def test_joint_variables_pmf():
animals = Variable(['cat', 'dog', 'cat', 'mouse', 'dog', 'cat'])
animals.ID = 3
animals.name = 'animals'
colors = Variable(['gray', 'yellow', 'brown', 'silver', 'white', 'gray'])
colors.ID = 2
colors.name = 'colors'
sizes = Variable(['small', 'small', 'large', 'small', 'normal', 'small'])
sizes.ID = 1
sizes.name = 'sizes'
fauna = JointVariables(sizes, colors, animals)
fauna.update_values()
assert [1, 2, 3] == fauna.variableIDs
assert fauna.variables[0] is sizes
assert fauna.variables[1] is colors
assert fauna.variables[2] is animals
expected_values = [('large', 'brown', 'cat'),
('normal', 'white', 'dog'),
('small', 'gray', 'cat'),
('small', 'silver', 'mouse'),
('small', 'yellow', 'dog')]
assert fauna.values == expected_values
PrFauna = PMF(fauna)
assert PrFauna.p('small', 'gray', 'cat') == 2 / 6
assert PrFauna.p('small', 'silver', 'mouse') == 1 / 6
assert PrFauna.p('small', 'silver', 'dog') == 0
singleton_joint = JointVariables(animals)
assert ['cat', 'dog', 'cat', 'mouse', 'dog', 'cat'] == singleton_joint.instances()
def test_conditional_pmf__multiple_values():
sizes = Variable(['small', 'small', 'large', 'small', 'normal', 'small'])
sizes.ID = 1
sizes.name = 'sizes'
colors = Variable(['gray', 'yellow', 'brown', 'silver', 'white', 'gray'])
colors.ID = 2
colors.name = 'colors'
animals = Variable(['cat', 'dog', 'cat', 'snake', 'dog', 'cat'])
animals.ID = 3
animals.name = 'animals'
is_pet = Variable(['yes', 'yes', 'yes', 'maybe', 'yes', 'yes'])
is_pet.ID = 4
is_pet.name = 'is_pet'
Pr = CPMF(JointVariables(colors, is_pet), JointVariables(sizes, animals))
assert Pr.given('small', 'cat').p('gray', 'yes') == 2 / 2
assert Pr.given('small', 'cat').p('yellow', 'yes') == 0 / 1
assert Pr.given('small', 'cat').p('brown', 'maybe') == 0 / 1
assert Pr.given('small', 'dog').p('yellow', 'yes') == 1 / 1
assert Pr.given('small', 'dog').p('yellow', 'maybe') == 0 / 1
assert Pr.given('small', 'dog').p('silver', 'maybe') == 0 / 1
assert Pr.given('large', 'cat').p('brown', 'yes') == 1 / 1
assert Pr.given('large', 'cat').p('yellow', 'yes') == 0 / 1
assert Pr.given('small', 'snake').p('silver', 'maybe') == 1 / 1
assert Pr.given('small', 'snake').p('silver', 'no') == 0 / 1
assert Pr.given('normal', 'dog').p('white', 'yes') == 1 / 1
assert Pr.given('normal', 'dog').p('silver', 'yes') == 0 / 1
assert Pr.given('normal', 'dog').p('yellow', 'maybe') == 0 / 1
SA = JointVariables(sizes, animals)
PrAll = CPMF(JointVariables(colors, is_pet), SA)
PrSA = PMF(SA)
PrCcSA = CPMF(colors, SA)
PrIPcSA = CPMF(is_pet, SA)
test_p_all = 0.0
test_p_c = 0.0
test_p_ip = 0.0
for (sa, psa) in PrSA.items():
for (c, pcsa) in PrCcSA.given(sa).items():
test_p_c += pcsa * PrSA.p(sa)
for (ip, pipsa) in PrIPcSA.given(sa).items():
