def test_cmi_uncorrelated_gaussians_three_dims():
"""Test CMI estimator on uncorrelated 3D Gaussian data."""
n_obs = 10000
dim = 3
np.random.seed(SEED)
var1 = np.random.randn(n_obs, dim)
var2 = np.random.randn(n_obs, dim)
var3 = np.random.randn(n_obs, dim)
# Run OpenCL estimator.
settings = {'debug': True, 'return_counts': True}
ocl_est = OpenCLKraskovCMI(settings=settings)
mi_ocl, dist, n_range_var1, n_range_var2 = ocl_est.estimate(var1, var2)
mi_ocl = mi_ocl[0]
# Run JIDT estimator.
jidt_est = JidtKraskovCMI(settings={})
mi_jidt = jidt_est.estimate(var1, var2)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to 0 nats for uncorrelated '
'Gaussians.'.format(mi_jidt, mi_ocl))
assert np.isclose(
mi_jidt, 0,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, 0,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, mi_jidt,
atol=0.0001), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
# Run with conditional
(mi_ocl, dist, n_range_var1, n_range_var2,
n_range_var3) = ocl_est.estimate(var1, var2, var3)
mi_ocl = mi_ocl[0]
mi_jidt = jidt_est.estimate(var1, var2, var3)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to 0 nats for uncorrelated '
'Gaussians.'.format(mi_jidt, mi_ocl))
assert np.isclose(
mi_jidt, 0,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, 0,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, mi_jidt,
atol=0.0001), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_cmi_uncorrelated_gaussians_three_dims():
"""Test CMI estimator on uncorrelated 3D Gaussian data."""
n_obs = 10000
dim = 3
var1 = np.random.randn(n_obs, dim)
var2 = np.random.randn(n_obs, dim)
var3 = np.random.randn(n_obs, dim)
# Run OpenCL estimator.
settings = {'debug': True}
ocl_est = OpenCLKraskovCMI(settings=settings)
mi_ocl, dist, n_range_var1, n_range_var2 = ocl_est.estimate(var1, var2)
mi_ocl = mi_ocl[0]
# Run JIDT estimator.
jidt_est = JidtKraskovCMI(settings={})
mi_jidt = jidt_est.estimate(var1, var2)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to 0 nats for uncorrelated '
'Gaussians.'.format(mi_jidt, mi_ocl))
assert np.isclose(mi_jidt, 0, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, 0, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, mi_jidt, atol=0.0001), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
# Run with conditional
(mi_ocl, dist, n_range_var1,
n_range_var2, n_range_var3) = ocl_est.estimate(var1, var2, var3)
mi_ocl = mi_ocl[0]
mi_jidt = jidt_est.estimate(var1, var2, var3)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to 0 nats for uncorrelated '
'Gaussians.'.format(mi_jidt, mi_ocl))
assert np.isclose(mi_jidt, 0, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, 0, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, mi_jidt, atol=0.0001), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_cmi_correlated_gaussians():
"""Test estimators on correlated Gaussian data with conditional."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
# Run OpenCL estimator.
settings = {'debug': True, 'return_counts': True}
ocl_est = OpenCLKraskovCMI(settings=settings)
(mi_ocl, dist, n_range_var1, n_range_var2,
n_range_cond) = ocl_est.estimate(source, target, source_uncorr)
mi_ocl = mi_ocl[0]
# Run JIDT estimator.
jidt_est = JidtKraskovCMI(settings={})
mi_jidt = jidt_est.estimate(source, target, source_uncorr)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to {2:.4f} nats for correlated '
'Gaussians.'.format(mi_jidt, mi_ocl, expected_mi))
assert np.isclose(
mi_jidt, expected_mi,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, expected_mi,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl, mi_jidt,
atol=0.0001), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_cmi_no_cond_correlated_gaussians():
"""Test estimators on correlated Gaussian data without conditional."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
# Run OpenCL estimator.
settings = {'debug': True}
ocl_est = OpenCLKraskovCMI(settings=settings)
mi_ocl, dist, n_range_var1, n_range_var2 = ocl_est.estimate(source, target)
mi_ocl = mi_ocl[0]
# Run JIDT estimator.
jidt_est = JidtKraskovCMI(settings={})
mi_jidt = jidt_est.estimate(source, target)
cov_effective = np.cov(np.squeeze(source), np.squeeze(target))[1, 0]
expected_mi = math.log(1 / (1 - math.pow(cov_effective, 2)))
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to {2:.4f} nats for correlated '
'Gaussians.'.format(mi_jidt, mi_ocl, expected_mi))
assert np.isclose(mi_jidt, expected_mi, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, expected_mi, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, mi_jidt, atol=0.0001), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_cmi_correlated_gaussians():
"""Test estimators on correlated Gaussian data with conditional."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
# Run OpenCL estimator.
settings = {'debug': True}
ocl_est = OpenCLKraskovCMI(settings=settings)
(mi_ocl, dist, n_range_var1,
n_range_var2, n_range_cond) = ocl_est.estimate(source, target,
source_uncorr)
mi_ocl = mi_ocl[0]
# Run JIDT estimator.
jidt_est = JidtKraskovCMI(settings={})
mi_jidt = jidt_est.estimate(source, target, source_uncorr)
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: {1:.4f} nats; '
'expected to be close to {2:.4f} nats for correlated '
'Gaussians.'.format(mi_jidt, mi_ocl, expected_mi))
assert np.isclose(mi_jidt, expected_mi, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'JIDT estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, expected_mi, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl, mi_jidt, atol=0.0001), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_cmi_gauss_data():
"""Test CMI estimation on two sets of Gaussian random data.
