def test_marginalize(self):
factor = Factor(
['A', 'B', 'C'],
{
"A": [0, 1],
"B": [0, 1, 2],
"C": [0, 1],
},
{
# (A, B, C): P(A, B, C)
(0, 0, 0): 0.01,
(0, 0, 1): 0.02,
(0, 1, 0): 0.03,
(0, 1, 1): 0.04,
(0, 2, 0): 0.05,
(0, 2, 1): 0.05,
(1, 0, 0): 0.06,
(1, 0, 1): 0.07,
(1, 1, 0): 0.08,
(1, 1, 1): 0.09,
(1, 2, 0): 0.1,
(1, 2, 1): 0.4,
})
factor_a = factor.marginalize(["A"])
self.assertAlmostEqual(factor_a[(0,)], 0.2)
self.assertAlmostEqual(factor_a[(1,)], 0.8)
factor_ac = factor.marginalize(["A", "C"])
self.assertAlmostEqual(factor_ac[(0, 0)], 0.09)
def test_expected_value_squared(self):
alpha = Factor(
['X0', 'X1'],
{
'X0': ['x0_0', 'x0_1'],
'X1': ['x1_0', 'x1_1'],
},
{
('x0_0', 'x1_0'): 8,
('x0_0', 'x1_1'): 1,
('x0_1', 'x1_0'): 2,
('x0_1', 'x1_1'): 1,
}
)
sum_of_alphas = alpha.marginalize(['X1'])
expected_value_squared = alpha * (alpha + 1) / (sum_of_alphas * (sum_of_alphas + 1))
self.assertAlmostEqual(expected_value_squared[('x0_0', 'x1_0')], 72.0/110)
self.assertAlmostEqual(expected_value_squared[('x0_0', 'x1_1')], 1.0/3)
self.assertAlmostEqual(expected_value_squared[('x0_1', 'x1_0')], 6.0/110)
self.assertAlmostEqual(expected_value_squared[('x0_1', 'x1_1')], 1.0/3)
def test_alphas(self):
alpha = Factor(
['X0', 'X1', 'X2', 'X3'],
{
'X0': ['x0_0', 'x0_1'],
'X1': ['x1_0', 'x1_1'],
'X2': ['x2_0', 'x2_1'],
'X3': ['x3_0', 'x3_1'],
},
{
('x0_0', 'x1_0', 'x2_0', 'x3_0'): 1,
('x0_0', 'x1_0', 'x2_0', 'x3_1'): 1,
('x0_0', 'x1_0', 'x2_1', 'x3_0'): 1,
('x0_0', 'x1_0', 'x2_1', 'x3_1'): 2,
('x0_0', 'x1_1', 'x2_0', 'x3_0'): 5,
('x0_0', 'x1_1', 'x2_0', 'x3_1'): 1,
('x0_0', 'x1_1', 'x2_1', 'x3_0'): 3,
('x0_0', 'x1_1', 'x2_1', 'x3_1'): 1,
('x0_1', 'x1_0', 'x2_0', 'x3_0'): 1,
('x0_1', 'x1_0', 'x2_0', 'x3_1'): 1,
('x0_1', 'x1_0', 'x2_1', 'x3_0'): 1,
('x0_1', 'x1_0', 'x2_1', 'x3_1'): 1,
('x0_1', 'x1_1', 'x2_0', 'x3_0'): 1,
('x0_1', 'x1_1', 'x2_0', 'x3_1'): 1,
('x0_1', 'x1_1', 'x2_1', 'x3_0'): 1,
('x0_1', 'x1_1', 'x2_1', 'x3_1'): 1,
})
X0 = Factor(
['X0'],
{
'X0': ['x0_0', 'x0_1']
},
{
('x0_0',): 1,
('x0_1',): 0,
})
X1 = Factor(
['X1'],
{
'X1': ['x1_0', 'x1_1']
},
{
('x1_0',): 0,
('x1_1',): 1,
})
X2 = Factor(
['X2'],
{
'X2': ['x2_0', 'x2_1']
},
{
('x2_0',): 1,
('x2_1',): 0,
})
X3 = Factor(
['X3'],
{
'X3': ['x3_0', 'x3_1']
},
{
('x3_0',): 1,
('x3_1',): 0,
})
