def test_sum_of_sums():
w \
= 0.3*(0.4*(X >> norm()) | 0.6*(X >> norm())) \
| 0.7*(0.1*(X >> norm()) | 0.9*(X >> norm()))
assert isinstance(w, SumSPE)
assert len(w.children) == 4
assert allclose(float(w.weights[0]), log(0.3) + log(0.4))
assert allclose(float(w.weights[1]), log(0.3) + log(0.6))
assert allclose(float(w.weights[2]), log(0.7) + log(0.1))
assert allclose(float(w.weights[3]), log(0.7) + log(0.9))
w \
= 0.3*(0.4*(X >> norm()) | 0.6*(X >> norm())) \
| 0.2*(0.1*(X >> norm()) | 0.9*(X >> norm()))
assert isinstance(w, PartialSumSPE)
assert allclose(float(w.weights[0]), 0.3)
assert allclose(float(w.weights[1]), 0.2)
a = w | 0.5*(X >> gamma(a=1))
assert isinstance(a, SumSPE)
assert len(a.children) == 5
assert allclose(float(a.weights[0]), log(0.3) + log(0.4))
assert allclose(float(a.weights[1]), log(0.3) + log(0.6))
assert allclose(float(a.weights[2]), log(0.2) + log(0.1))
assert allclose(float(a.weights[3]), log(0.2) + log(0.9))
assert allclose(float(a.weights[4]), log(0.5))
# Wrong symbol.
with pytest.raises(ValueError):
z = w | 0.4*(Y >> gamma(a=1))
def test_or_and():
with pytest.raises(ValueError):
(0.3*(X >> norm()) | 0.7*(Y >> gamma(a=1))) & (Z >> norm())
a = (0.3*(X >> norm()) | 0.7*(X >> gamma(a=1))) & (Z >> norm())
assert isinstance(a, ProductSPE)
assert isinstance(a.children[0], SumSPE)
assert isinstance(a.children[1], ContinuousLeaf)
def test_product_leaf():
with pytest.raises(TypeError):
0.3*(X >> gamma(a=1)) & (X >> norm())
with pytest.raises(TypeError):
(X >> norm()) & 0.3*(X >> gamma(a=1))
with pytest.raises(ValueError):
(X >> norm()) & (X >> gamma(a=1))
y = (X >> norm()) & (Y >> gamma(a=1)) & (Z >> norm())
assert isinstance(y, ProductSPE)
assert len(y.children) == 3
assert y.get_symbols() == frozenset([X, Y, Z])
def test_sum_leaf():
# Cannot sum leaves without weights.
with pytest.raises(TypeError):
(X >> norm()) | (X >> gamma(a=1))
# Cannot sum a leaf with a partial sum.
with pytest.raises(TypeError):
0.3*(X >> norm()) | (X >> gamma(a=1))
# Cannot sum a leaf with a partial sum.
with pytest.raises(TypeError):
(X >> norm()) | 0.3*(X >> gamma(a=1))
# Wrong symbol.
with pytest.raises(ValueError):
0.4*(X >> norm()) | 0.6*(Y >> gamma(a=1))
# Sum exceeds one.
with pytest.raises(ValueError):
0.4*(X >> norm()) | 0.7*(Y >> gamma(a=1))
y = 0.4*(X >> norm()) | 0.3*(X >> gamma(a=1))
assert isinstance(y, PartialSumSPE)
assert len(y.weights) == 2
assert allclose(float(y.weights[0]), 0.4)
assert allclose(float(y.weights[1]), 0.3)
y = 0.4*(X >> norm()) | 0.6*(X >> gamma(a=1))
assert isinstance(y, SumSPE)
assert len(y.weights) == 2
assert allclose(float(y.weights[0]), log(0.4))
assert allclose(float(y.weights[1]), log(0.6))
