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test_dist_math.py
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import numpy as np
import numpy.testing as npt
import theano.tensor as tt
import theano
import theano.tests.unittest_tools as utt
import pymc3 as pm
from scipy import stats, interpolate
import pytest
from ..theanof import floatX
from ..distributions import Discrete
from ..distributions.dist_math import (
bound, factln, alltrue_scalar, MvNormalLogp, SplineWrapper)
def test_bound():
logp = tt.ones((10, 10))
cond = tt.ones((10, 10))
assert np.all(bound(logp, cond).eval() == logp.eval())
logp = tt.ones((10, 10))
cond = tt.zeros((10, 10))
assert np.all(bound(logp, cond).eval() == (-np.inf * logp).eval())
logp = tt.ones((10, 10))
cond = True
assert np.all(bound(logp, cond).eval() == logp.eval())
logp = tt.ones(3)
cond = np.array([1, 0, 1])
assert not np.all(bound(logp, cond).eval() == 1)
assert np.prod(bound(logp, cond).eval()) == -np.inf
logp = tt.ones((2, 3))
cond = np.array([[1, 1, 1], [1, 0, 1]])
assert not np.all(bound(logp, cond).eval() == 1)
assert np.prod(bound(logp, cond).eval()) == -np.inf
def test_alltrue_scalar():
assert alltrue_scalar([]).eval()
assert alltrue_scalar([True]).eval()
assert alltrue_scalar([tt.ones(10)]).eval()
assert alltrue_scalar([tt.ones(10),
5 * tt.ones(101)]).eval()
assert alltrue_scalar([np.ones(10),
5 * tt.ones(101)]).eval()
assert alltrue_scalar([np.ones(10),
True,
5 * tt.ones(101)]).eval()
assert alltrue_scalar([np.array([1, 2, 3]),
True,
5 * tt.ones(101)]).eval()
assert not alltrue_scalar([False]).eval()
assert not alltrue_scalar([tt.zeros(10)]).eval()
assert not alltrue_scalar([True,
False]).eval()
assert not alltrue_scalar([np.array([0, -1]),
tt.ones(60)]).eval()
assert not alltrue_scalar([np.ones(10),
False,
5 * tt.ones(101)]).eval()
def test_alltrue_shape():
vals = [True, tt.ones(10), tt.zeros(5)]
assert alltrue_scalar(vals).eval().shape == ()
class MultinomialA(Discrete):
def __init__(self, n, p, *args, **kwargs):
super(MultinomialA, self).__init__(*args, **kwargs)
self.n = n
self.p = p
def logp(self, value):
n = self.n
p = self.p
return bound(factln(n) - factln(value).sum() + (value * tt.log(p)).sum(),
value >= 0,
0 <= p, p <= 1,
tt.isclose(p.sum(), 1),
broadcast_conditions=False
)
class MultinomialB(Discrete):
def __init__(self, n, p, *args, **kwargs):
super(MultinomialB, self).__init__(*args, **kwargs)
self.n = n
self.p = p
def logp(self, value):
n = self.n
p = self.p
return bound(factln(n) - factln(value).sum() + (value * tt.log(p)).sum(),
tt.all(value >= 0),
tt.all(0 <= p), tt.all(p <= 1),
tt.isclose(p.sum(), 1),
broadcast_conditions=False
)
def test_multinomial_bound():
x = np.array([1, 5])
n = x.sum()
with pm.Model() as modelA:
p_a = pm.Dirichlet('p', floatX(np.ones(2)))
MultinomialA('x', n, p_a, observed=x)
with pm.Model() as modelB:
p_b = pm.Dirichlet('p', floatX(np.ones(2)))
MultinomialB('x', n, p_b, observed=x)
assert np.isclose(modelA.logp({'p_stickbreaking__': [0]}),
modelB.logp({'p_stickbreaking__': [0]}))
class TestMvNormalLogp():
def test_logp(self):
np.random.seed(42)
chol_val = np.array([[1, 0.9], [0, 2]])
cov_val = np.dot(chol_val, chol_val.T)
cov = tt.matrix('cov')
cov.tag.test_value = cov_val
delta_val = np.random.randn(5, 2)
delta = tt.matrix('delta')
delta.tag.test_value = delta_val
expect = stats.multivariate_normal(mean=np.zeros(2), cov=cov_val)
expect = expect.logpdf(delta_val).sum()
logp = MvNormalLogp()(cov, delta)
logp_f = theano.function([cov, delta], logp)
logp = logp_f(cov_val, delta_val)
npt.assert_allclose(logp, expect)
def test_grad(self):
np.random.seed(42)
def func(chol_vec, delta):
chol = tt.stack([
tt.stack([tt.exp(0.1 * chol_vec[0]), 0]),
tt.stack([chol_vec[1], 2 * tt.exp(chol_vec[2])]),
])
cov = tt.dot(chol, chol.T)
return MvNormalLogp()(cov, delta)
chol_vec_val = np.array([0.5, 1., -0.1])
delta_val = np.random.randn(1, 2)
try:
utt.verify_grad(func, [chol_vec_val, delta_val])
except ValueError as e:
print(e.args[0])
delta_val = np.random.randn(5, 2)
utt.verify_grad(func, [chol_vec_val, delta_val])
@pytest.mark.skip(reason="Fix in theano not released yet: Theano#5908")
@theano.configparser.change_flags(compute_test_value="ignore")
def test_hessian(self):
chol_vec = tt.vector('chol_vec')
chol_vec.tag.test_value = np.array([0.1, 2, 3])
chol = tt.stack([
tt.stack([tt.exp(0.1 * chol_vec[0]), 0]),
tt.stack([chol_vec[1], 2 * tt.exp(chol_vec[2])]),
])
cov = tt.dot(chol, chol.T)
delta = tt.matrix('delta')
delta.tag.test_value = np.ones((5, 2))
logp = MvNormalLogp()(cov, delta)
g_cov, g_delta = tt.grad(logp, [cov, delta])
tt.grad(g_delta.sum() + g_cov.sum(), [delta, cov])
class TestSplineWrapper(object):
def test_grad(self):
x = np.linspace(0, 1, 100)
y = x * x
spline = SplineWrapper(interpolate.InterpolatedUnivariateSpline(x, y, k=1))
utt.verify_grad(spline, [0.5])
def test_hessian(self):
x = np.linspace(0, 1, 100)
y = x * x
spline = SplineWrapper(interpolate.InterpolatedUnivariateSpline(x, y, k=1))
x_var = tt.dscalar('x')
g_x, = tt.grad(spline(x_var), [x_var])
with pytest.raises(NotImplementedError):
tt.grad(g_x, [x_var])