def test_shuffle_vs_alpha(self):
print("Checking that shuffle sig_thres equals analytical thres "
"for sig_lev = %.2f, sig_samples = %d" % (self.sig_lev,
self.sig_samples))
numpy.random.seed(42)
# array = numpy.random.randn(2, self.T)
links_coeffs = {0: [],
1: [((0, 0), .06)], }
data, links = pp.var_process(links_coeffs, T=self.T,
use='inno_cov', verbosity=verbosity)
array = data.T
xyz = numpy.array([0, 1])
for measure in ['par_corr', 'reg']:
expected = te._get_estimate(array=array, measure=measure, xyz=xyz,
significance='analytic',
sig_samples=self.sig_samples,
sig_lev=self.sig_lev,
measure_params=self.measure_params,
verbosity=0)['sig_thres']
res = te._get_estimate(array=array, measure=measure, xyz=xyz,
significance='full_shuffle',
sig_samples=self.sig_samples,
sig_lev=self.sig_lev,
measure_params=self.measure_params,
verbosity=0)['sig_thres']
print("shuffle %.2f sig thres for %s = %.4f (analytic = %.4f)"
% (self.sig_lev, measure, res, expected))
numpy.testing.assert_allclose(res, expected, rtol=self.rtol)
def __init__(self):
print("\nChecking confidence tests analytic and shuffle")
self.conf_lev = .9
self.conf_samples = 1000
self.T = 500
self.links_coeffs = {0: [],
1: [],
}
ax = 0.8
ay = 0.9
cxy = .7
links_coeffs = {0: [((0, -1), ax)],
1: [((1, -1), ay), ((0, -1), -cxy)],
}
self.rtol = .1
self.measure_params = {'knn': 10}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs, T=self.T,
use='inno_cov', verbosity=verbosity)
self.array, self.xyz = te._construct_array(X=[(0, -1)], Y=[(1, 0)],
Z=[(0, -2), (1, -1)],
tau_max=2,
data=data, mask=False)
def __init__(self):
print("\nChecking confidence tests analytic and shuffle")
self.conf_lev = .9
self.conf_samples = 1000
self.T = 500
self.links_coeffs = {
0: [],
1: [],
}
ax = 0.8
ay = 0.9
cxy = .7
links_coeffs = {
0: [((0, -1), ax)],
1: [((1, -1), ay), ((0, -1), -cxy)],
}
self.rtol = .1
self.measure_params = {'knn': 10}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs,
T=self.T,
use='inno_cov',
verbosity=verbosity)
self.array, self.xyz = te._construct_array(X=[(0, -1)],
Y=[(1, 0)],
Z=[(0, -2), (1, -1)],
tau_max=2,
data=data,
selector=False)
def test_shuffle_vs_alpha(self):
print("Checking that shuffle sig_thres equals analytical thres "
"for sig_lev = %.2f, sig_samples = %d" %
(self.sig_lev, self.sig_samples))
numpy.random.seed(42)
# array = numpy.random.randn(2, self.T)
links_coeffs = {
0: [],
1: [((0, 0), .06)],
}
data, links = pp.var_process(links_coeffs,
T=self.T,
use='inno_cov',
verbosity=verbosity)
array = data.T
xyz = numpy.array([0, 1])
for measure in ['par_corr', 'reg']:
expected = te._get_estimate(array=array,
measure=measure,
xyz=xyz,
significance='analytic',
sig_samples=self.sig_samples,
sig_lev=self.sig_lev,
measure_params=self.measure_params,
verbosity=0)['sig_thres']
res = te._get_estimate(array=array,
measure=measure,
xyz=xyz,
significance='full_shuffle',
sig_samples=self.sig_samples,
sig_lev=self.sig_lev,
measure_params=self.measure_params,
verbosity=0)['sig_thres']
print("shuffle %.2f sig thres for %s = %.4f (analytic = %.4f)" %
(self.sig_lev, measure, res, expected))
numpy.testing.assert_allclose(res, expected, rtol=self.rtol)
def test_pc_algo_all():
print("\nTesting function 'pc_algo_all' to check whether PC algorithm "
"returns the correct set of parents.")
