def test_conditional_probability(self):
# test if conditional probability is correct
# same spn as in entropy test
# only for generating the ds_context
train_data = np.array([[0.0, 1.0, 0.0], [1.0, 0.0, 1.0], [2.0, 0.0, 1.0]])
# spn
ds_context = Context(meta_types=[MetaType.DISCRETE] * 3)
ds_context.add_domains(train_data)
ds_context.parametric_type = [Categorical] * 3
spn = 0.64 * (
(
Categorical(p=[0.25, 0.75, 0.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
) + 0.36 * (
(
Categorical(p=[0.0, 0.0, 1.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
)
# tests
x_instance = np.array([1, 1, 0], dtype=float).reshape(1, -1)
self.assertAlmostEqual(conditional_probability(spn, 2, x_instance)[0][0], 0.9)
self.assertAlmostEqual(conditional_probability(spn, 0, x_instance)[0][0], 0.48)
x_instance = np.array([2, 1, 0], dtype=float).reshape(1, -1)
self.assertAlmostEqual(conditional_probability(spn, 0, x_instance)[0][0], 0.36)
def test_we_score(self):
# test if we_score is correct
"""
# explain how training data and the spn comes
# number of RVs
M = 3
# table of probabilities
p1 = 0.6
p2 = 0.3
p31 = 0.1
p32 = 0.9
# generate x1 and x2
x1 = np.random.binomial(1, p1, size=N) + np.random.binomial(1, p1, size=N)
x2 = np.random.binomial(1, p2, size=N)
x3 = np.zeros(N)
# generate x3
for i in range(N):
if x2[i] == 1:
x3[i] = np.random.binomial(1, p31, size=1)
else:
x3[i] = np.random.binomial(1, p32, size=1)
# form a matrix, rows are instances and columns are RVs
train_data = np.concatenate((x1, x2, x3)).reshape((M, N)).transpose()
"""
# only for generating the ds_context
train_data = np.array([[0.0, 1.0, 0.0], [1.0, 0.0, 1.0], [2.0, 0.0, 1.0]])
# spn
ds_context = Context(meta_types=[MetaType.DISCRETE] * 3)
ds_context.add_domains(train_data)
ds_context.parametric_type = [Categorical] * 3
spn = 0.64 * (
(
Categorical(p=[0.25, 0.75, 0.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
) + 0.36 * (
(
Categorical(p=[0.0, 0.0, 1.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
)
# test
n = 40000
x_instance = np.array([1, 1, 0], dtype=float).reshape(1, -1)
y_index = 0
we = weight_of_evidence(spn, 0, x_instance, n, ds_context.domains[y_index].shape[0])
we_true = np.array([[np.nan, 0, 0]])
we = we[~np.isnan(we)]
we_true = we_true[~np.isnan(we_true)]
self.assertTrue((we == we_true).all())
def test_mutual_info(self):
# test if mutual info is correct
# same spn as in entropy test
# only for generating the ds_context
train_data = np.array([[0.0, 1.0, 0.0], [1.0, 0.0, 1.0], [2.0, 0.0, 1.0]])
# spn
ds_context = Context(meta_types=[MetaType.DISCRETE] * 3)
ds_context.add_domains(train_data)
ds_context.parametric_type = [Categorical] * 3
spn = 0.64 * (
(
Categorical(p=[0.25, 0.75, 0.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
) + 0.36 * (
(
Categorical(p=[0.0, 0.0, 1.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
)
# real mutual info
p2 = 0.3
p3 = 0.66
h_x2 = -p2 * np.log(p2) - (1 - p2) * np.log(1 - p2)
h_x3 = -p3 * np.log(p3) - (1 - p3) * np.log(1 - p3)
h_x2x3 = -(p2 * np.log(p2) + (1 - p2) * np.log(1 - p2) + 0.9 * np.log(0.9) + 0.1 * np.log(0.1))
mi_x2x3 = h_x2 + h_x3 - h_x2x3
self.assertAlmostEqual(mi_x2x3, mutual_information(spn, ds_context, {1}, {2}))
mi_x1x2 = 0
self.assertAlmostEqual(mi_x1x2, mutual_information(spn, ds_context, {1}, {0}))
# test symmetry
self.assertAlmostEqual(
mutual_information(spn, ds_context, {2}, {1}), mutual_information(spn, ds_context, {1}, {2})
)
self.assertAlmostEqual(
mutual_information(spn, ds_context, {0, 2}, {1}), mutual_information(spn, ds_context, {1}, {0, 2})
)
# rest 0
self.assertAlmostEqual(0, mutual_information(spn, ds_context, {2, 1}, {0}))
def test_conditional_mutual_info(self):
