156 lines
6 KiB
Python
156 lines
6 KiB
Python
""" Test the graph_lasso module.
|
|
"""
|
|
import sys
|
|
|
|
import numpy as np
|
|
from scipy import linalg
|
|
|
|
from sklearn.utils.testing import assert_array_almost_equal
|
|
from sklearn.utils.testing import assert_array_less
|
|
from sklearn.utils.testing import assert_warns_message
|
|
|
|
from sklearn.covariance import (graph_lasso, GraphLasso, GraphLassoCV,
|
|
empirical_covariance)
|
|
from sklearn.datasets.samples_generator import make_sparse_spd_matrix
|
|
from sklearn.externals.six.moves import StringIO
|
|
from sklearn.utils import check_random_state
|
|
from sklearn import datasets
|
|
|
|
from numpy.testing import assert_equal
|
|
|
|
|
|
def test_graph_lasso(random_state=0):
|
|
# Sample data from a sparse multivariate normal
|
|
dim = 20
|
|
n_samples = 100
|
|
random_state = check_random_state(random_state)
|
|
prec = make_sparse_spd_matrix(dim, alpha=.95,
|
|
random_state=random_state)
|
|
cov = linalg.inv(prec)
|
|
X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
|
|
emp_cov = empirical_covariance(X)
|
|
|
|
for alpha in (0., .1, .25):
|
|
covs = dict()
|
|
icovs = dict()
|
|
for method in ('cd', 'lars'):
|
|
cov_, icov_, costs = graph_lasso(emp_cov, alpha=alpha, mode=method,
|
|
return_costs=True)
|
|
covs[method] = cov_
|
|
icovs[method] = icov_
|
|
costs, dual_gap = np.array(costs).T
|
|
# Check that the costs always decrease (doesn't hold if alpha == 0)
|
|
if not alpha == 0:
|
|
assert_array_less(np.diff(costs), 0)
|
|
# Check that the 2 approaches give similar results
|
|
assert_array_almost_equal(covs['cd'], covs['lars'], decimal=4)
|
|
assert_array_almost_equal(icovs['cd'], icovs['lars'], decimal=4)
|
|
|
|
# Smoke test the estimator
|
|
model = GraphLasso(alpha=.25).fit(X)
|
|
model.score(X)
|
|
assert_array_almost_equal(model.covariance_, covs['cd'], decimal=4)
|
|
assert_array_almost_equal(model.covariance_, covs['lars'], decimal=4)
|
|
|
|
# For a centered matrix, assume_centered could be chosen True or False
|
|
# Check that this returns indeed the same result for centered data
|
|
Z = X - X.mean(0)
|
|
precs = list()
|
|
for assume_centered in (False, True):
|
|
prec_ = GraphLasso(assume_centered=assume_centered).fit(Z).precision_
|
|
precs.append(prec_)
|
|
assert_array_almost_equal(precs[0], precs[1])
|
|
|
|
|
|
def test_graph_lasso_iris():
