def test_zero_lag():
"""Test analysis for 0 lag."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
data = Data(np.hstack((source, target)), dim_order='sp', normalise=False)
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'tau_sources':
0, # this is not required, but shouldn't throw an error if provided
'max_lag_sources': 0,
'min_lag_sources': 0
}
nw = MultivariateMI()
results = nw.analyse_single_target(settings, data, target=1, sources='all')
mi_estimator = JidtKraskovMI(settings={'normalise': False})
jidt_mi = mi_estimator.estimate(source, target)
omnibus_mi = results.get_single_target(1, fdr=False).omnibus_mi
print('Estimated omnibus MI: {0:0.6f}, estimated MI using JIDT core '
'estimator: {1:0.6f} (expected: {2:0.6f}).'.format(
omnibus_mi, jidt_mi, expected_mi))
assert np.isclose(omnibus_mi, jidt_mi, atol=0.005), (
'Zero-lag omnibus MI ({0:0.6f}) differs from JIDT estimate '
'({1:0.6f}).'.format(omnibus_mi, jidt_mi))
assert np.isclose(
omnibus_mi, expected_mi,
atol=0.05), ('Zero-lag omnibus MI ({0:0.6f}) differs from expected MI '
'({1:0.6f}).'.format(omnibus_mi, expected_mi))
def test_zero_lag():
"""Test analysis for 0 lag."""
covariance = 0.4
n = 10000
source = np.random.normal(0, 1, size=n)
target = (covariance * source +
(1 - covariance) * np.random.normal(0, 1, size=n))
# expected_corr = covariance / (np.sqrt(covariance**2 + (1-covariance)**2))
corr = np.corrcoef(source, target)[0, 1]
expected_mi = -0.5 * np.log(1 - corr**2)
data = Data(np.vstack((source, target)), dim_order='ps', normalise=False)
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'max_lag_sources': 0,
'min_lag_sources': 0
}
nw = MultivariateMI()
results = nw.analyse_single_target(settings, data, target=1, sources='all')
mi_estimator = JidtKraskovMI(settings={})
jidt_mi = mi_estimator.estimate(source, target)
omnibus_mi = results.get_single_target(1, fdr=False).omnibus_mi
print('Estimated omnibus MI: {0:0.6f}, estimated MI using JIDT core '
'estimator: {1:0.6f} (expected: {2:0.6f}).'.format(
omnibus_mi, jidt_mi, expected_mi))
assert np.isclose(omnibus_mi, jidt_mi, rtol=0.05), (
'Zero-lag omnibus MI ({0:0.6f}) differs from JIDT estimate ({1:0.6f}).'
.format(omnibus_mi, jidt_mi))
assert np.isclose(omnibus_mi, expected_mi, rtol=0.05), (
'Zero-lag omnibus MI ({0:0.6f}) differs from expected MI ({1:0.6f}).'.
format(omnibus_mi, expected_mi))
def test_discrete_input():
"""Test multivariate MI estimation from discrete data."""
# Generate Gaussian test data
covariance = 0.4
data = _get_discrete_gauss_data(covariance=covariance,
n=10000,
delay=1,
normalise=False,
seed=SEED)
corr_expected = covariance / (1 * np.sqrt(covariance**2 +
(1 - covariance)**2))
expected_mi = calculate_mi(corr_expected)
settings = {
'cmi_estimator': 'JidtDiscreteCMI',
'discretise_method': 'none',
'n_discrete_bins': 5, # alphabet size of the variables analysed
'n_perm_max_stat': 21,
'n_perm_omnibus': 30,
'n_perm_max_seq': 30,
'min_lag_sources': 1,
'max_lag_sources': 2
}
nw = MultivariateMI()
res = nw.analyse_single_target(settings=settings, data=data, target=1)
assert np.isclose(
res._single_target[1].omnibus_mi, expected_mi, atol=0.05), (
'Estimated MI for discrete variables is not correct. Expected: '
'{0}, Actual results: {1}.'.format(expected_mi,
res['selected_sources_te'][0]))
def test_gauss_data():
"""Test bivariate MI estimation from correlated Gaussians."""