# test if conditional mutual info is correct
# same spn as in entropy test
# only for generating the ds_context
train_data = np.array([[0.0, 1.0, 0.0], [1.0, 0.0, 1.0], [2.0, 0.0, 1.0]])
# spn
ds_context = Context(meta_types=[MetaType.DISCRETE] * 3)
ds_context.add_domains(train_data)
ds_context.parametric_type = [Categorical] * 3
spn = 0.64 * (
(
Categorical(p=[0.25, 0.75, 0.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
) + 0.36 * (
(
Categorical(p=[0.0, 0.0, 1.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
)
# real mutual info
p2 = 0.3
p3 = 0.66
h_x1 = -(0.16 * np.log(0.16) + 0.36 * np.log(0.36) + 0.48 * np.log(0.48))
h_x2x1 = -(0.7 * np.log(0.7) + 0.3 * np.log(0.3)) + h_x1
h_x3x1 = -(0.66 * np.log(0.66) + 0.34 * np.log(0.34)) + h_x1
h_x2x3 = -(p2 * np.log(p2) + (1 - p2) * np.log(1 - p2) + 0.9 * np.log(0.9) + 0.1 * np.log(0.1))
h_x2x3x1 = h_x1 + h_x2x3
cmi_x2x3_x1 = h_x2x1 + h_x3x1 - h_x2x3x1 - h_x1
self.assertAlmostEqual(cmi_x2x3_x1, conditional_mutual_information(spn, ds_context, {1}, {2}, {0}))
h_x1x3 = h_x3x1
h_x1x2x3 = h_x2x3x1
h_x3 = -p3 * np.log(p3) - (1 - p3) * np.log(1 - p3)
cmi_x1x2_x3 = h_x1x3 + h_x2x3 - h_x1x2x3 - h_x3
self.assertAlmostEqual(cmi_x1x2_x3, conditional_mutual_information(spn, ds_context, {1}, {0}, {2}))
h_x1x2x3 = h_x2x3x1
h_x2 = -p2 * np.log(p2) - (1 - p2) * np.log(1 - p2)
cmi_x1x3_x2 = h_x2x1 + h_x2x3 - h_x1x2x3 - h_x2
self.assertAlmostEqual(cmi_x1x3_x2, conditional_mutual_information(spn, ds_context, {2}, {0}, {1}))
def test_entropy(self):
# test if entropy is correct
"""
# explain how training data and the spn comes
# number of RVs
M = 3
# table of probabilities
p1 = 0.6
p2 = 0.3
p31 = 0.1
p32 = 0.9
# generate x1 and x2
x1 = np.random.binomial(1, p1, size=N) + np.random.binomial(1, p1, size=N)
x2 = np.random.binomial(1, p2, size=N)
x3 = np.zeros(N)
# generate x3
for i in range(N):
if x2[i] == 1:
x3[i] = np.random.binomial(1, p31, size=1)
else:
x3[i] = np.random.binomial(1, p32, size=1)
# form a matrix, rows are instances and columns are RVs
train_data = np.concatenate((x1, x2, x3)).reshape((M, N)).transpose()
"""
# only for generating the ds_context
train_data = np.array([[0.0, 1.0, 0.0], [1.0, 0.0, 1.0], [2.0, 0.0, 1.0]])
# spn
ds_context = Context(meta_types=[MetaType.DISCRETE] * 3)
ds_context.add_domains(train_data)
ds_context.parametric_type = [Categorical] * 3
spn = 0.64 * (
(
Categorical(p=[0.25, 0.75, 0.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
) + 0.36 * (
(
Categorical(p=[0.0, 0.0, 1.0], scope=0)
* (
0.34 * ((Categorical(p=[7 / 34, 27 / 34], scope=1) * Categorical(p=[1.0, 0.0], scope=2)))
+ 0.66 * ((Categorical(p=[21 / 22, 1 / 22], scope=1) * Categorical(p=[0.0, 1.0], scope=2)))
)
)
)
# real entropy
p2 = 0.3
h_x2 = -p2 * np.log(p2) - (1 - p2) * np.log(1 - p2)
self.assertAlmostEqual(h_x2, entropy(spn, ds_context, {1}))
h_x2x3 = -(p2 * np.log(p2) + (1 - p2) * np.log(1 - p2) + 0.9 * np.log(0.9) + 0.1 * np.log(0.1))
self.assertAlmostEqual(h_x2x3, entropy(spn, ds_context, {1, 2}))
h_x1 = -(0.16 * np.log(0.16) + 0.36 * np.log(0.36) + 0.48 * np.log(0.48))
self.assertAlmostEqual(h_x1, entropy(spn, ds_context, {0}))
h_x2x1 = -(0.7 * np.log(0.7) + 0.3 * np.log(0.3)) + h_x1
self.assertAlmostEqual(h_x2x1, entropy(spn, ds_context, {1, 0}))
h_x3x1 = -(0.66 * np.log(0.66) + 0.34 * np.log(0.34)) + h_x1
self.assertAlmostEqual(h_x3x1, entropy(spn, ds_context, {2, 0}))
h_x2x3x1 = h_x1 + h_x2x3
self.assertAlmostEqual(h_x2x3x1, entropy(spn, ds_context, {1, 2, 0}))
# test symmetry
self.assertAlmostEqual(entropy(spn, ds_context, {0, 2}), entropy(spn, ds_context, {2, 0}))
self.assertAlmostEqual(entropy(spn, ds_context, {1, 2}), entropy(spn, ds_context, {2, 1}))
