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()