# Test data:
T = 1000
numpy.random.seed(42)
# Graph as in Runge PRE 2012 Fig. 1
cxz = .5
ax = .5
cxy = .5
cwy = .5
links_coeffs = {0: [((1, -1), cxz)],
1: [((1, -1), ax)],
2: [((1, -2), cxy), ((3, -1), cwy)],
3: [],
}
fulldata, true_parents_neighbors = pp.var_process(links_coeffs, T=T)
T, N = fulldata.shape
max_trials = 5
measure_params = {'knn': 100}
significance = 'analytic'
print("Checking different initial_conds...")
for initial_conds in range(1, 4):
# print("%d" % initial_conds)
parents_neighbors = te.pc_algo_all(
fulldata, estimate_parents_neighbors='both',
tau_min=0, tau_max=4,
initial_conds=initial_conds, max_conds=6, max_trials=max_trials,
measure='par_corr',
significance=significance, sig_lev=0.999995, sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
mask=False, mask_type=['y'], data_mask=numpy.array([0]),
initial_parents_neighbors=None,
verbosity=verbosity)
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
print("Checking initial_parents_neighbors...")
parents_neighbors = te.pc_algo_all(
fulldata, estimate_parents_neighbors='both',
tau_min=0, tau_max=4,
initial_conds=1, max_conds=6, max_trials=max_trials,
measure='par_corr',
significance=significance, sig_lev=0.995, sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
mask=False, mask_type=['y'], data_mask=numpy.array([0]),
initial_parents_neighbors=true_parents_neighbors,
verbosity=verbosity)
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
print("Checking estimate_parents_neighbors...")
for estimate_parents_neighbors in ['parents', 'both']:
# print("%s" % estimate_parents_neighbors)
parents_neighbors = te.pc_algo_all(
fulldata,
estimate_parents_neighbors=estimate_parents_neighbors,
tau_min=0, tau_max=4,
initial_conds=1, max_conds=6, max_trials=max_trials,
measure='par_corr',
significance='analytic', sig_lev=0.995, sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
mask=False, mask_type=['y'], data_mask=numpy.array([0]),
initial_parents_neighbors=None,
verbosity=verbosity)
if estimate_parents_neighbors == 'both':
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
elif estimate_parents_neighbors == 'parents':
assert_graphs_equal(_get_parent_graph(parents_neighbors),
_get_parent_graph(true_parents_neighbors))
def test_measures():
print("\nTesting function '_calculate_lag_function' to check dependence "
"measures are correctly estimated.")
measure_params = {'knn': 10, }
ax = 0.6
ay = 0.3
cxy = .7
links_coeffs = {0: [((0, -1), ax)],
1: [((1, -1), ay), ((0, -1), cxy)],
}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs, T=5000,
use='inno_cov', verbosity=verbosity)
T, N = data.shape
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
gamma_x = 1.**2 / (1. - ax**2)
gamma_xy = (ax * cxy * gamma_x) / (1. - ax * ay)
gamma_y = (cxy**2 * gamma_x + 1.**2 + 2. *
ay * cxy * gamma_xy) / (1. - ay**2)
expected_reg = cxy * numpy.sqrt(gamma_x / gamma_y)
for measure in ['par_corr', 'reg', 'cmi_knn', 'cmi_gauss']:
res = te._calculate_lag_function(
measure=measure,
data=data,
var_x=0, var_y=1,
conds_x=links[0], conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
if measure == 'par_corr':
print("%s = %.3f (expected = %.3f)"
% (measure, res[1], expected_parcorr))
numpy.testing.assert_allclose(res[1], expected_parcorr, rtol=0.1)
elif measure == 'reg':
print("%s = %.3f (expected = %.3f)"
% (measure, res[1], expected_reg))
numpy.testing.assert_allclose(res[1], expected_reg, rtol=0.1)
elif (measure == 'cmi_knn' or measure == 'cmi_gauss'):
print("%s = %.3f (expected = %.3f)"
% (measure, res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.1)
# binning estimator
symb_data = pp.quantile_bin_array(data, bins=5)
res = te._calculate_lag_function(
measure='cmi_symb',
data=symb_data,
var_x=0, var_y=1,
conds_x=links[0], conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
print("%s = %.3f (expected = %.3f)"
% ('symb', res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.3)
# ordinal pattern estimator
symb_data = pp.ordinal_patt_array(data,
array_mask=numpy.ones(data.shape,
dtype='int32'),
dim=3, step=2)[0]
res = te._calculate_lag_function(
measure='cmi_symb',
data=symb_data,
var_x=0, var_y=1,
conds_x=links[0], conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
print("%s = %.3f (expected = %.3f)"
% ('ordinal-symb', res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.4)
def test_get_lagfunctions():
print("\nTesting function 'get_lagfunctions' to check whether conditioning"
" measures MI, ITY, ITX, and MIT work as expected.")
