def test_coi1():
""" Test I for xor """
d = n_mod_m(3, 2)
assert_almost_equal(I(d), -1.0)
assert_almost_equal(I(d, [[0], [1], [2]]), -1.0)
assert_almost_equal(I(d, [[0], [1], [2]], [2]), 0.0)
assert_almost_equal(I(d, [[0], [1]], [2]), 1.0)
def test_coi1():
""" Test I for xor """
d = n_mod_m(3, 2)
assert I(d) == pytest.approx(-1.0)
assert I(d, [[0], [1], [2]]) == pytest.approx(-1.0)
assert I(d, [[0], [1], [2]], [2]) == pytest.approx(0.0)
assert I(d, [[0], [1]], [2]) == pytest.approx(1.0)
def getTE(timeseriesa, timeseriesb, history=1):
"""
Takes two time series and calculates the pairwise transfer entropies
Parameters
----------
a,b: np.array
Two time series
history: int
Markov Order
Returns
---------
list of Floats containing Transfer Entropy, Intrinsic Transfer Entropy, Transfer Entropy,
backwards Transfer Entropy, backwards intrinsic Transfer Entropy of the pairs of nodes addressed by input a,b
"""
pairofnodes = list(zip(timeseriesa, timeseriesb))
#list(zip(two lists of ints))
# pairofnodes=list(zip(rbn.histories[a],rbn.histories[b]))
distribution = distribution_from_data(pairofnodes,
history + 1,
base='linear')
dist = dit.distconst.modify_outcomes(
distribution,
lambda o: (tuple([oo[0] for oo in o[:-1]]),
tuple([oo[1] for oo in o[:-1]]), o[-1][0], o[-1][1]))
I0, J0, I1, J1 = ([0], [1], [2], [3])
TE = I(dist, [J1, I0], J0)
# ITE=IMI(dist,[J1,I0],J0)
backTE = I(dist, [I1, J0], I0)
# backITE=IMI(dist,[I1,J0],I0)
return [TE, backTE, 0, 0]
def test_data_processing_inequality(dist):
"""
given X - Y - Z:
I(X:Z) <= I(X:Y)
"""
i_xy = I(dist, [[0], [1]])
i_xz = I(dist, [[0], [2]])
assert i_xz <= i_xy + epsilon
def test_mi_hc(dist):
"""
given U - X - Y:
I[U:Y] <= s*(X||Y)*I[U:X]
"""
a = I(dist, [[0], [2]])
b = hypercontractivity_coefficient(dist, [[1], [2]], niter=20)
c = I(dist, [[0], [1]])
assert a <= b * c + epsilon
def test_zhang_yeung_inequality(dist):
"""
2I(C:D) <= I(A:B)+I(A:CD)+3I(C:D|A)+I(C:D|B)
"""
I_a_b = I(dist, [[0], [1]])
I_c_d = I(dist, [[2], [3]])
I_a_cd = I(dist, [[0], [2, 3]])
I_c_d_g_a = I(dist, [[2], [3]], [0])
I_c_d_g_b = I(dist, [[2], [3]], [1])
assert 2 * I_c_d <= I_a_b + I_a_cd + 3 * I_c_d_g_a + I_c_d_g_b + epsilon
def test_giant_bit2(n, k):
"""
tests for the giant bit coinformation
"""
d = giant_bit(n, k)
assert I(d) == pytest.approx(np.log2(k))
def test_caekl_2(d):
"""
Ensure that it reduces to the mutual information for bivariate
distributions reduced from multivariate.
"""
rvs = [[0], [1]]
assert I(d, rvs) == pytest.approx(J(d, rvs))
def test_iidsum():
"""
Test against known value.
"""
d = iid_sum(2, 6)
cmi = I(d, [[0], [1]], [2])
assert cmi == pytest.approx(1.8955230821535425)
def test_sp2():
""" Test all possible info measures, with rv_names """
d = n_mod_m(4, 2)
d.set_rv_names('xyzw')
ip = ShannonPartition(d)
for meas in all_info_measures('xyzw'):
yield assert_almost_equal, ip[meas], I(d, meas[0], meas[1])
def test_max_correlation_mutual_information(dist):
"""
(p_min * rho(X:Y))^2 <= (2 ln 2)I(X:Y)
"""
p_min = dist.marginal([0]).pmf.min()
rho = maximum_correlation(dist, [[0], [1]])
i = I(dist, [[0], [1]])
assert (p_min * rho)**2 <= (2 * np.log(2)) * i + epsilon
def test_mincoinfo_1():
"""
Test mincoinfo
"""
d = uniform(['000', '111'])
mcio = MinCoInfoOptimizer(d, [[0], [1], [2]])
mcio.optimize()
dp = mcio.construct_dist()
assert I(dp) == pytest.approx(-1)
def test_mis1(d):
"""
Test that all the mutual informations match for bivariate distributions.