# Sum exceeds one.
with pytest.raises(TypeError):
y | 0.7 * (X >> norm())
y = 0.4*(X >> norm()) | 0.3*(X >> gamma(a=1)) | 0.1*(X >> norm())
assert isinstance(y, PartialSumSPE)
assert len(y.weights) == 3
assert allclose(float(y.weights[0]), 0.4)
assert allclose(float(y.weights[1]), 0.3)
assert allclose(float(y.weights[2]), 0.1)
y = 0.4*(X >> norm()) | 0.3*(X >> gamma(a=1)) | 0.3*(X >> norm())
assert isinstance(y, SumSPE)
assert len(y.weights) == 3
assert allclose(float(y.weights[0]), log(0.4))
assert allclose(float(y.weights[1]), log(0.3))
assert allclose(float(y.weights[2]), log(0.3))
with pytest.raises(TypeError):
(0.3)*(0.3*(X >> norm()))
with pytest.raises(TypeError):
(0.3*(X >> norm())) * (0.3)
with pytest.raises(TypeError):
0.3*(0.3*(X >> norm()) | 0.5*(X >> norm()))
w = 0.3*(0.4*(X >> norm()) | 0.6*(X >> norm()))
assert isinstance(w, PartialSumSPE)
def test_sum_normal_gamma():
X = Id('X')
weights = [log(Fraction(2, 3)), log(Fraction(1, 3))]
spe = SumSPE([
X >> norm(loc=0, scale=1),
X >> gamma(loc=0, a=1),
], weights)
assert spe.logprob(X > 0) == logsumexp([
spe.weights[0] + spe.children[0].logprob(X > 0),
spe.weights[1] + spe.children[1].logprob(X > 0),
])
assert spe.logprob(X < 0) == log(Fraction(2, 3)) + log(Fraction(1, 2))
samples = spe.sample(100, prng=numpy.random.RandomState(1))
assert all(s[X] for s in samples)
spe.sample_func(lambda X: abs(X**3), 100)
with pytest.raises(ValueError):
spe.sample_func(lambda Y: abs(X**3), 100)
spe_condition = spe.condition(X < 0)
assert isinstance(spe_condition, ContinuousLeaf)
assert spe_condition.conditioned
assert spe_condition.logprob(X < 0) == 0
samples = spe_condition.sample(100)
assert all(s[X] < 0 for s in samples)
assert spe.logprob(X < 0) == logsumexp([
spe.weights[0] + spe.children[0].logprob(X < 0),
spe.weights[1] + spe.children[1].logprob(X < 0),
])
def test_logpdf_mixture_real_continuous_continuous():
spe = X >> (.3*norm() | .7*gamma(a=1))
assert allclose(
spe.logpdf({X: .5}),
logsumexp([
log(.3) + spe.children[0].logpdf({X: 0.5}),
log(.7) + spe.children[1].logpdf({X: 0.5}),
]))
def test_product_condition_or_probabilithy_zero():
X = Id('X')
Y = Id('Y')
spe = ProductSPE([X >> norm(loc=0, scale=1), Y >> gamma(a=1)])
# Condition on event which has probability zero.
event = (X > 2) & (X < 2)
with pytest.raises(ValueError):
spe.condition(event)
assert spe.logprob(event) == -float('inf')
# Condition on event which has probability zero.
event = (Y < 0) | (Y < -1)
with pytest.raises(ValueError):
spe.condition(event)
assert spe.logprob(event) == -float('inf')
# Condition on an event where one clause has probability
# zero, yielding a single product.
spe_condition = spe.condition((Y < 0) | ((Log(X) >= 0) & (1 <= Y)))
assert isinstance(spe_condition, ProductSPE)
assert spe_condition.children[0].symbol == X
assert spe_condition.children[0].conditioned
assert spe_condition.children[0].support == Interval(1, oo)
assert spe_condition.children[1].symbol == Y
assert spe_condition.children[1].conditioned
assert spe_condition.children[0].support == Interval(1, oo)