The first test is on correlated variables, the second on uncorrelated
variables.
Note that the calculation is based on a random variable (because the
generated data is a set of random variables) - the result will be of the
order of what we expect, but not exactly equal to it; in fact, there will
be a large variance around it.
"""
expected_mi, source1, source2, target = _get_gauss_data()
# Test Kraskov
mi_estimator = JidtKraskovCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtKraskovCMI', 'CMI (uncorr.)')
# Test Gaussian
mi_estimator = JidtGaussianCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtGaussianCMI', 'CMI (uncorr.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'num_discrete_bins': 5}
mi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtDiscreteCMI', 'CMI (uncorr.)')
def test_cmi_gauss_data_no_cond():
"""Test estimators on correlated Gauss data without a conditional.
The estimators should return the MI if no conditional variable is
provided.
Note that the calculation is based on a random variable (because the
generated data is a set of random variables) - the result will be of the
order of what we expect, but not exactly equal to it; in fact, there will
be a large variance around it.
"""
expected_mi, source1, source2, target = _get_gauss_data()
# Test Kraskov
mi_estimator = JidtKraskovCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtKraskovCMI', 'CMI (uncorr., no cond.)')
# Test Gaussian
mi_estimator = JidtGaussianCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtGaussianCMI', 'CMI (uncorr., no cond.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'num_discrete_bins': 5}
mi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtDiscreteCMI', 'CMI (uncorr., no cond.)')
def test_cmi_gauss_data():
"""Test CMI estimation on two sets of Gaussian random data.
The first test is on correlated variables, the second on uncorrelated
variables.
Note that the calculation is based on a random variable (because the
generated data is a set of random variables) - the result will be of the
order of what we expect, but not exactly equal to it; in fact, there will
be a large variance around it.
"""
expected_mi, source1, source2, target = _get_gauss_data()
# Test Kraskov
mi_estimator = JidtKraskovCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtKraskovCMI', 'CMI (uncorr.)')
# Test Gaussian
mi_estimator = JidtGaussianCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtGaussianCMI', 'CMI (uncorr.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
mi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteCMI', 'CMI (corr.)')
_assert_result(mi_uncor, 0, 'JidtDiscreteCMI', 'CMI (uncorr.)')
def test_cmi_gauss_data_no_cond():
"""Test estimators on correlated Gauss data without a conditional.
The estimators should return the MI if no conditional variable is
provided.
Note that the calculation is based on a random variable (because the
generated data is a set of random variables) - the result will be of the
order of what we expect, but not exactly equal to it; in fact, there will
be a large variance around it.
"""
expected_mi, source1, source2, target = _get_gauss_data()
# Test Kraskov
mi_estimator = JidtKraskovCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtKraskovCMI', 'CMI (uncorr., no cond.)')
# Test Gaussian
mi_estimator = JidtGaussianCMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtGaussianCMI', 'CMI (uncorr., no cond.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
mi_estimator = JidtDiscreteCMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteCMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtDiscreteCMI', 'CMI (uncorr., no cond.)')