"""
i = I(d)
t = T(d)
b = B(d)
j = J(d)
ii = II(d)
assert i == pytest.approx(t)
assert t == pytest.approx(b)
assert b == pytest.approx(j)
assert j == pytest.approx(ii)
def _measure(d, sources, target):
"""
I_ME*, the maximum entropy distribution satisfying the * assumption of
BROJA.
Parameters
----------
d : Distribution
The distribution to compute i_mes for.
sources : iterable of iterables
The source variables.
target : iterable
The target variable.
Returns
-------
i_mes : float
The value of I_ME*.
"""
dp = maxent_dist(d, [source + target for source in sources])
i_mes = I(dp)
return i_mes
def test_coi8():
""" Test that I fails on ScalarDistributions """
d = SD([1 / 3] * 3)
with pytest.raises(ditException):
I(d)
def test_coi7():
""" Test that H = I for one variable """
outcomes = "ABC"
pmf = [1 / 3] * 3
d = D(outcomes, pmf)
assert H(d) == pytest.approx(I(d))
def test_coi4():
""" Test conditional I, with and without names """
d = n_mod_m(4, 2)
assert_almost_equal(I(d, [[0], [1], [2]], [3]), -1.0)
d.set_rv_names("XYZW")
assert_almost_equal(I(d, [['X'], ['Y'], ['Z']], ['W']), -1.0)
def test_sp2(meas):
""" Test all possible info measures, with rv_names """
d = n_mod_m(4, 2)
d.set_rv_names('xyzw')
ip = ShannonPartition(d)
assert ip[meas] == pytest.approx(I(d, meas[0], meas[1]))
def test_coi7():
""" Test that H = I for one variable """
outcomes = "ABC"
pmf = [1/3]*3
d = D(outcomes, pmf)
assert_almost_equal(H(d), I(d))
def test_coi6():
""" Test conditional I, with and without names """
d = n_mod_m(4, 2)
assert_almost_equal(I(d, [[0]], [1, 2, 3]), 0.0)
d.set_rv_names("XYZW")
assert_almost_equal(I(d, [['X']], ['Y', 'Z', 'W']), 0.0)
def test_caekl_1(d):
"""
Ensure that it reduces to the mutual information for bivariate
distributions.
"""
assert I(d) == pytest.approx(J(d))
def test_coi2():
""" Test I for larger parity distribution """
d = n_mod_m(4, 2)
assert_almost_equal(I(d), 1.0)
def test_sp1(meas):
""" Test all possible info measures """
d = n_mod_m(4, 2)
ip = ShannonPartition(d)
assert ip[meas] == pytest.approx(I(d, meas[0], meas[1]))
def test_coi2():
""" Test I for larger parity distribution """
d = n_mod_m(4, 2)
assert I(d) == pytest.approx(1.0)
def test_shannon_inequality(dist):
"""
I(X:Y|Z) >= 0
"""
i = I(dist, [[0], [1]], [2])
assert i >= 0 - epsilon
def test_sp1():
""" Test all possible info measures """
d = n_mod_m(4, 2)
ip = ShannonPartition(d)
for meas in all_info_measures(range(4)):
yield assert_almost_equal, ip[meas], I(d, meas[0], meas[1])
def test_coi4():
""" Test conditional I, with and without names """
d = n_mod_m(4, 2)
assert I(d, [[0], [1], [2]], [3]) == pytest.approx(-1.0)
d.set_rv_names("XYZW")
assert I(d, [['X'], ['Y'], ['Z']], ['W']) == pytest.approx(-1.0)
def test_coi6():
""" Test conditional I, with and without names """
d = n_mod_m(4, 2)
assert I(d, [[0]], [1, 2, 3]) == pytest.approx(0.0)
d.set_rv_names("XYZW")
assert I(d, [['X']], ['Y', 'Z', 'W']) == pytest.approx(0.0)
def test_coi3():
""" Test I for subsets of variables, with and without names """
d = n_mod_m(4, 2)
assert I(d, [[0], [1], [2]]) == pytest.approx(0.0)
d.set_rv_names("XYZW")
assert I(d, [['X'], ['Y'], ['Z']]) == pytest.approx(0.0)
def test_coi3():
""" Test I for subsets of variables, with and without names """
d = n_mod_m(4, 2)
assert_almost_equal(I(d, [[0], [1], [2]]), 0.0)
d.set_rv_names("XYZW")
assert_almost_equal(I(d, [['X'], ['Y'], ['Z']]), 0.0)