# We have (X < 2) & ~(1 < exp(|3X**2|) is empty.
# Thus Y remains unconditioned,
# and X is partitioned into (-oo, 0) U (0, oo) with equal weight.
event = (Exp(abs(3 * X**2)) > 1) | ((Log(Y) < 0.5) & (X < 2))
spe_condition = spe.condition(event)
#
# The most concise representation of spe_condition is:
# (Product (Sum [.5 .5] X|X<0 X|X>0) Y)
assert isinstance(spe_condition, ProductSPE)
assert isinstance(spe_condition.children[0], SumSPE)
assert spe_condition.children[0].weights == (-log(2), -log(2))
assert spe_condition.children[0].children[0].conditioned
assert spe_condition.children[0].children[1].conditioned
assert spe_condition.children[0].children[0].support \
in [Interval.Ropen(-oo, 0), Interval.Lopen(0, oo)]
assert spe_condition.children[0].children[1].support \
in [Interval.Ropen(-oo, 0), Interval.Lopen(0, oo)]
assert spe_condition.children[0].children[0].support \
!= spe_condition.children[0].children[1].support
assert spe_condition.children[1].symbol == Y
assert not spe_condition.children[1].conditioned
def test_sum_simplify_nested_sum_1():
X = Id('X')
children = [
SumSPE(
[X >> norm(loc=0, scale=1), X >> norm(loc=0, scale=2)],
[log(0.4), log(0.6)]),
X >> gamma(loc=0, a=1),
]
spe = SumSPE(children, [log(0.7), log(0.3)])
assert spe.size() == 4
assert spe.children == (
children[0].children[0],
children[0].children[1],
children[1]
)
assert allclose(spe.weights[0], log(0.7) + log(0.4))
assert allclose(spe.weights[1], log(0.7) + log(0.6))
assert allclose(spe.weights[2], log(0.3))
def test_product_distribution_normal_gamma_basic():
X1 = Id('X1')
X2 = Id('X2')
X3 = Id('X3')
X4 = Id('X4')
children = [
ProductSPE([
X1 >> norm(loc=0, scale=1),
X4 >> norm(loc=10, scale=1),
]), X2 >> gamma(loc=0, a=1), X3 >> norm(loc=2, scale=3)
]
spe = ProductSPE(children)
assert spe.children == (
children[0].children[0],
children[0].children[1],
children[1],
children[2],
)
assert spe.get_symbols() == frozenset([X1, X2, X3, X4])
assert spe.size() == 5
samples = spe.sample(2)
assert len(samples) == 2
for sample in samples:
assert len(sample) == 4
assert all([X in sample for X in (X1, X2, X3, X4)])
samples = spe.sample_subset((X1, X2), 10)
assert len(samples) == 10
for sample in samples:
assert len(sample) == 2
assert X1 in sample
assert X2 in sample
samples = spe.sample_func(lambda X1, X2, X3: (X1, (X2**2, X3)), 1)
assert len(samples) == 1
assert len(samples[0]) == 2
assert len(samples[0][1]) == 2
with pytest.raises(ValueError):
spe.sample_func(lambda X1, X5: X1 + X4, 1)
def test_sum_normal_gamma_exposed():
X = Id('X')
W = Id('W')
weights = W >> choice({
'0': Fraction(2, 3),
'1': Fraction(1, 3),
})
children = {
'0': X >> norm(loc=0, scale=1),
'1': X >> gamma(loc=0, a=1),
}
spe = ExposedSumSPE(children, weights)
assert spe.logprob(W << {'0'}) == log(Fraction(2, 3))
assert spe.logprob(W << {'1'}) == log(Fraction(1, 3))
assert allclose(spe.logprob((W << {'0'}) | (W << {'1'})), 0)
assert spe.logprob((W << {'0'}) & (W << {'1'})) == -float('inf')
assert allclose(spe.logprob((W << {'0', '1'}) & (X < 1)),
spe.logprob(X < 1))
assert allclose(spe.logprob((W << {'0'}) & (X < 1)),
spe.weights[0] + spe.children[0].logprob(X < 1))
spe_condition = spe.condition((W << {'1'}) | (W << {'0'}))
assert isinstance(spe_condition, SumSPE)
assert len(spe_condition.weights) == 2
assert \
allclose(spe_condition.weights[0], log(Fraction(2,3))) \
and allclose(spe_condition.weights[0], log(Fraction(2,3))) \
