, -3.14334831], [-3.14334831, 8.19753385]])
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X = datasets.load_iris().data[:, 2:]
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emp_cov = empirical_covariance(X)
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for method in ("cd", "lars"):
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cov, icov = graphical_lasso(emp_cov, alpha=0.1, return_costs=False, mode=method)
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assert_array_almost_equal(cov, cov_skggm)
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assert_array_almost_equal(icov, icov_skggm)
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def test_graphical_lasso_iris_singular():
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# Small subset of rows to test the rank-deficient case
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# Need to choose samples such that none of the variances are zero
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indices = np.arange(10, 13)
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# Hard-coded solution from R glasso package for alpha=0.01
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cov_R = np.array(
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[
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[0.08, 0.056666662595, 0.00229729713223, 0.00153153142149],
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[0.056666662595, 0.082222222222, 0.00333333333333, 0.00222222222222],
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[0.002297297132, 0.003333333333, 0.00666666666667, 0.00009009009009],
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[0.001531531421, 0.002222222222, 0.00009009009009, 0.00222222222222],
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]
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)
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icov_R = np.array(
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[
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[24.42244057, -16.831679593, 0.0, 0.0],
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[-16.83168201, 24.351841681, -6.206896552, -12.5],
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[0.0, -6.206896171, 153.103448276, 0.0],
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[0.0, -12.499999143, 0.0, 462.5],
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]
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)
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X = datasets.load_iris().data[indices, :]
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emp_cov = empirical_covariance(X)
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for method in ("cd", "lars"):
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cov, icov = graphical_lasso(
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emp_cov, alpha=0.01, return_costs=False, mode=method
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)
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assert_array_almost_equal(cov, cov_R, decimal=5)
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assert_array_almost_equal(icov, icov_R, decimal=5)
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def test_graphical_lasso_cv(random_state=1):
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# Sample data from a sparse multivariate normal
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dim = 5
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n_samples = 6
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random_state = check_random_state(random_state)
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prec = make_sparse_spd_matrix(dim, alpha=0.96, random_state=random_state)
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cov = linalg.inv(prec)
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X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
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# Capture stdout, to smoke test the verbose mode
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orig_stdout = sys.stdout
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try:
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sys.stdout = StringIO()
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# We need verbose very high so that Parallel prints on stdout
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GraphicalLassoCV(verbose=100, alphas=5, tol=1e-1).fit(X)
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finally:
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sys.stdout = orig_stdout
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@pytest.mark.parametrize("alphas_container_type", ["list", "tuple", "array"])
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def test_graphical_lasso_cv_alphas_iterable(alphas_container_type):
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"""Check that we can pass an array-like to `alphas`.
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Non-regression test for:
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https://github.com/scikit-learn/scikit-learn/issues/22489
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"""
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true_cov = np.array(
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[
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[0.8, 0.0, 0.2, 0.0],
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[0.0, 0.4, 0.0, 0.0],
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[0.2, 0.0, 0.3, 0.1],
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[0.0, 0.0, 0.1, 0.7],
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]
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)
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rng = np.random.RandomState(0)
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X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
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alphas = _convert_container([0.02, 0.03], alphas_container_type)
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GraphicalLassoCV(alphas=alphas, tol=1e-1, n_jobs=1).fit(X)
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@pytest.mark.parametrize(
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"alphas,err_type,err_msg",
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[
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([-0.02, 0.03], ValueError, "must be > 0"),
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([0, 0.03], ValueError, "must be > 0"),
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(["not_number", 0.03], TypeError, "must be an instance of float"),
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],
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)
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def test_graphical_lasso_cv_alphas_invalid_array(alphas, err_type, err_msg):
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"""Check that if an array-like containing a value
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outside of (0, inf] is passed to `alphas`, a ValueError is raised.
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Check if a string is passed, a TypeError is raised.
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"""
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true_cov = np.array(
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[
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[0.8, 0.0, 0.2, 0.0],
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[0.0, 0.4, 0.0, 0.0],
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[0.2, 0.0, 0.3, 0.1],
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[0.0, 0.0, 0.1, 0.7],
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]
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)
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rng = np.random.RandomState(0)
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X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
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with pytest.raises(err_type, match=err_msg):
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GraphicalLassoCV(alphas=alphas, tol=1e-1, n_jobs=1).fit(X)
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def test_graphical_lasso_cv_scores():
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splits = 4
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n_alphas = 5
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n_refinements = 3
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true_cov = np.array(
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[
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[0.8, 0.0, 0.2, 0.0],
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[0.0, 0.4, 0.0, 0.0],
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[0.2, 0.0, 0.3, 0.1],
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[0.0, 0.0, 0.1, 0.7],
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]
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)
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rng = np.random.RandomState(0)
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X = rng.multivariate_normal(mean=[0, 0, 0, 0], cov=true_cov, size=200)
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cov = GraphicalLassoCV(cv=splits, alphas=n_alphas, n_refinements=n_refinements).fit(
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X
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)
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cv_results = cov.cv_results_
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# alpha and one for each split
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total_alphas = n_refinements * n_alphas + 1
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keys = ["alphas"]
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split_keys = [f"split{i}_test_score" for i in range(splits)]
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for key in keys + split_keys:
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assert key in cv_results
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assert len(cv_results[key]) == total_alphas
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cv_scores = np.asarray([cov.cv_results_[key] for key in split_keys])
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expected_mean = cv_scores.mean(axis=0)
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expected_std = cv_scores.std(axis=0)
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assert_allclose(cov.cv_results_["mean_test_score"], expected_mean)
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assert_allclose(cov.cv_results_["std_test_score"], expected_std)
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# TODO(1.5): remove in 1.5
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def test_graphical_lasso_cov_init_deprecation():
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"""Check that we raise a deprecation warning if providing `cov_init` in
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`graphical_lasso`."""
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rng, dim, n_samples = np.random.RandomState(0), 20, 100
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prec = make_sparse_spd_matrix(dim, alpha=0.95, random_state=0)
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cov = linalg.inv(prec)
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X = rng.multivariate_normal(np.zeros(dim), cov, size=n_samples)
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emp_cov = empirical_covariance(X)
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with pytest.warns(FutureWarning, match="cov_init parameter is deprecated"):
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graphical_lasso(emp_cov, alpha=0.1, cov_init=emp_cov)
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