# Graph as in Runge PRE 2012 Fig. 1
cxz = .5
ax = .5
cxy = .5
cwy = .5
links_coeffs = {0: [((1, -1), cxz)],
1: [((1, -1), ax)],
2: [((1, -2), cxy), ((3, -1), cwy)],
3: [],
}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs, T=10000, verbosity=verbosity)
T, N = data.shape
i = 1
j = 2
tau = 2
# Test that cross correlation is correct
cond_mode = 'none'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1. - ax**2) /
(cwy**2 * 1.**2 + 1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data, parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2, verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau], expected_parcorr,
rtol=0.1)
# Test that ITY is correct
cond_mode = 'parents_y'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1. - ax**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data, parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2, verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau], expected_parcorr,
rtol=0.1)
# Test that ITX is correct
cond_mode = 'parents_x'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) /
(cwy**2 * 1.**2 + 1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data, parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2, verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau], expected_parcorr,
rtol=0.1)
# Test that MIT is correct
cond_mode = 'parents_xy'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data, parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2, verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau], expected_parcorr,
rtol=0.1)
# All non-links should be almost zero
for nj in range(N):
for ni in range(N):
for ntau in range(3):
if (ni, -ntau) not in links[nj]:
numpy.testing.assert_allclose(res[0][ni, nj, ntau], 0.,
atol=0.05)
# Now testing a contemporaneous MIT
# Graph below
az = .5
ax = .5
ay = .5
sxy = .3
syz = .5
sxz = .6
links_coeffs = {0: [((0, -1), az), ((1, 0), sxz), ((2, 0), syz)],
1: [((1, -1), ax), ((0, 0), sxz), ((2, 0), sxy)],
2: [((2, -1), ay), ((0, 0), syz), ((1, 0), sxy)],
}
data, links = pp.var_process(links_coeffs, T=5000,
use='inno_cov', verbosity=verbosity)
T, N = data.shape
i = 0
j = 1
tau = 0
cond_mode = 'parents_xy'
expected_parcorr = - (syz * sxy - sxz * 1.**2) / numpy.sqrt(
(syz**2 - 1.**2 * 1.**2) * (sxy**2 - 1.**2 * 1.**2))
res = te.get_lagfunctions(data, parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2, verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau], expected_parcorr,
rtol=0.1)
def test_pc_algo_all():
print("\nTesting function 'pc_algo_all' to check whether PC algorithm "
"returns the correct set of parents.")
