def test_mi_correlated_gaussians():
"""Test estimators on correlated Gaussian data."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
# Run OpenCL estimator.
settings = {'debug': True}
ocl_est = OpenCLKraskovMI(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 = JidtKraskovMI(settings={})
mi_jidt = jidt_est.estimate(source, target)
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_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_mi_uncorrelated_gaussians_three_dims():
"""Test MI 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)
# Run OpenCL estimator.
settings = {'debug': True}
ocl_est = OpenCLKraskovMI(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 = JidtKraskovMI(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).')
def test_mi_uncorrelated_gaussians_three_dims():
"""Test MI 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)
# Run OpenCL estimator.
settings = {'debug': True, 'return_counts': True}
ocl_est = OpenCLKraskovMI(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 = JidtKraskovMI(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).')
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_lagged_mi():
"""Test estimation of lagged MI."""
n = 10000
cov = 0.4
source = [rn.normalvariate(0, 1) for r in range(n)]
target = [0] + [sum(pair) for pair in zip(
[cov * y for y in source[0:n - 1]],
[(1 - cov) * y for y in
[rn.normalvariate(0, 1) for r in range(n - 1)]])]
source = np.array(source)
target = np.array(target)
settings = {
'discretise_method': 'equal',
'n_discrete_bins': 4,
'history': 1,
'history_target': 1,
'lag_mi': 1,
'source_target_delay': 1}
est_te_k = JidtKraskovTE(settings)
te_k = est_te_k.estimate(source, target)
est_te_d = JidtDiscreteTE(settings)
te_d = est_te_d.estimate(source, target)
est_d = JidtDiscreteMI(settings)
mi_d = est_d.estimate(source, target)
est_k = JidtKraskovMI(settings)
mi_k = est_k.estimate(source, target)
est_g = JidtGaussianMI(settings)
mi_g = est_g.estimate(source, target)
_compare_result(mi_d, te_d, 'JidtDiscreteMI', 'JidtDiscreteTE',
'lagged MI', tol=0.05)
_compare_result(mi_k, te_k, 'JidtKraskovMI', 'JidtKraskovTE',
'lagged MI', tol=0.05)
_compare_result(mi_g, te_k, 'JidtGaussianMI', 'JidtKraskovTE',
'lagged MI', tol=0.05)
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_mi_correlated_gaussians():
"""Test estimators on correlated Gaussian data."""
expected_mi, source, source_uncorr, target = _get_gauss_data()
# Run OpenCL estimator.
settings = {'debug': True, 'return_counts': True}
ocl_est = OpenCLKraskovMI(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 = JidtKraskovMI(settings={})
mi_jidt = jidt_est.estimate(source, target)
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_jidt_kraskov_alg1And2():
""" Test that JIDT estimate changes properly when we change KSG algorithm """
n = 100
source = [
sum(pair)
for pair in zip([y for y in range(n)],
[rn.normalvariate(0, 0.000001) for r in range(n)])
]
source = np.array(source)
target = np.array(source) # Target copies source on purpose
# We've generated simple data 0:99, plus a little noise to ensure
# we only even get K nearest neighbours in each space.
# So result should be:
settings = {'lag': 0, 'kraskov_k': 4, 'noise_level': 0, 'algorithm_num': 1}
for k in range(4, 16):
settings['kraskov_k'] = k
settings['algorithm_num'] = 1
est1 = JidtKraskovMI(settings)
mi_alg1 = est1.estimate(source, target)
# Neighbour counts n_x and n_y will be k-1 because they are
# *strictly* within the boundary
expected_alg1 = digamma(k) - 2 * digamma((k - 1) + 1) + digamma(n)
_compare_result(mi_alg1,
expected_alg1,
'JidtDiscreteMI_alg1',
'Analytic',
'MI',
tol=0.00001)
settings['algorithm_num'] = 2
est2 = JidtKraskovMI(settings)
mi_alg2 = est2.estimate(source, target)
expected_alg2 = digamma(k) - 1 / k - 2 * digamma(k) + digamma(n)
_compare_result(mi_alg2,
expected_alg2,
'JidtDiscreteMI_alg2',
'Analytic',
'MI',
tol=0.00001)
# And now check that it doesn't work for algorithm "3"
settings['algorithm_num'] = 3
caughtAssertionError = False
try:
est3 = JidtKraskovMI(settings)
except AssertionError:
caughtAssertionError = True
assert caughtAssertionError, 'Assertion error not raised for KSG algorithm 3 request'
def test_estimate_parallel():
"""Test estimate_parallel() against estimate()."""
