150 lines
5.8 KiB
Python
150 lines
5.8 KiB
Python
""" Test the graphical_lasso module.
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"""
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import sys
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import numpy as np
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from scipy import linalg
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from sklearn.utils._testing import assert_array_almost_equal
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from sklearn.utils._testing import assert_array_less
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from sklearn.covariance import (graphical_lasso, GraphicalLasso,
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GraphicalLassoCV, empirical_covariance)
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from sklearn.datasets import make_sparse_spd_matrix
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from io import StringIO
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from sklearn.utils import check_random_state
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from sklearn import datasets
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def test_graphical_lasso(random_state=0):
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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=.95,
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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., .1, .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(emp_cov, return_costs=True,
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alpha=alpha, mode=method)
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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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assert_array_less(np.diff(costs), 0)
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# Check that the 2 approaches give similar results
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assert_array_almost_equal(covs['cd'], covs['lars'], decimal=4)
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assert_array_almost_equal(icovs['cd'], icovs['lars'], decimal=4)
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# Smoke test the estimator
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model = GraphicalLasso(alpha=.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(
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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_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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[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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icov_R = np.array([
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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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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,
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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],
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[1.186972, 0.57713289]])
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icov_skggm = np.array([[1.52836773, -3.14334831],
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[-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=.1, return_costs=False,
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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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[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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icov_R = np.array([
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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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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(emp_cov, alpha=0.01, return_costs=False,
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mode=method)
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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=.96,
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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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# Smoke test with specified alphas
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GraphicalLassoCV(alphas=[0.8, 0.5], tol=1e-1, n_jobs=1).fit(X)
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