def test_one_two_dim_input_discrete():
"""Test one- and two-dimensional input for discrete estimators."""
expected_mi, src_one, s, target_one = _get_gauss_data(expand=False,
seed=SEED)
src_two = np.expand_dims(src_one, axis=1)
target_two = np.expand_dims(target_one, axis=1)
ar_src_one, s = _get_ar_data(expand=False, seed=SEED)
ar_src_two = np.expand_dims(ar_src_one, axis=1)
settings = {
'discretise_method': 'equal',
'n_discrete_bins': 4,
'history_target': 1,
'history': 2
}
# MI
mi_estimator = JidtDiscreteMI(settings=settings)
mi_cor_one = mi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteMI', 'MI',
0.08) # More variability here
mi_cor_two = mi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteMI', 'MI',
0.08) # More variability here
_compare_result(mi_cor_one, mi_cor_two, 'JidtDiscreteMI one dim',
'JidtDiscreteMI two dim', 'MI')
# CMI
cmi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor_one = cmi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteCMI', 'CMI',
0.08) # More variability here
mi_cor_two = cmi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteCMI', 'CMI',
0.08) # More variability here
_compare_result(mi_cor_one, mi_cor_two, 'JidtDiscreteMI one dim',
'JidtDiscreteMI two dim', 'CMI')
# TE
te_estimator = JidtDiscreteTE(settings=settings)
mi_cor_one = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteTE', 'TE',
0.08) # More variability here
mi_cor_two = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteTE', 'TE',
0.08) # More variability here
_compare_result(mi_cor_one, mi_cor_two, 'JidtDiscreteMI one dim',
'JidtDiscreteMI two dim', 'TE')
# AIS
ais_estimator = JidtDiscreteAIS(settings=settings)
mi_cor_one = ais_estimator.estimate(ar_src_one)
mi_cor_two = ais_estimator.estimate(ar_src_two)
_compare_result(mi_cor_one, mi_cor_two, 'JidtDiscreteAIS one dim',
'JidtDiscreteAIS two dim', 'AIS (AR process)')
def test_one_two_dim_input_discrete():
"""Test one- and two-dimensional input for discrete estimators."""
expected_mi, src_one, s, target_one = _get_gauss_data(expand=False)
src_two = np.expand_dims(src_one, axis=1)
target_two = np.expand_dims(target_one, axis=1)
ar_src_one, s = _get_ar_data(expand=False)
ar_src_two = np.expand_dims(ar_src_one, axis=1)
settings = {'discretise_method': 'equal',
'n_discrete_bins': 4,
'history_target': 1,
'history': 2}
# MI
mi_estimator = JidtDiscreteMI(settings=settings)
mi_cor_one = mi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteMI', 'MI')
mi_cor_two = mi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteMI', 'MI')
_compare_result(mi_cor_one, mi_cor_two,
'JidtDiscreteMI one dim', 'JidtDiscreteMI two dim', 'MI')
# CMI
cmi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor_one = cmi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteCMI', 'CMI')
mi_cor_two = cmi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteCMI', 'CMI')
_compare_result(mi_cor_one, mi_cor_two,
'JidtDiscreteMI one dim', 'JidtDiscreteMI two dim', 'CMI')
# TE
te_estimator = JidtDiscreteTE(settings=settings)
mi_cor_one = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_one, expected_mi, 'JidtDiscreteTE', 'TE')
mi_cor_two = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_two, expected_mi, 'JidtDiscreteTE', 'TE')
_compare_result(mi_cor_one, mi_cor_two,
'JidtDiscreteMI one dim', 'JidtDiscreteMI two dim', 'TE')
# AIS
ais_estimator = JidtDiscreteAIS(settings=settings)
mi_cor_one = ais_estimator.estimate(ar_src_one)
mi_cor_two = ais_estimator.estimate(ar_src_two)
_compare_result(mi_cor_one, mi_cor_two,
'JidtDiscreteAIS one dim', 'JidtDiscreteAIS two dim',
'AIS (AR process)')
def test_local_values():
"""Test estimation of local values and their return type."""