expected_mi, source1, source2, target = _get_gauss_data()
source_chunks = np.vstack((source1, source1))
target_chunks = np.vstack((target, target))
# Compare MI-estimates from serial and parallel estimator.
mi_estimator = JidtKraskovMI(settings={'noise_level': 0})
mi = mi_estimator.estimate(source1, target)
with pytest.raises(AssertionError):
mi_estimator.estimate_parallel(
n_chunks=2,
var1=source_chunks,
var2=target)
mi_parallel1 = mi_estimator.estimate_parallel(
n_chunks=2,
re_use=['var2'],
var1=source_chunks,
var2=target)
mi_parallel2 = mi_estimator.estimate_parallel(
n_chunks=2,
var1=source_chunks,
var2=target_chunks)
assert (mi_parallel1 == mi_parallel2).all(), (
'Results for stacked ({0}) and re-used ({1}) target differ.'.format(
mi_parallel1, mi_parallel2))
assert mi_parallel1[0] == mi, (
'Results for first chunk differ from serial estimate.')
assert mi_parallel1[1] == mi, (
'Results for second chunk differ from serial estimate.')
assert np.isclose(mi, expected_mi, rtol=0.05), (
'Estimated ({0}) and expected ({1}) MI differ.'.format(
mi, expected_mi))
# Check if a single chunk is returned if all variables are defined as
# reusable.
mi_parallel3 = mi_estimator.estimate_parallel(
n_chunks=2,
re_use=['var1', 'var2'],
var1=source1,
var2=target)
assert len(mi_parallel3) == 1, (
'Single chunk data returned more than one estimate.')
assert np.isclose(mi_parallel3[0], expected_mi, rtol=0.05), (
'Estimated ({0}) and expected ({1}) MI differ.'.format(
mi_parallel3[0], expected_mi))
# Check assertion for incorrect number of samples in data to be reused in
# parallel estimator.
with pytest.raises(AssertionError):
mi_estimator.estimate_parallel(
n_chunks=2,
re_use=['var2'],
var1=source_chunks,
var2=target[:100])
def test_estimate_parallel():
"""Test estimate_parallel() against estimate()."""
expected_mi, source1, source2, target = _get_gauss_data()
source_chunks = np.vstack((source1, source1))
target_chunks = np.vstack((target, target))
# Compare MI-estimates from serial and parallel estimator.
mi_estimator = JidtKraskovMI(settings={'noise_level': 0})
mi = mi_estimator.estimate(source1, target)
with pytest.raises(AssertionError):
mi_estimator.estimate_parallel(n_chunks=2,
var1=source_chunks,
var2=target)
mi_parallel1 = mi_estimator.estimate_parallel(n_chunks=2,
re_use=['var2'],
var1=source_chunks,
var2=target)
mi_parallel2 = mi_estimator.estimate_parallel(n_chunks=2,
var1=source_chunks,
var2=target_chunks)
assert (mi_parallel1 == mi_parallel2).all(), (
'Results for stacked ({0}) and re-used ({1}) target differ.'.format(
mi_parallel1, mi_parallel2))
assert mi_parallel1[0] == mi, (
'Results for first chunk differ from serial estimate.')
assert mi_parallel1[1] == mi, (
'Results for second chunk differ from serial estimate.')
assert np.isclose(
mi, expected_mi,
rtol=0.05), ('Estimated ({0}) and expected ({1}) MI differ.'.format(
mi, expected_mi))
# Check if a single chunk is returned if all variables are defined as
# reusable.
mi_parallel3 = mi_estimator.estimate_parallel(n_chunks=2,
re_use=['var1', 'var2'],
var1=source1,
var2=target)
assert len(mi_parallel3) == 1, (
'Single chunk data returned more than one estimate.')
assert np.isclose(
mi_parallel3[0], expected_mi,
rtol=0.05), ('Estimated ({0}) and expected ({1}) MI differ.'.format(
mi_parallel3[0], expected_mi))
# Check assertion for incorrect number of samples in data to be reused in
# parallel estimator.
with pytest.raises(AssertionError):
mi_estimator.estimate_parallel(n_chunks=2,
re_use=['var2'],
var1=source_chunks,
var2=target[:100])
def test_mi_gauss_data():
"""Test MI estimators on correlated Gauss data.