# Compute message to X1.
cavity = X0 * X2 * X3
self.assertAlmostEqual(cavity[('x0_0', 'x2_0', 'x3_0')], 1.0)
sum_of_alphas = alpha.marginalize(['X1', 'X2', 'X3'])
self.assertAlmostEqual(sum_of_alphas[('x1_1', 'x2_0', 'x3_0')], 6)
expected_value = alpha / sum_of_alphas
self.assertAlmostEqual(expected_value[('x0_0', 'x1_1', 'x2_1', 'x3_0')], 0.75)
factor = cavity * expected_value
self.assertAlmostEqual(factor[('x0_0', 'x1_1', 'x2_0', 'x3_0')], 5.0/6)
msg = factor.marginalize(['X1'])
self.assertAlmostEqual(msg[('x1_0',)], 0.5)
# Compute message to X0.
cavity = X1 * X2 * X3
self.assertAlmostEqual(cavity[('x1_1', 'x2_0', 'x3_0')], 1.0)
self.assertAlmostEqual(cavity[('x1_0', 'x2_0', 'x3_0')], 0.0)
sum_of_alphas = alpha.marginalize(['X1', 'X2', 'X3'])
expected_value = alpha / sum_of_alphas
self.assertAlmostEqual(expected_value[('x0_0', 'x1_1', 'x2_0', 'x3_1')], 0.5)
factor = cavity * expected_value
msg = factor.marginalize(['X0'])
self.assertAlmostEqual(msg[('x0_0',)], 5.0/6)
# Compute w_0.
sum_of_alphas = alpha.marginalize(['X1', 'X2', 'X3'])
expected_value = alpha / sum_of_alphas
belief = X0 * X1 * X2 * X3
factor = belief * expected_value
msg = factor.marginalize(['X1', 'X2', 'X3'])
w0 = msg.sum_other()
self.assertAlmostEqual(w0[('x1_0', 'x2_0', 'x3_0')], 5.0/6)
# Compute w_k.
# When we want to compute w_k for each j, we can just compute the belief.
# Each j is denoted by an assignment of parents, which in this case is
# the assignment of X1, X2, X3, and each k is a value of a child, in
# this case it's the value of X0.
# For given j and k, we can get the value of w_jk, by getting one row
# from w_k.
w_k = X0 * X1 * X2 * X3
self.assertAlmostEqual(w_k[('x0_0', 'x1_0', 'x2_0', 'x3_0')], 0)
self.assertAlmostEqual(w_k[('x0_0', 'x1_1', 'x2_0', 'x3_0')], 1)
# Compute expected value of p(theta)
sum_of_alphas = alpha.marginalize(['X1', 'X2', 'X3'])
expected_value_0 = alpha / sum_of_alphas
sum_of_alphas_plus_1 = alpha.marginalize(['X1', 'X2', 'X3'])
sum_of_alphas_plus_1 += 1
expected_values = [w0 * expected_value_0]
self.assertAlmostEqual(expected_values[0][('x0_0', 'x1_0', 'x2_0', 'x3_0')], 5.0/12)
self.assertAlmostEqual(expected_values[0][('x0_1', 'x1_0', 'x2_0', 'x3_0')], 5.0/12)
for k in X0.variable_values['X0']:
new_alpha = copy.deepcopy(alpha)
for i, item in enumerate(new_alpha):
(assignment, value) = item
if assignment[0] == k:
new_alpha[assignment] += 1
expected_value_k = new_alpha / sum_of_alphas_plus_1
expected_values.append(w_k * expected_value * expected_value_k)
expected_value_sum = reduce(operator.add, expected_values)