or \
allclose(spe_condition.weights[1], log(Fraction(2,3))) \
and allclose(spe_condition.weights[0], log(Fraction(2,3))
)
spe_condition = spe.condition((W << {'1'}))
assert isinstance(spe_condition, ProductSPE)
assert isinstance(spe_condition.children[0], NominalLeaf)
assert isinstance(spe_condition.children[1], ContinuousLeaf)
assert spe_condition.logprob(X < 5) == spe.children[1].logprob(X < 5)
def test_product_inclusion_exclusion_basic():
X = Id('X')
Y = Id('Y')
spe = ProductSPE([X >> norm(loc=0, scale=1), Y >> gamma(a=1)])
a = spe.logprob(X > 0.1)
b = spe.logprob(Y < 0.5)
c = spe.logprob((X > 0.1) & (Y < 0.5))
d = spe.logprob((X > 0.1) | (Y < 0.5))
e = spe.logprob((X > 0.1) | ((Y < 0.5) & ~(X > 0.1)))
f = spe.logprob(~(X > 0.1))
g = spe.logprob((Y < 0.5) & ~(X > 0.1))
assert allclose(a, spe.children[0].logprob(X > 0.1))
assert allclose(b, spe.children[1].logprob(Y < 0.5))
# Pr[A and B] = Pr[A] * Pr[B]
assert allclose(c, a + b)
# Pr[A or B] = Pr[A] + Pr[B] - Pr[AB]
assert allclose(d, logdiffexp(logsumexp([a, b]), c))
# Pr[A or B] = Pr[A] + Pr[B & ~A]
assert allclose(e, d)
# Pr[A and B] = Pr[A] * Pr[B]
assert allclose(g, b + f)
# Pr[A or (B & ~A)] = Pr[A] + Pr[B & ~A]
assert allclose(e, logsumexp([a, b + f]))
# (A => B) => Pr[A or B] = Pr[B]
# i.e.,k (X > 1) => (X > 0).
assert allclose(spe.logprob((X > 0) | (X > 1)), spe.logprob(X > 0))
# Positive probability event.
# Pr[A] = 1 - Pr[~A]
event = ((0 < X) < 0.5) | ((Y < 0) & (1 < X))
assert allclose(spe.logprob(event), logdiffexp(0, spe.logprob(~event)))
# Probability zero event.
event = ((0 < X) < 0.5) & ((Y < 0) | (1 < X))
assert isinf_neg(spe.logprob(event))
assert allclose(spe.logprob(~event), 0)
def test_product_condition_basic():
X = Id('X')
Y = Id('Y')
spe = ProductSPE([X >> norm(loc=0, scale=1), Y >> gamma(a=1)])
# Condition on (X > 0) and ((X > 0) | (Y < 0))
# where the second clause reduces to first as Y < 0
# has probability zero.
for event in [(X > 0), (X > 0) | (Y < 0)]:
dX = spe.condition(event)
assert isinstance(dX, ProductSPE)
assert dX.children[0].symbol == Id('X')
assert dX.children[0].conditioned
assert dX.children[0].support == Interval.open(0, oo)
assert dX.children[1].symbol == Id('Y')
assert not dX.children[1].conditioned
assert dX.children[1].Fl == 0
assert dX.children[1].Fu == 1
# Condition on (Y < 0.5)
dY = spe.condition(Y < 0.5)
assert isinstance(dY, ProductSPE)
assert dY.children[0].symbol == Id('X')
assert not dY.children[0].conditioned
assert dY.children[1].symbol == Id('Y')
assert dY.children[1].conditioned
assert dY.children[1].support == Interval.Ropen(0, 0.5)
# Condition on (X > 0) & (Y < 0.5)
dXY_and = spe.condition((X > 0) & (Y < 0.5))
assert isinstance(dXY_and, ProductSPE)
assert dXY_and.children[0].symbol == Id('X')
assert dXY_and.children[0].conditioned
assert dXY_and.children[0].support == Interval.open(0, oo)
assert dXY_and.children[1].symbol == Id('Y')
assert dXY_and.children[1].conditioned
assert dXY_and.children[1].support == Interval.Ropen(0, 0.5)
# Condition on (X > 0) | (Y < 0.5)
event = (X > 0) | (Y < 0.5)
dXY_or = spe.condition((X > 0) | (Y < 0.5))
assert isinstance(dXY_or, SumSPE)
assert all(isinstance(d, ProductSPE) for d in dXY_or.children)
assert allclose(dXY_or.logprob(X > 0), dXY_or.weights[0])
samples = dXY_or.sample(100, prng=numpy.random.RandomState(1))
assert all(event.evaluate(sample) for sample in samples)