# Generate data and add a delay one one sample.
expected_mi, source, source_uncorr, target = _get_gauss_data()
source = source[1:]
source_uncorr = source_uncorr[1:]
target = target[:-1]
data = Data(np.hstack((source, source_uncorr, target)), dim_order='sp')
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'max_lag_sources': 2,
'min_lag_sources': 1}
nw = MultivariateMI()
results = nw.analyse_single_target(
settings, data, target=2, sources=[0, 1])
mi = results.get_single_target(2, fdr=False)['mi'][0]
sources = results.get_target_sources(2, fdr=False)
# Assert that only the correlated source was detected.
assert len(sources) == 1, 'Wrong no. inferred sources: {0}.'.format(
len(sources))
assert sources[0] == 0, 'Wrong inferred source: {0}.'.format(sources[0])
# Compare BivarateMI() estimate to JIDT estimate.
est = JidtKraskovMI({'lag_mi': 1})
jidt_mi = est.estimate(var1=source, var2=target)
print('Estimated MI: {0:0.6f}, estimated MI using JIDT core estimator: '
'{1:0.6f} (expected: {2:0.6f}).'.format(mi, jidt_mi, expected_mi))
assert np.isclose(mi, jidt_mi, atol=0.005), (
'Estimated MI {0:0.6f} differs from JIDT estimate {1:0.6f} (expected: '
'MI {2:0.6f}).'.format(mi, jidt_mi, expected_mi))
def test_zero_lag():
"""Test analysis for 0 lag."""
covariance = 0.4
n = 10000
source = np.random.normal(0, 1, size=n)
target = (covariance * source + (1 - covariance) *
np.random.normal(0, 1, size=n))
# expected_corr = covariance / (np.sqrt(covariance**2 + (1-covariance)**2))
corr = np.corrcoef(source, target)[0, 1]
expected_mi = -0.5 * np.log(1 - corr**2)
data = Data(np.vstack((source, target)), dim_order='ps', normalise=False)
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'max_lag_sources': 0,
'min_lag_sources': 0}
nw = MultivariateMI()
results = nw.analyse_single_target(
settings, data, target=1, sources='all')
mi_estimator = JidtKraskovMI(settings={})
jidt_mi = mi_estimator.estimate(source, target)
omnibus_mi = results.get_single_target(1, fdr=False).omnibus_mi
print('Estimated omnibus MI: {0:0.6f}, estimated MI using JIDT core '
'estimator: {1:0.6f} (expected: {2:0.6f}).'.format(
omnibus_mi, jidt_mi, expected_mi))
assert np.isclose(omnibus_mi, jidt_mi, rtol=0.05), (
'Zero-lag omnibus MI ({0:0.6f}) differs from JIDT estimate ({1:0.6f}).'.format(
omnibus_mi, jidt_mi))
assert np.isclose(omnibus_mi, expected_mi, rtol=0.05), (
'Zero-lag omnibus MI ({0:0.6f}) differs from expected MI ({1:0.6f}).'.format(
omnibus_mi, expected_mi))
def test_gauss_data():
"""Test multivariate MI estimation from correlated Gaussians."""
# Generate data and add a delay one one sample.
expected_mi, source, source_uncorr, target = _get_gauss_data()
source = source[1:]
source_uncorr = source_uncorr[1:]
target = target[:-1]
data = Data(np.hstack((source, source_uncorr, target)),
dim_order='sp',
normalise=False)
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'max_lag_sources': 2,
'min_lag_sources': 1
}
nw = MultivariateMI()
results = nw.analyse_single_target(settings,
data,
target=2,
sources=[0, 1])
mi = results.get_single_target(2, fdr=False)['mi'][0]
sources = results.get_target_sources(2, fdr=False)
# Assert that only the correlated source was detected.
assert len(sources) == 1, 'Wrong no. inferred sources: {0}.'.format(
len(sources))
assert sources[0] == 0, 'Wrong inferred source: {0}.'.format(sources[0])
# Compare BivarateMI() estimate to JIDT estimate. Mimick realisations used
# internally by the algorithm.
est = JidtKraskovMI({'lag_mi': 0, 'normalise': False})
jidt_mi = est.estimate(var1=source[1:-1], var2=target[2:])
print('Estimated MI: {0:0.6f}, estimated MI using JIDT core estimator: '
'{1:0.6f} (expected: {2:0.6f}).'.format(mi, jidt_mi, expected_mi))
assert np.isclose(mi, jidt_mi, atol=0.005), (
'Estimated MI {0:0.6f} differs from JIDT estimate {1:0.6f} (expected: '
'MI {2:0.6f}).'.format(mi, jidt_mi, expected_mi))
assert np.isclose(mi, expected_mi, atol=0.05), (
'Estimated MI {0:0.6f} differs from expected MI {1:0.6f}.'.format(
mi, expected_mi))
def test_discrete_input():
"""Test multivariate MI estimation from discrete data."""