expected_mi, source, s, target = _get_gauss_data(expand=False)
ar_proc, s = _get_ar_data(expand=False)
settings = {
'discretise_method': 'equal',
'n_discrete_bins': 4,
'history_target': 1,
'history': 2,
'local_values': True
}
# MI - Discrete
mi_estimator = JidtDiscreteMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteMI', 'MI',
0.08) # More variability here
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Gaussian
mi_estimator = JidtGaussianMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Kraskov
mi_estimator = JidtKraskovMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# CMI - Discrete
cmi_estimator = JidtDiscreteCMI(settings=settings)
mi = cmi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteCMI', 'CMI',
0.08) # More variability here
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Gaussian
mi_estimator = JidtGaussianCMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianCMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Kraskov
mi_estimator = JidtKraskovCMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovCMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Discrete
te_estimator = JidtDiscreteTE(settings=settings)
mi = te_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteTE', 'TE',
0.08) # More variability here
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Gaussian
mi_estimator = JidtGaussianTE(settings=settings)
mi = mi_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianTE', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Kraskov
mi_estimator = JidtKraskovTE(settings=settings)
mi = mi_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovTE', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# AIS - Kraskov
ais_estimator = JidtKraskovAIS(settings=settings)
mi_k = ais_estimator.estimate(ar_proc)
assert type(mi_k) is np.ndarray, 'Local values are not a numpy array.'
# AIS - Discrete
ais_estimator = JidtDiscreteAIS(settings=settings)
mi_d = ais_estimator.estimate(ar_proc)
assert type(mi_d) is np.ndarray, 'Local values are not a numpy array.'
# TODO should we compare these?
# _compare_result(np.mean(mi_k), np.mean(mi_d),
# 'JidtKraskovAIS', 'JidtDiscreteAIS', 'AIS (AR process)')
# AIS - Gaussian
ais_estimator = JidtGaussianAIS(settings=settings)
mi_g = ais_estimator.estimate(ar_proc)
assert type(mi_g) is np.ndarray, 'Local values are not a numpy array.'
_compare_result(np.mean(mi_k), np.mean(mi_g), 'JidtKraskovAIS',
'JidtGaussianAIS', 'AIS (AR process)')
def test_local_values():
"""Test estimation of local values and their return type."""
expected_mi, source, s, target = _get_gauss_data(expand=False)
ar_proc, s = _get_ar_data(expand=False)
settings = {'discretise_method': 'equal',
'n_discrete_bins': 4,
'history_target': 1,
'history': 2,
'local_values': True}
# MI - Discrete
mi_estimator = JidtDiscreteMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Gaussian
mi_estimator = JidtGaussianMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Kraskov
mi_estimator = JidtKraskovMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# CMI - Discrete
cmi_estimator = JidtDiscreteCMI(settings=settings)
mi = cmi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteCMI', 'CMI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Gaussian
mi_estimator = JidtGaussianCMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianCMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# MI - Kraskov
mi_estimator = JidtKraskovCMI(settings=settings)
mi = mi_estimator.estimate(source, target)
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovCMI', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Discrete
te_estimator = JidtDiscreteTE(settings=settings)
mi = te_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtDiscreteTE', 'TE')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Gaussian
mi_estimator = JidtGaussianTE(settings=settings)
mi = mi_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtGaussianTE', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# TE - Kraskov
mi_estimator = JidtKraskovTE(settings=settings)
mi = mi_estimator.estimate(source[1:], target[:-1])
_assert_result(np.mean(mi), expected_mi, 'JidtKraskovTE', 'MI')
assert type(mi) is np.ndarray, 'Local values are not a numpy array.'