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 = JidtKraskovMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtKraskovMI', 'CMI (uncorr., no cond.)')
# Test Gaussian
mi_estimator = JidtGaussianMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtGaussianMI', 'CMI (uncorr., no cond.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
mi_estimator = JidtDiscreteMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtDiscreteMI', 'CMI (uncorr., no cond.)')
def test_mi_gauss_data():
"""Test MI estimators on correlated Gauss data.
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 = JidtKraskovMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtKraskovMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtKraskovMI', 'CMI (uncorr., no cond.)')
# Test Gaussian
mi_estimator = JidtGaussianMI(settings={})
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtGaussianMI', 'CMI (no cond.)')
_assert_result(mi_uncor, 0, 'JidtGaussianMI', 'CMI (uncorr., no cond.)')
# Test Discrete
settings = {'discretise_method': 'equal', 'n_discrete_bins': 5}
mi_estimator = JidtDiscreteMI(settings=settings)
mi_cor = mi_estimator.estimate(source1, target)
mi_uncor = mi_estimator.estimate(source2, target)
_assert_result(mi_cor, expected_mi, 'JidtDiscreteMI', 'CMI (no cond.)',
0.08) # More variability here
_assert_result(mi_uncor, 0, 'JidtDiscreteMI', 'CMI (uncorr., no cond.)',
0.08) # More variability here
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_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_lagged_mi():
"""Test estimation of lagged MI."""
n = 10000
cov = 0.4
source = [rn.normalvariate(0, 1) for r in range(n)]
target = [0] + [
sum(pair) for pair in zip([cov * y for y in source[0:n - 1]], [
(1 - cov) * y
for y in [rn.normalvariate(0, 1) for r in range(n - 1)]
])
]
source = np.array(source)
target = np.array(target)
settings = {
'discretise_method': 'equal',
'n_discrete_bins': 4,
'history': 1,
'history_target': 1,
'lag_mi': 1,
'source_target_delay': 1
}
est_te_k = JidtKraskovTE(settings)
te_k = est_te_k.estimate(source, target)
est_te_d = JidtDiscreteTE(settings)
te_d = est_te_d.estimate(source, target)
est_d = JidtDiscreteMI(settings)
mi_d = est_d.estimate(source, target)
est_k = JidtKraskovMI(settings)
mi_k = est_k.estimate(source, target)
est_g = JidtGaussianMI(settings)
mi_g = est_g.estimate(source, target)
_compare_result(mi_d,
te_d,
'JidtDiscreteMI',
'JidtDiscreteTE',
'lagged MI',
tol=0.05)
_compare_result(mi_k,
te_k,
'JidtKraskovMI',
'JidtKraskovTE',
'lagged MI',
tol=0.05)
_compare_result(mi_g,
te_k,
'JidtGaussianMI',
'JidtKraskovTE',
'lagged MI',
tol=0.05)
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_mi_correlated_gaussians_two_chunks():
"""Test estimators on two chunks of correlated Gaussian data."""
expected_mi, source, source_uncorr, target = _get_gauss_data(n=20000,
seed=SEED)
n_points = source.shape[0]
# Run OpenCL estimator.
n_chunks = 2
settings = {'debug': True, 'return_counts': True}
ocl_est = OpenCLKraskovMI(settings=settings)
mi_ocl, dist, n_range_var1, n_range_var2 = ocl_est.estimate(
source, target, n_chunks=n_chunks)
# Run JIDT estimator.
jidt_est = JidtKraskovMI(settings={})
mi_jidt = jidt_est.estimate(source[0:int(n_points / 2), :],
target[0:int(n_points / 2), :])
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: [{1:.4f}, {2:.4f}] '
'nats; expected to be close to {3:.4f} nats for correlated '
'Gaussians.'.format(mi_jidt, mi_ocl[0], mi_ocl[1], 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[0], expected_mi,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl[0], mi_jidt,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl[1], mi_jidt,
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(
mi_ocl[0], mi_ocl[1],
atol=0.05), ('MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
def test_mi_correlated_gaussians_two_chunks():
"""Test estimators on two chunks of correlated Gaussian data."""