def test_one_two_dim_input_kraskov():
"""Test one- and two-dimensional input for Kraskov 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)
# MI
mi_estimator = JidtKraskovMI(settings={})
mi_cor_one = mi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovMI', 'MI')
mi_cor_two = mi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovMI', 'MI')
_compare_result(mi_cor_one, mi_cor_two,
'JidtKraskovMI one dim', 'JidtKraskovMI two dim', 'MI')
# CMI
cmi_estimator = JidtKraskovCMI(settings={})
mi_cor_one = cmi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovCMI', 'CMI')
mi_cor_two = cmi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovCMI', 'CMI')
_compare_result(mi_cor_one, mi_cor_two,
'JidtKraskovMI one dim', 'JidtKraskovMI two dim', 'CMI')
# TE
te_estimator = JidtKraskovTE(settings={'history_target': 1})
mi_cor_one = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovTE', 'TE')
mi_cor_two = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovTE', 'TE')
_compare_result(mi_cor_one, mi_cor_two,
'JidtKraskovMI one dim', 'JidtKraskovMI two dim', 'TE')
# AIS
ais_estimator = JidtKraskovAIS(settings={'history': 2})
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,
'JidtKraskovAIS one dim', 'JidtKraskovAIS two dim',
'AIS (AR process)')
def test_one_two_dim_input_kraskov():
"""Test one- and two-dimensional input for Kraskov 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)
# MI
mi_estimator = JidtKraskovMI(settings={})
mi_cor_one = mi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovMI', 'MI')
mi_cor_two = mi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovMI', 'MI')
_compare_result(mi_cor_one, mi_cor_two, 'JidtKraskovMI one dim',
'JidtKraskovMI two dim', 'MI')
# CMI
cmi_estimator = JidtKraskovCMI(settings={})
mi_cor_one = cmi_estimator.estimate(src_one, target_one)
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovCMI', 'CMI')
mi_cor_two = cmi_estimator.estimate(src_two, target_two)
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovCMI', 'CMI')
_compare_result(mi_cor_one, mi_cor_two, 'JidtKraskovMI one dim',
'JidtKraskovMI two dim', 'CMI')
# TE
te_estimator = JidtKraskovTE(settings={'history_target': 1})
mi_cor_one = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_one, expected_mi, 'JidtKraskovTE', 'TE')
mi_cor_two = te_estimator.estimate(src_one[1:], target_one[:-1])
_assert_result(mi_cor_two, expected_mi, 'JidtKraskovTE', 'TE')
_compare_result(mi_cor_one, mi_cor_two, 'JidtKraskovMI one dim',
'JidtKraskovMI two dim', 'TE')
# AIS
ais_estimator = JidtKraskovAIS(settings={'history': 2})
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, 'JidtKraskovAIS one dim',
'JidtKraskovAIS two dim', 'AIS (AR process)')
def test_gauss_data():
"""Test bivariate TE 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,
'max_lag_target': 1
}
nw = BivariateTE()
results = nw.analyse_single_target(settings,
data,
target=2,
sources=[0, 1])
te = results.get_single_target(2, fdr=False)['te'][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 BivarateTE() estimate to JIDT estimate.
current_value = (2, 2)
source_vars = results.get_single_target(2, False)['selected_vars_sources']
target_vars = results.get_single_target(2, False)['selected_vars_target']
var1 = data.get_realisations(current_value, source_vars)[0]
var2 = data.get_realisations(current_value, [current_value])[0]
cond = data.get_realisations(current_value, target_vars)[0]
est = JidtKraskovCMI({})
jidt_cmi = est.estimate(var1=var1, var2=var2, conditional=cond)
print('Estimated TE: {0:0.6f}, estimated TE using JIDT core estimator: '
'{1:0.6f} (expected: {2:0.6f}).'.format(te, jidt_cmi, expected_mi))
assert np.isclose(te, jidt_cmi, atol=0.005), (
'Estimated TE {0:0.6f} differs from JIDT estimate {1:0.6f} (expected: '
'TE {2:0.6f}).'.format(te, jidt_cmi, expected_mi))
def test_gauss_data():
"""Test bivariate TE 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,
'max_lag_target': 1}
nw = BivariateTE()
results = nw.analyse_single_target(
settings, data, target=2, sources=[0, 1])
te = results.get_single_target(2, fdr=False)['te'][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 BivarateTE() estimate to JIDT estimate.
current_value = (2, 2)
source_vars = results.get_single_target(2, False)['selected_vars_sources']
target_vars = results.get_single_target(2, False)['selected_vars_target']
var1 = data.get_realisations(current_value, source_vars)[0]
var2 = data.get_realisations(current_value, [current_value])[0]
cond = data.get_realisations(current_value, target_vars)[0]
est = JidtKraskovCMI({})
jidt_cmi = est.estimate(var1=var1, var2=var2, conditional=cond)
print('Estimated TE: {0:0.6f}, estimated TE using JIDT core estimator: '
'{1:0.6f} (expected: {2:0.6f}).'.format(te, jidt_cmi, expected_mi))
assert np.isclose(te, jidt_cmi, atol=0.005), (
'Estimated TE {0:0.6f} differs from JIDT estimate {1:0.6f} (expected: '
'TE {2:0.6f}).'.format(te, jidt_cmi, expected_mi))
from idtxl.multivariate_te import MultivariateTE
from idtxl.data import Data
## Use IDTxl's core esitmator if lags/embeddings are known
# Generate high-dimensional example processes
n = 1000
source_dim = 3
cond_dim = 2
target = np.random.randn(n)
source = np.random.randn(n, source_dim)
conditional = np.random.randn(n, cond_dim)
settings = {}
est = JidtKraskovCMI(settings)
cmi = est.estimate(source, target, conditional)
print(f'CMI estimate: {cmi:.4f}')
## Use IDTxl's network inference algorithm to optimize lags/embeddings
# Generate test data, we assume that the processes represent sources, a target,
# and additional processes, we want to condition on. For the conditioning, we
# have to provide tuples of past variables plus a lag.
data = Data(np.random.randn(5, n), dim_order='ps')
target = 0
sources = [1, 2]
cond_1_ind = 3
cond_2_ind = 4
cond_1_lag = 1
cond_2_lag = 1