# AIS - Kraskov
ais_estimator = JidtKraskovAIS(settings=settings)
mi_k = ais_estimator.estimate(ar_proc)
assert type(mi_k) is np.ndarray, 'Local values are not a numpy array.'
# AIS - Discrete
ais_estimator = JidtDiscreteAIS(settings=settings)
mi_d = ais_estimator.estimate(ar_proc)
assert type(mi_d) is np.ndarray, 'Local values are not a numpy array.'
# TODO should we compare these?
# _compare_result(np.mean(mi_k), np.mean(mi_d),
# 'JidtKraskovAIS', 'JidtDiscreteAIS', 'AIS (AR process)')
# AIS - Gaussian
ais_estimator = JidtGaussianAIS(settings=settings)
mi_g = ais_estimator.estimate(ar_proc)
assert type(mi_g) is np.ndarray, 'Local values are not a numpy array.'
_compare_result(np.mean(mi_k), np.mean(mi_g),
'JidtKraskovAIS', 'JidtGaussianAIS', 'AIS (AR process)')
from idtxl.idtxl_utils import calculate_mi
# Generate Gaussian test data
n = 10000
covariance = 0.4
corr_expected = covariance / (1 * np.sqrt(covariance**2 + (1-covariance)**2))
expected_mi = calculate_mi(corr_expected)
source_cor = np.random.normal(0, 1, size=n) # correlated src
source_uncor = np.random.normal(0, 1, size=n) # uncorrelated src
target = (covariance * source_cor +
(1 - covariance) * np.random.normal(0, 1, size=n))
# JIDT Discrete estimators
settings = {'discretise_method': 'equal', 'alph1': 5, 'alph2': 5}
est = JidtDiscreteCMI(settings)
cmi = est.estimate(source_cor, target, source_uncor)
print('Estimated CMI: {0:.5f}, expected CMI: {1:.5f}'.format(cmi, expected_mi))
est = JidtDiscreteMI(settings)
mi = est.estimate(source_cor, target)
print('Estimated MI: {0:.5f}, expected MI: {1:.5f}'.format(mi, expected_mi))
settings['history_target'] = 1
est = JidtDiscreteTE(settings)
te = est.estimate(source_cor[1:n], target[0:n - 1])
print('Estimated TE: {0:.5f}, expected TE: {1:.5f}'.format(te, expected_mi))
settings['history'] = 1
est = JidtDiscreteAIS(settings)
ais = est.estimate(target)
print('Estimated AIS: {0:.5f}, expected AIS: ~0'.format(ais))
# JIDT Kraskov estimators
settings = {}
from idtxl.multivariate_te import MultivariateTE
# 1 Use core esimtators with data discretisation. Generate Gaussian test data
# and call JIDT Discrete estimators using the build-in discretization.
n = 1000
covariance = 0.4
corr_expected = covariance / (1 * np.sqrt(covariance**2 + (1 - covariance)**2))
expected_mi = calculate_mi(corr_expected)
source_cor = np.random.normal(0, 1, size=n) # correlated src
source_uncor = np.random.normal(0, 1, size=n) # uncorrelated src
target = (covariance * source_cor +
(1 - covariance) * np.random.normal(0, 1, size=n))
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
est = JidtDiscreteCMI(settings)
cmi = est.estimate(source_cor, target, source_uncor)
print('Estimated CMI: {0:.5f}, expected CMI: {1:.5f}'.format(cmi, expected_mi))
settings['history_target'] = 1
est = JidtDiscreteTE(settings)
te = est.estimate(source_cor[1:n], target[0:n - 1])
print('Estimated TE: {0:.5f}, expected TE: {1:.5f}'.format(te, expected_mi))
# 2 Use network inference algorithms on discrete data.
n_procs = 5
alphabet_size = 5
data = Data(np.random.randint(0, alphabet_size, size=(n, n_procs)),
dim_order='sp',
normalise=False) # don't normalize discrete data
# Initialise analysis object and define settings
network_analysis = MultivariateTE()