pall = PrAll.given(sa).p(c, ip)
test_p_all += pall * PrSA.p(sa)
test_p_ip += pipsa * PrSA.p(sa)
assert almostEqual(1, test_p_all)
assert almostEqual(1, test_p_c)
assert almostEqual(1, test_p_ip)
def test_make_cpmf_PrXcZ_variant_1() -> None:
V0 = Variable([0, 1, 1, 1, 0, 1, 0, 1])
V1 = Variable([0, 0, 1, 1, 0, 1, 1, 1])
PrXZ = PMF(JointVariables(V0, V1))
PrXZ.IDs(1000, 1111)
assert PrXZ.IDs() == (1000, 1111)
assert PrXZ.p((0, 0)) == 2 / 8
assert PrXZ.p((0, 1)) == 1 / 8
assert PrXZ.p((1, 0)) == 1 / 8
assert PrXZ.p((1, 1)) == 4 / 8
def test_pmf_summing_over_variable():
V0 = Variable([0, 1, 1, 1, 0, 1, 0, 1])
V1 = Variable([0, 0, 1, 1, 0, 1, 1, 1])
V2 = Variable([0, 0, 0, 0, 1, 0, 1, 1])
V3 = Variable([0, 0, 0, 0, 0, 0, 1, 1])
V0.ID = 1000
V1.ID = 1111
V2.ID = 1222
V3.ID = 1333
Pr = PMF(JointVariables(V0, V1, V2, V3))
assert Pr.IDs() == (1000, 1111, 1222, 1333)
assert Pr.p((0, 0, 0, 0)) == 1 / 8
assert Pr.p((1, 0, 0, 0)) == 1 / 8
assert Pr.p((1, 1, 0, 0)) == 3 / 8
assert Pr.p((0, 0, 1, 0)) == 1 / 8
assert Pr.p((0, 1, 1, 1)) == 1 / 8
assert Pr.p((1, 1, 1, 1)) == 1 / 8
Pr = Pr.sum_over(V2.ID)
assert sum(Pr.probabilities.values()) == 1
assert Pr.p((0, 0, 0)) == 2 / 8
assert Pr.p((1, 0, 0)) == 1 / 8
assert Pr.p((1, 1, 0)) == 3 / 8
assert Pr.p((0, 1, 1)) == 1 / 8
assert Pr.p((1, 1, 1)) == 1 / 8
assert Pr.IDs() == (V0.ID, V1.ID, V3.ID)
Pr = Pr.sum_over(V1.ID)
assert sum(Pr.probabilities.values()) == 1
assert Pr.p((0, 0)) == 2 / 8
assert Pr.p((1, 0)) == 4 / 8
assert Pr.p((0, 1)) == 1 / 8
assert Pr.p((1, 1)) == 1 / 8
assert Pr.IDs() == (V0.ID, V3.ID)
Pr = Pr.sum_over(V0.ID)
assert sum(Pr.probabilities.values()) == 1
print(Pr.probabilities)
assert Pr.p(0) == 6 / 8
assert Pr.p(1) == 2 / 8
assert Pr.IDs() == (V3.ID,)
def test_single_variable_pmf():
variable = Variable(numpy.array([3, 5, 1, 1, 4, 3, 7, 0, 2, 1, 0, 5, 4, 7, 2, 4]))
variable.ID = 1
variable.name = 'test_variable_1'
variable.update_values()
assert [0, 1, 2, 3, 4, 5, 7] == variable.values
PrVariable = PMF(variable)
expected_counts = {0: 2,
1: 3,
2: 2,
3: 2,
4: 3,
5: 2,
7: 2}
assert PrVariable.value_counts == expected_counts
expected_counts = {0: 2 / 16,
1: 3 / 16,
2: 2 / 16,
3: 2 / 16,
4: 3 / 16,
5: 2 / 16,
7: 2 / 16}
assert PrVariable.probabilities == expected_counts
assert 1 == sum(PrVariable.values())
assert 2 / 16 == PrVariable.p(3)
assert 2 / 16 == PrVariable.p(2)
assert 2 / 16 == PrVariable.p(5)
ev = 0
for (v, pv) in PrVariable.items():
ev += pv * v
assert 3.0625 == ev
def mutual_information(
PrXY: PMF,
PrX: PMF,
PrY: PMF,
base=2,
) -> float:
logarithm = create_logarithm_function(base)
MI = 0.0
for (x, px) in PrX.items():
for (y, py) in PrY.items():
pxy = PrXY.p(x, y)
if pxy == 0 or px == 0 or py == 0:
continue
else:
pMI = pxy * logarithm(pxy / (px * py))
MI += pMI
return MI