# Condition on a disjoint union with one term in second clause.
dXY_disjoint_one = spe.condition((X > 0) & (Y < 0.5) | (X <= 0))
assert isinstance(dXY_disjoint_one, SumSPE)
component_0 = dXY_disjoint_one.children[0]
assert component_0.children[0].symbol == Id('X')
assert component_0.children[0].conditioned
assert component_0.children[0].support == Interval.open(0, oo)
assert component_0.children[1].symbol == Id('Y')
assert component_0.children[1].conditioned
assert component_0.children[1].support == Interval.Ropen(0, 0.5)
component_1 = dXY_disjoint_one.children[1]
assert component_1.children[0].symbol == Id('X')
assert component_1.children[0].conditioned
assert component_1.children[0].support == Interval(-oo, 0)
assert component_1.children[1].symbol == Id('Y')
assert not component_1.children[1].conditioned
# Condition on a disjoint union with two terms in each clause
dXY_disjoint_two = spe.condition((X > 0) & (Y < 0.5)
| ((X <= 0) & ~(Y < 3)))
assert isinstance(dXY_disjoint_two, SumSPE)
component_0 = dXY_disjoint_two.children[0]
assert component_0.children[0].symbol == Id('X')
assert component_0.children[0].conditioned
assert component_0.children[0].support == Interval.open(0, oo)
assert component_0.children[1].symbol == Id('Y')
assert component_0.children[1].conditioned
assert component_0.children[1].support == Interval.Ropen(0, 0.5)
component_1 = dXY_disjoint_two.children[1]
assert component_1.children[0].symbol == Id('X')
assert component_1.children[0].conditioned
assert component_1.children[0].support == Interval(-oo, 0)
assert component_1.children[1].symbol == Id('Y')
assert component_1.children[1].conditioned
assert component_1.children[1].support == Interval(3, oo)
# Some various conditioning.
spe.condition((X > 0) & (Y < 0.5) | ((X <= 1) | ~(Y < 3)))
spe.condition((X > 0) & (Y < 0.5) | ((X <= 1) & (Y < 3)))
from sppl.sets import EmptySet
from sppl.transforms import EventFiniteNominal
from sppl.transforms import Exp
from sppl.transforms import Exponential
from sppl.transforms import Id
from sppl.transforms import Log
from sppl.transforms import Logarithm
X = Id('X')
Y = Id('Y')
spes = [
X >> norm(loc=0, scale=1),
X >> poisson(mu=7),
Y >> choice({'a': 0.5, 'b': 0.5}),
(X >> norm(loc=0, scale=1)) & (Y >> gamma(a=1)),
0.2*(X >> norm(loc=0, scale=1)) | 0.8*(X >> gamma(a=1)),
((X >> norm(loc=0, scale=1)) & (Y >> gamma(a=1))).constrain({Y:1}),
]
@pytest.mark.parametrize('spe', spes)
def test_serialize_equal(spe):
metadata = spe_to_dict(spe)
spe_json_encoded = json.dumps(metadata)
spe_json_decoded = json.loads(spe_json_encoded)
spe2 = spe_from_dict(spe_json_decoded)
assert spe2 == spe
transforms = [
X,
X**(1,3),
Exponential(X, base=3),