def test_random_spec():
def add_noise_(i1, i2, o1):
if i2:
# Random Coin toss
o1[:] = .5
else:
# Otherwise specific
o1[i1] = 1.0
c1, c2, s1, a = make_variables('C1 C2 S1 A', 2)
eq1 = Equation('Send1', [c1, c2], [s1], add_noise_)
eq2 = Equation('Send2', [s1], [a], equations.same_)
network = CausalGraph([eq1, eq2])
root_dist = JointDist({c1: [.2, .8], c2: [.5, .5]})
m = MeasureCause(network, root_dist)
# Spec is the same
assert m.mutual_info(s1, a) == m.average_sad(s1, a)
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_random_spec():
def add_noise_(i1, i2, o1):
if i2:
# Random Coin toss
o1[:] = .5
else:
# Otherwise specific
o1[i1] = 1.0
c1, c2, s1, a = make_variables('C1 C2 S1 A', 2)
eq1 = Equation('Send1', [c1, c2], [s1], add_noise_)
eq2 = Equation('Send2', [s1], [a], equations.same_)
network = CausalGraph([eq1, eq2])
root_dist = JointDist({c1: [.2, .8], c2: [.5, .5]})
m = MeasureCause(network, root_dist)
# Spec is the same
assert m.mutual_info(s1, a) == m.average_sad(s1, a)
def test_signal3():
def merge_(i1, i2, o1):
if i2:
# Perfect spec
o1[i1] = 1.0
else:
o1[i1 / 2] = 1.0
c1, s1, s3, a = make_variables('C1 S1 S3 A', 4)
c2, s2 = make_variables('C2 S2', 2)
eq1 = Equation('Send1', [c1], [s1], equations.same_)
eq2 = Equation('Send2', [c2], [s2], equations.same_)
eq3 = Equation('Rec1', [s1, s2], [a], merge_)
network = CausalGraph([eq1, eq2, eq3])
root_dist = JointDist({c1: [.25] * 4, c2: [.5, .5]})
m = MeasureCause(network, root_dist)
j_observe = network.generate_joint(root_dist)
# We check on the equivalence of these.
assert_allclose(m.causal_flow(s1, a, s2), m.average_sad(s1, a))
assert_allclose(m.causal_flow(s2, a, s1), m.average_sad(s2, a))
def test_signal3():
def merge_(i1, i2, o1):
if i2:
# Perfect spec
o1[i1] = 1.0
else:
o1[i1/2] = 1.0
c1, s1, s3, a = make_variables('C1 S1 S3 A', 4)
c2, s2 = make_variables('C2 S2', 2)
eq1 = Equation('Send1', [c1], [s1], equations.same_)
eq2 = Equation('Send2', [c2], [s2], equations.same_)
eq3 = Equation('Rec1', [s1, s2], [a], merge_)
network = CausalGraph([eq1, eq2, eq3])
root_dist = JointDist({c1: [.25] * 4, c2: [.5, .5]})
m = MeasureCause(network, root_dist)
j_observe = network.generate_joint(root_dist)
# We check on the equivalence of these.
assert_allclose(m.causal_flow(s1, a, s2), m.average_sad(s1, a))
assert_allclose(m.causal_flow(s2, a, s1), m.average_sad(s2, a))
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_correlation():
c, s, a, k = make_variables('C S A K', 2)
eq1 = Equation('Send', [c], [s, k], equations.branch_same_)
eq2 = Equation('Recv', [s], [a], equations.same_)
network = CausalGraph([eq1, eq2])
root_dist = JointDist({c: [.7, .3]})
m = MeasureCause(network, root_dist)
assert_allclose(m.mutual_info(s, a), m.mutual_info(k, a))
assert_allclose(m.causal_flow(s, a), m.average_sad(s, a))
assert m.causal_flow(k, a) == 0
assert m.average_sad(k, a) == 0
assert_allclose(m.average_sad(s, a), m.mutual_info(s, a))
assert m.mutual_info(k, a) == m.mutual_info(s, a)
assert m.mutual_info(k, a, s) == 0
assert m.mutual_info(s, a, k) == 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_correlation():
c, s, a, k = make_variables('C S A K', 2)
eq1 = Equation('Send', [c], [s, k], equations.branch_same_)
eq2 = Equation('Recv', [s], [a], equations.same_)
network = CausalGraph([eq1, eq2])
root_dist = JointDist({c: [.7, .3]})
m = MeasureCause(network, root_dist)
assert_allclose(m.mutual_info(s, a), m.mutual_info(k, a))
assert_allclose(m.causal_flow(s, a), m.average_sad(s, a))
assert m.causal_flow(k, a) == 0
assert m.average_sad(k, a) == 0
assert_allclose(m.average_sad(s, a), m.mutual_info(s, a))
assert m.mutual_info(k, a) == m.mutual_info(s, a)
assert m.mutual_info(k, a, s) == 0
assert m.mutual_info(s, a, k) == 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)