# Generate Gaussian test data
covariance = 0.4
n = 10000
delay = 1
source = np.random.normal(0, 1, size=n)
target = (covariance * source +
(1 - covariance) * np.random.normal(0, 1, size=n))
corr_expected = covariance / (1 * np.sqrt(covariance**2 +
(1 - covariance)**2))
expected_mi = calculate_mi(corr_expected)
source = source[delay:]
target = target[:-delay]
# Discretise data
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
est = JidtDiscreteCMI(settings)
source_dis, target_dis = est._discretise_vars(var1=source, var2=target)
data = Data(np.vstack((source_dis, target_dis)),
dim_order='ps',
normalise=False)
settings = {
'cmi_estimator': 'JidtDiscreteCMI',
'discretise_method': 'none',
'n_discrete_bins': 5, # alphabet size of the variables analysed
'n_perm_max_stat': 21,
'n_perm_omnibus': 30,
'n_perm_max_seq': 30,
'min_lag_sources': 1,
'max_lag_sources': 2
}
nw = MultivariateMI()
res = nw.analyse_single_target(settings=settings, data=data, target=1)
assert np.isclose(
res._single_target[1].omnibus_mi, expected_mi, atol=0.05), (
'Estimated MI for discrete variables is not correct. Expected: '
'{0}, Actual results: {1}.'.format(expected_mi,
res['selected_sources_te'][0]))
def test_discrete_input():
"""Test multivariate MI estimation from discrete data."""
# Generate Gaussian test data
covariance = 0.4
n = 10000
delay = 1
source = np.random.normal(0, 1, size=n)
target = (covariance * source + (1 - covariance) *
np.random.normal(0, 1, size=n))
corr_expected = covariance / (
1 * np.sqrt(covariance**2 + (1-covariance)**2))
expected_mi = calculate_mi(corr_expected)
source = source[delay:]
target = target[:-delay]
# Discretise data
settings = {'discretise_method': 'equal',
'n_discrete_bins': 5}
est = JidtDiscreteCMI(settings)
source_dis, target_dis = est._discretise_vars(var1=source, var2=target)
data = Data(np.vstack((source_dis, target_dis)),
dim_order='ps', normalise=False)
settings = {
'cmi_estimator': 'JidtDiscreteCMI',
'discretise_method': 'none',
'n_discrete_bins': 5, # alphabet size of the variables analysed
'n_perm_max_stat': 21,
'n_perm_omnibus': 30,
'n_perm_max_seq': 30,
'min_lag_sources': 1,
'max_lag_sources': 2}
nw = MultivariateMI()
res = nw.analyse_single_target(settings=settings, data=data, target=1)
assert np.isclose(
res._single_target[1].omnibus_mi, expected_mi, atol=0.05), (
'Estimated MI for discrete variables is not correct. Expected: '
'{0}, Actual results: {1}.'.format(
expected_mi, res['selected_sources_te'][0]))
def test_return_local_values():
"""Test estimation of local values."""
max_lag = 5
data = Data()
data.generate_mute_data(500, 5)
settings = {
'cmi_estimator': 'JidtKraskovCMI',
'noise_level': 0,
'local_values': True, # request calculation of local values
'n_perm_max_stat': 21,
'n_perm_min_stat': 21,
'n_perm_max_seq': 21,
'n_perm_omnibus': 21,
'max_lag_sources': max_lag,
'min_lag_sources': 4,
'max_lag_target': max_lag
}
target = 3
sources = [0, 4]
mi = MultivariateMI()
results = mi.analyse_single_target(settings,
data,
target=target,
sources=sources)
settings['local_values'] = False
results_avg = mi.analyse_single_target(settings,
data,
target=target,
sources=sources)
# Test if any sources were inferred. If not, return (this may happen
# sometimes due to too few samples, however, a higher no. samples is not
# feasible for a unit test).
if results.get_single_target(target, fdr=False)['mi'] is None:
return
if results_avg.get_single_target(target, fdr=False)['mi'] is None:
return
lmi = results.get_single_target(target, fdr=False)['mi']
n_sources = len(results.get_target_sources(target, fdr=False))
assert type(lmi) is np.ndarray, (
'LMI estimation did not return an array of values: {0}'.format(lmi))
assert lmi.shape[0] == n_sources, (
'Wrong dim (no. sources) in LMI estimate: {0}'.format(lmi.shape))
assert lmi.shape[1] == data.n_realisations_samples(
(0, max_lag)), ('Wrong dim (no. samples) in LMI estimate: {0}'.format(
lmi.shape))
assert lmi.shape[2] == data.n_replications, (
'Wrong dim (no. replications) in LMI estimate: {0}'.format(lmi.shape))
# Check if average and mean local values are the same. Test each source
# separately. Inferred sources and variables may differ between the two
# calls to analyse_single_target() due to low number of surrogates used in
# unit testing.
mi_single_link = results_avg.get_single_target(target, fdr=False)['mi']
sources_local = results.get_target_sources(target, fdr=False)
sources_avg = results_avg.get_target_sources(target, fdr=False)
for s in list(set(sources_avg).intersection(sources_local)):
i1 = np.where(sources_avg == s)[0][0]
i2 = np.where(sources_local == s)[0][0]