# Test data:
T = 1000
numpy.random.seed(42)
# Graph as in Runge PRE 2012 Fig. 1
cxz = .5
ax = .5
cxy = .5
cwy = .5
links_coeffs = {
0: [((1, -1), cxz)],
1: [((1, -1), ax)],
2: [((1, -2), cxy), ((3, -1), cwy)],
3: [],
}
fulldata, true_parents_neighbors = pp.var_process(links_coeffs, T=T)
T, N = fulldata.shape
max_trials = 5
measure_params = {'knn': 100}
significance = 'analytic'
print("Checking different initial_conds...")
for initial_conds in range(1, 4):
# print("%d" % initial_conds)
parents_neighbors = te.pc_algo_all(fulldata,
estimate_parents_neighbors='both',
tau_min=0,
tau_max=4,
initial_conds=initial_conds,
max_conds=6,
max_trials=max_trials,
measure='par_corr',
significance=significance,
sig_lev=0.999995,
sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
selector=False,
selector_type=['y'],
sample_selector=numpy.array([0]),
initial_parents_neighbors=None,
verbosity=verbosity)
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
print("Checking initial_parents_neighbors...")
parents_neighbors = te.pc_algo_all(
fulldata,
estimate_parents_neighbors='both',
tau_min=0,
tau_max=4,
initial_conds=1,
max_conds=6,
max_trials=max_trials,
measure='par_corr',
significance=significance,
sig_lev=0.995,
sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
selector=False,
selector_type=['y'],
sample_selector=numpy.array([0]),
initial_parents_neighbors=true_parents_neighbors,
verbosity=verbosity)
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
print("Checking estimate_parents_neighbors...")
for estimate_parents_neighbors in ['parents', 'both']:
# print("%s" % estimate_parents_neighbors)
parents_neighbors = te.pc_algo_all(
fulldata,
estimate_parents_neighbors=estimate_parents_neighbors,
tau_min=0,
tau_max=4,
initial_conds=1,
max_conds=6,
max_trials=max_trials,
measure='par_corr',
significance='analytic',
sig_lev=0.995,
sig_samples=100,
fixed_thres=0.015,
measure_params=measure_params,
selector=False,
selector_type=['y'],
sample_selector=numpy.array([0]),
initial_parents_neighbors=None,
verbosity=verbosity)
if estimate_parents_neighbors == 'both':
assert_graphs_equal(parents_neighbors, true_parents_neighbors)
elif estimate_parents_neighbors == 'parents':
assert_graphs_equal(_get_parent_graph(parents_neighbors),
_get_parent_graph(true_parents_neighbors))
def test_measures():
print("\nTesting function '_calculate_lag_function' to check dependence "
"measures are correctly estimated.")
measure_params = {
'knn': 10,
}
ax = 0.6
ay = 0.3
cxy = .7
links_coeffs = {
0: [((0, -1), ax)],
1: [((1, -1), ay), ((0, -1), cxy)],
}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs,
T=10000,
use='inno_cov',
verbosity=verbosity)
T, N = data.shape
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
gamma_x = 1.**2 / (1. - ax**2)
gamma_xy = (ax * cxy * gamma_x) / (1. - ax * ay)
gamma_y = (cxy**2 * gamma_x + 1.**2 + 2. * ay * cxy * gamma_xy) / (1. -
ay**2)
expected_reg = cxy * numpy.sqrt(gamma_x / gamma_y)
for measure in ['par_corr', 'reg', 'cmi_knn', 'cmi_gauss']:
res = te._calculate_lag_function(measure=measure,
data=data,
var_x=0,
var_y=1,
conds_x=links[0],
conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
if measure == 'par_corr':
print("%s = %.3f (expected = %.3f)" %
(measure, res[1], expected_parcorr))
numpy.testing.assert_allclose(res[1], expected_parcorr, rtol=0.1)
elif measure == 'reg':
print("%s = %.3f (expected = %.3f)" %
(measure, res[1], expected_reg))
numpy.testing.assert_allclose(res[1], expected_reg, rtol=0.1)
elif (measure == 'cmi_knn' or measure == 'cmi_gauss'):
print("%s = %.3f (expected = %.3f)" %
(measure, res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.1)
# binning estimator
symb_data = pp.quantile_bin_array(data, bins=6)
res = te._calculate_lag_function(measure='cmi_symb',
data=symb_data,
var_x=0,
var_y=1,
conds_x=links[0],
conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
print("%s = %.3f (expected = %.3f)" % ('symb', res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.3)
# ordinal pattern estimator
symb_data = pp.ordinal_patt_array(data,
array_mask=numpy.ones(data.shape,
dtype='int32'),
dim=3,
step=2)[0]
res = te._calculate_lag_function(measure='cmi_symb',
data=symb_data,
var_x=0,
var_y=1,
conds_x=links[0],
conds_y=links[1],
measure_params=measure_params,
tau_max=1,
selected_lags=[1],
verbosity=verbosity)['cmi']
print("%s = %.3f (expected = %.3f)" %
('ordinal-symb', res[1], expected_cmi))
numpy.testing.assert_allclose(res[1], expected_cmi, rtol=0.4)
def test_get_lagfunctions():
print("\nTesting function 'get_lagfunctions' to check whether conditioning"
" measures MI, ITY, ITX, and MIT work as expected.")