|
|
# Hard-coded solution from R glasso package for alpha=1.0
|
|
# The iris datasets in R and scikit-learn do not match in a few places,
|
|
# these values are for the scikit-learn version.
|
|
cov_R = np.array([
|
|
[0.68112222, 0.0, 0.2651911, 0.02467558],
|
|
[0.00, 0.1867507, 0.0, 0.00],
|
|
[0.26519111, 0.0, 3.0924249, 0.28774489],
|
|
[0.02467558, 0.0, 0.2877449, 0.57853156]
|
|
])
|
|
icov_R = np.array([
|
|
[1.5188780, 0.0, -0.1302515, 0.0],
|
|
[0.0, 5.354733, 0.0, 0.0],
|
|
[-0.1302515, 0.0, 0.3502322, -0.1686399],
|
|
[0.0, 0.0, -0.1686399, 1.8123908]
|
|
])
|
|
X = datasets.load_iris().data
|
|
emp_cov = empirical_covariance(X)
|
|
for method in ('cd', 'lars'):
|
|
cov, icov = graph_lasso(emp_cov, alpha=1.0, return_costs=False,
|
|
mode=method)
|
|
assert_array_almost_equal(cov, cov_R)
|
|
assert_array_almost_equal(icov, icov_R)
|
|
|
|
|
|
def test_graph_lasso_iris_singular():
|
|
# Small subset of rows to test the rank-deficient case
|
|
# Need to choose samples such that none of the variances are zero
|
|
indices = np.arange(10, 13)
|
|
|
|
# Hard-coded solution from R glasso package for alpha=0.01
|
|
cov_R = np.array([
|
|
[0.08, 0.056666662595, 0.00229729713223, 0.00153153142149],
|
|
[0.056666662595, 0.082222222222, 0.00333333333333, 0.00222222222222],
|
|
[0.002297297132, 0.003333333333, 0.00666666666667, 0.00009009009009],
|
|
[0.001531531421, 0.002222222222, 0.00009009009009, 0.00222222222222]
|
|
])
|
|
icov_R = np.array([
|
|
[24.42244057, -16.831679593, 0.0, 0.0],
|
|
[-16.83168201, 24.351841681, -6.206896552, -12.5],
|
|
[0.0, -6.206896171, 153.103448276, 0.0],
|
|
[0.0, -12.499999143, 0.0, 462.5]
|
|
])
|
|
X = datasets.load_iris().data[indices, :]
|
|
emp_cov = empirical_covariance(X)
|
|
for method in ('cd', 'lars'):
|
|
cov, icov = graph_lasso(emp_cov, alpha=0.01, return_costs=False,
|
|
mode=method)
|
|
assert_array_almost_equal(cov, cov_R, decimal=5)
|
|
assert_array_almost_equal(icov, icov_R, decimal=5)
|
|
|
|
|
|
def test_graph_lasso_cv(random_state=1):
|
|
# Sample data from a sparse multivariate normal
|
|
dim = 5
|
|
n_samples = 6
|
|
random_state = check_random_state(random_state)
|
|
prec = make_sparse_spd_matrix(dim, alpha=.96,
|
|
random_state=random_state)
|
|
cov = linalg.inv(prec)
|
|
X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
|
|
# Capture stdout, to smoke test the verbose mode
|
|
orig_stdout = sys.stdout
|
|
try:
|
|
sys.stdout = StringIO()
|
|
# We need verbose very high so that Parallel prints on stdout
|
|
GraphLassoCV(verbose=100, alphas=5, tol=1e-1).fit(X)
|
|
finally:
|
|
sys.stdout = orig_stdout
|
|
|
|
# Smoke test with specified alphas
|
|
GraphLassoCV(alphas=[0.8, 0.5], tol=1e-1, n_jobs=1).fit(X)
|
|
|
|
|
|
def test_deprecated_grid_scores(random_state=1):
|
|
dim = 5
|
|
n_samples = 6
|
|
random_state = check_random_state(random_state)
|
|
prec = make_sparse_spd_matrix(dim, alpha=.96,
|
|
random_state=random_state)
|
|
cov = linalg.inv(prec)
|
|
X = random_state.multivariate_normal(np.zeros(dim), cov, size=n_samples)
|
|
graph_lasso = GraphLassoCV(alphas=[0.8, 0.5], tol=1e-1, n_jobs=1)
|
|
graph_lasso.fit(X)
|
|
|
|
depr_message = ("Attribute grid_scores was deprecated in version "
|
|
"0.19 and will be removed in 0.21. Use "
|
|
"``grid_scores_`` instead")
|
|
|
|
assert_warns_message(DeprecationWarning, depr_message,
|
|
lambda: graph_lasso.grid_scores)
|
|
assert_equal(graph_lasso.grid_scores, graph_lasso.grid_scores_)
|