expected_mi, source, source_uncorr, target = _get_gauss_data(n=20000)
n_points = source.shape[0]
# Run OpenCL estimator.
n_chunks = 2
settings = {'debug': True}
ocl_est = OpenCLKraskovMI(settings=settings)
mi_ocl, dist, n_range_var1, n_range_var2 = ocl_est.estimate(
source, target,
n_chunks=n_chunks)
# Run JIDT estimator.
jidt_est = JidtKraskovMI(settings={})
mi_jidt = jidt_est.estimate(source[0:int(n_points/2), :],
target[0:int(n_points/2), :])
print('JIDT MI result: {0:.4f} nats; OpenCL MI result: [{1:.4f}, {2:.4f}] '
'nats; expected to be close to {3:.4f} nats for correlated '
'Gaussians.'.format(mi_jidt, mi_ocl[0], mi_ocl[1], 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[0], expected_mi, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl[0], mi_jidt, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl[1], mi_jidt, atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
assert np.isclose(mi_ocl[0], mi_ocl[1], atol=0.05), (
'MI estimation for uncorrelated Gaussians using the '
'OpenCL estimator failed (error larger 0.05).')
class MutualInfoIDTxl(MutualInfoPCA):
"""
IDTxl Mutual Information Estimator [1]_, followed by PCA dimensionality
reduction.
Parameters
----------
data_loader : DataLoader
The data loader.
pca_size : int, optional
PCA dimension size.
Default: 100
debug : bool, optional
If True, shows more informative plots.
Default: False
Attributes
----------
ignore_layers : tuple
A tuple to ignore layer classes to monitor for MI.
References
----------
.. [1] P. Wollstadt, J. T. Lizier, R. Vicente, C. Finn, M. Martinez-Zarzuela,
P. Mediano, L. Novelli, M. Wibral (2018). IDTxl: The Information
Dynamics Toolkit xl: a Python package for the efficient analysis of
multivariate information dynamics in networks. Journal of Open Source
Software, 4(34), 1081. https://doi.org/10.21105/joss.01081.
Source code: https://github.com/pwollstadt/IDTxl
"""
def __init__(self, data_loader: DataLoader, pca_size=50, debug=False):
super().__init__(data_loader=data_loader,
pca_size=pca_size,
debug=debug)
settings = {'kraskov_k': 4}
try:
self.estimator = OpenCLKraskovMI(settings=settings)
except RuntimeError:
warnings.warn("No OpenCL backed detected. Run "
"'conda install -c conda-forge pyopencl' "
"in a terminal.")
self.estimator = JidtKraskovMI(settings=settings)
def _prepare_input_finished(self):
super()._prepare_input_finished()
for key in ['input', 'target']:
self.quantized[key] = self.quantized[key].numpy().astype(
np.float64)
def _process_activations(self, layer_name: str,
activations: List[torch.FloatTensor]):
pass
def _save_mutual_info(self):
hidden_layers_name = set(self.activations.keys())
hidden_layers_name.difference_update({'input', 'target'})
for layer_name in hidden_layers_name:
activations = torch.cat(self.activations[layer_name]).numpy()
if self.pca_size is not None and activations.shape[
-1] > self.pca_size:
pca = sklearn.decomposition.PCA(n_components=self.pca_size)
activations = pca.fit_transform(activations)
activations = (activations -
activations.mean()) / activations.std()
activations = activations.astype(np.float64)
info_x = self.estimator.estimate(self.quantized['input'],
activations)
info_y = self.estimator.estimate(activations,
self.quantized['target'])
self.information[layer_name] = (self.to_bits(float(info_x)),
self.to_bits(float(info_y)))