# Graph as in Runge PRE 2012 Fig. 1
cxz = .5
ax = .5
cxy = .5
cwy = .5
links_coeffs = {
0: [((1, -1), cxz)],
1: [((1, -1), ax)],
2: [((1, -2), cxy), ((3, -1), cwy)],
3: [],
}
numpy.random.seed(42)
data, links = pp.var_process(links_coeffs, T=10000, verbosity=verbosity)
T, N = data.shape
i = 1
j = 2
tau = 2
# Test that cross correlation is correct
cond_mode = 'none'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1. - ax**2) /
(cwy**2 * 1.**2 + 1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data,
parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2,
verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau],
expected_parcorr,
rtol=0.1)
# Test that ITY is correct
cond_mode = 'parents_y'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1. - ax**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data,
parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2,
verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau],
expected_parcorr,
rtol=0.1)
# Test that ITX is correct
cond_mode = 'parents_x'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) /
(cwy**2 * 1.**2 + 1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data,
parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2,
verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau],
expected_parcorr,
rtol=0.1)
# Test that MIT is correct
cond_mode = 'parents_xy'
expected_cmi = 0.5 * numpy.log(1. + (cxy**2 * 1.**2) / (1.**2))
expected_parcorr = cmi2parcorr_trafo(expected_cmi)
res = te.get_lagfunctions(data,
parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2,
verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau],
expected_parcorr,
rtol=0.1)
# All non-links should be almost zero
for nj in range(N):
for ni in range(N):
for ntau in range(3):
if (ni, -ntau) not in links[nj]:
numpy.testing.assert_allclose(res[0][ni, nj, ntau],
0.,
atol=0.05)
# Now testing a contemporaneous MIT
# Graph below
az = .5
ax = .5
ay = .5
sxy = .3
syz = .5
sxz = .6
links_coeffs = {
0: [((0, -1), az), ((1, 0), sxz), ((2, 0), syz)],
1: [((1, -1), ax), ((0, 0), sxz), ((2, 0), sxy)],
2: [((2, -1), ay), ((0, 0), syz), ((1, 0), sxy)],
}
data, links = pp.var_process(links_coeffs,
T=5000,
use='inno_cov',
verbosity=verbosity)
T, N = data.shape
i = 0
j = 1
tau = 0
cond_mode = 'parents_xy'
expected_parcorr = -(syz * sxy - sxz * 1.**2) / numpy.sqrt(
(syz**2 - 1.**2 * 1.**2) * (sxy**2 - 1.**2 * 1.**2))
res = te.get_lagfunctions(data,
parents_neighbors=links,
cond_mode=cond_mode,
measure='par_corr',
tau_max=2,
verbosity=verbosity)
numpy.testing.assert_allclose(res[0][i, j, tau],
expected_parcorr,
rtol=0.2)