# Skip comparison if inferred variables differ between links.
vars_local = [
v for v in results.get_single_target(
target, fdr=False).selected_vars_sources if v[0] == s
]
vars_avg = [
v for v in results_avg.get_single_target(
target, fdr=False).selected_vars_sources if v[0] == s
]
if vars_local != vars_avg:
continue
print('Compare average ({0:.4f}) and local values ({1:.4f}).'.format(
mi_single_link[i1], np.mean(lmi[i2, :, :])))
assert np.isclose(
mi_single_link[i1], np.mean(lmi[i2, :, :]), rtol=0.00005), (
'Single link average MI ({0:.6f}) and mean LMI ({1:.6f}) '
' deviate.'.format(mi_single_link[i1], np.mean(lmi[i2, :, :])))
def test_multivariate_mi_init():
"""Test instance creation for MultivariateMI class."""
# Test error on missing estimator
settings = {
'n_perm_max_stat': 21,
'n_perm_omnibus': 30,
'max_lag_sources': 7,
'min_lag_sources': 2
}
nw = MultivariateMI()
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=Data(), target=1)
# Test setting of min and max lags
settings['cmi_estimator'] = 'JidtKraskovCMI'
data = Data()
data.generate_mute_data(n_samples=10, n_replications=5)
# Invalid: min lag sources bigger than max lag
settings['min_lag_sources'] = 8
settings['max_lag_sources'] = 7
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: tau bigger than lags
settings['min_lag_sources'] = 2
settings['max_lag_sources'] = 4
settings['tau_sources'] = 10
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: negative lags or taus
settings['tau_sources'] = 1
settings['min_lag_sources'] = 1
settings['max_lag_sources'] = -7
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['max_lag_sources'] = 7
settings['min_lag_sources'] = -4
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['min_lag_sources'] = 4
settings['tau_sources'] = -1
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: lags or taus are no integers
settings['min_lag_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['min_lag_sources'] = 1
settings['max_lag_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['max_lag_sources'] = 7
settings['tau_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: sources or target is no int
with pytest.raises(RuntimeError): # no int
nw.analyse_single_target(settings=settings, data=data, target=1.5)
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings, data=data, target=-1)
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings, data=data, target=10)
with pytest.raises(RuntimeError): # wrong type
nw.analyse_single_target(settings=settings, data=data, target={})
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings,
data=data,
target=0,
sources=-1)
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings,
data=data,
target=0,
sources=[-1])
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings,
data=data,
target=0,
sources=20)
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings,
data=data,
target=0,
sources=[20])
def test_multivariate_mi_init():
"""Test instance creation for MultivariateMI class."""
# Test error on missing estimator
settings = {
'n_perm_max_stat': 21,
'n_perm_omnibus': 30,
'max_lag_sources': 7,
'min_lag_sources': 2}
nw = MultivariateMI()
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=Data(), target=1)
# Test setting of min and max lags
settings['cmi_estimator'] = 'JidtKraskovCMI'
data = Data()
data.generate_mute_data(n_samples=10, n_replications=5)
# Invalid: min lag sources bigger than max lag
settings['min_lag_sources'] = 8
settings['max_lag_sources'] = 7
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: tau bigger than lags
settings['min_lag_sources'] = 2
settings['max_lag_sources'] = 4
settings['tau_sources'] = 10
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: negative lags or taus
settings['tau_sources'] = 1
settings['min_lag_sources'] = 1
settings['max_lag_sources'] = -7
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['max_lag_sources'] = 7
settings['min_lag_sources'] = -4
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['min_lag_sources'] = 4
settings['tau_sources'] = -1
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: lags or taus are no integers
settings['min_lag_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['min_lag_sources'] = 1
settings['max_lag_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
settings['max_lag_sources'] = 7
settings['tau_sources'] = 1.5
with pytest.raises(RuntimeError):
nw.analyse_single_target(settings=settings, data=data, target=1)
# Invalid: sources or target is no int
with pytest.raises(RuntimeError): # no int
nw.analyse_single_target(settings=settings, data=data, target=1.5)
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings, data=data, target=-1)
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings, data=data, target=10)
with pytest.raises(RuntimeError): # wrong type
nw.analyse_single_target(settings=settings, data=data, target={})
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings, data=data, target=0,
sources=-1)
with pytest.raises(RuntimeError): # negative
nw.analyse_single_target(settings=settings, data=data, target=0,
sources=[-1])
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings, data=data, target=0,
sources=20)
with pytest.raises(RuntimeError): # not in data
nw.analyse_single_target(settings=settings, data=data, target=0,
sources=[20])
