def test_entropy():
a, b = make_variables("A B", 2)
c, d = make_variables("C D", 4)
j = UniformDist(a, b, c, d)
assert j.entropy(a) == 1
assert j.entropy(c) == 2
assert j.entropy([a, b]) == j.entropy(a, b)
def test_entropy():
a, b = make_variables("A B", 2)
c, d = make_variables("C D", 4)
j = UniformDist(a, b, c, d)
assert j.entropy(a) == 1
assert j.entropy(c) == 2
assert j.entropy([a, b]) == j.entropy(a, b)
def test_uniform():
a, b = make_variables("A B", 4)
c = Variable("C", 2)
j = UniformDist(a, b, c)
assert j.probabilities.size == 4 * 4 * 2
assert j.entropy(a) == 2.0
assert j.entropy(b) == 2.0
assert j.entropy(c) == 1.0
def test_uniform():
a, b = make_variables("A B", 4)
c = Variable("C", 2)
j = UniformDist(a, b, c)
assert j.probabilities.size == 4 * 4 * 2
assert j.entropy(a) == 2.0
assert j.entropy(b) == 2.0
assert j.entropy(c) == 1.0
def test_ay_polani():
w, x, y, z = make_variables("W X Y Z", 2)
wdist = UniformDist(w)
# Ay & Polani, Example 3
eq1 = Equation('BR', [w], [x, y], equations.branch_same_)
eq2 = Equation('XOR', [x, y], [z], equations.xor_)
# Build the graph
eg3 = CausalGraph([eq1, eq2])
m_eg3 = MeasureCause(eg3, wdist)
# See the table on p29
assert m_eg3.mutual_info(x, y) == 1
assert m_eg3.mutual_info(x, y, w) == 0
assert m_eg3.mutual_info(w, z, y) == 0
assert m_eg3.causal_flow(x, y) == 0
assert m_eg3.causal_flow(x, y, w) == 0
assert m_eg3.causal_flow(w, z, y) == 1
# Ay & Polani, Example 5.1
def copy_first_(i1, i2, o1):
o1[i1] = 1.0
eq2 = Equation('COPYX', [x, y], [z], copy_first_)
eg51 = CausalGraph([eq1, eq2])
m_eg51 = MeasureCause(eg51, wdist)
# See paragraph at top of page 30
assert m_eg51.mutual_info(x, z, y) == 0
assert m_eg51.causal_flow(x, z, y) == 1
assert m_eg51.causal_flow(x, z) == 1
# Ay & Polani, Example 5.2
def random_sometimes_(i1, i2, o1):
if i1 != i2:
o1[:] = .5
else:
equations.xor_(i1, i2, o1)
eq2 = Equation('RAND', [x, y], [z], random_sometimes_)
eg52 = CausalGraph([eq1, eq2])
m_eg52 = MeasureCause(eg52, wdist)
# See pg 30
expected = 3.0 / 4.0 * log2(4.0 / 3.0)
assert_allclose(m_eg52.causal_flow(x, z, y), expected)
def test_controlled_diamond():
"""This examples can move us from a correlation case to a diamond
"""
c1, c2, s1, s2, s3, s4, a1 = make_variables('c1 c2 s1 s2 s3 s4 a1', 2)
eq1 = Equation('SAME', [c1], [s1], equations.same_)
eq2 = Equation('SAMEB', [c2], [s2, s3], equations.branch_same_)
eq3 = Equation('AND', [s1, s2], [s4], equations.and_)
eq4 = Equation('OR', [s3, s4], [a1], equations.or_)
net = CausalGraph([eq1, eq2, eq3, eq4])
# Let's just use Uniform
m = MeasureCause(net, UniformDist(c1, c2))
# Mutual info is pretty useless, as it is the same across these...
assert m.mutual_info(s2, a1) == m.mutual_info(s3, a1)
# Look how much better average sad is!
assert m.average_sad(s2, a1) < m.average_sad(s3, a1)
def test_distribution():
a, b, c = make_variables("A B C", 2)
eq1 = Equation('xor', [a, b], [c], equations.xor_)
net = CausalGraph([eq1])
ab = UniformDist(a, b)
j_obs = net.generate_joint(ab)
j_do_a = net.generate_joint(ab, do_dist=JointDistByState({a: 0}))
# for ass, p in j_obs.iter_conditional(c, a):
# print ass, p
# # assert p == 0.5
#
# for ass, p in j_do_a.iter_conditional(c, a):
# # assert p == 0.5
# print ass, p
assert j_obs.mutual_info(b, c) == 0
# Very different under "Doing"
assert j_do_a.mutual_info(b, c) == 1.0
def test_mutual_info():
a, b = make_variables("A B", 2)
c, d = make_variables("C D", 4)
j = UniformDist(a, b, c, d)
assert j.mutual_info([a, b], c) == 0
assert j.mutual_info(a, b, c) == 0
def test_joint():
a, b, c, d = make_variables("A B C D", 2)
j = UniformDist(a, b, c, d)
assert_frame_equal(j.joint([a, b]).probabilities, j.joint(a, b).probabilities)
def test_mutual_info():
a, b = make_variables("A B", 2)
c, d = make_variables("C D", 4)
j = UniformDist(a, b, c, d)
assert j.mutual_info([a, b], c) == 0
assert j.mutual_info(a, b, c) == 0
def test_joint():
a, b, c, d = make_variables("A B C D", 2)
j = UniformDist(a, b, c, d)
assert_frame_equal(
j.joint([a, b]).probabilities,
j.joint(a, b).probabilities)
