def test_lognormal_distribution(moment):
num_samples = 100000
inputs = OrderedDict(batch=bint(10))
loc = random_tensor(inputs)
scale = random_tensor(inputs).exp()
log_measure = dist.LogNormal(loc, scale)(value='x')
probe = Variable('x', reals())**moment
with monte_carlo_interpretation(particle=bint(num_samples)):
with xfail_if_not_implemented():
actual = Integrate(log_measure, probe, frozenset(['x']))
samples = backend_dist.LogNormal(loc, scale).sample((num_samples, ))
expected = (samples**moment).mean(0)
assert_close(actual.data, expected, atol=1e-2, rtol=1e-2)
def test_integrate_gaussian(int_inputs, real_inputs):
int_inputs = OrderedDict(sorted(int_inputs.items()))
real_inputs = OrderedDict(sorted(real_inputs.items()))
inputs = int_inputs.copy()
inputs.update(real_inputs)
log_measure = random_gaussian(inputs)
integrand = random_gaussian(inputs)
reduced_vars = frozenset(real_inputs)
with monte_carlo_interpretation(particle=bint(10000)):
approx = Integrate(log_measure, integrand, reduced_vars)
assert isinstance(approx, Tensor)
exact = Integrate(log_measure, integrand, reduced_vars)
assert isinstance(exact, Tensor)
assert_close(approx, exact, atol=0.1, rtol=0.1)
def test_reduce_moment_matching_moments():
x = Variable('x', reals(2))
gaussian = random_gaussian(
OrderedDict([('i', bint(2)), ('j', bint(3)), ('x', reals(2))]))
with interpretation(moment_matching):
approx = gaussian.reduce(ops.logaddexp, 'j')
with monte_carlo_interpretation(s=bint(100000)):
actual = Integrate(approx, Number(1.), 'x')
expected = Integrate(gaussian, Number(1.), {'j', 'x'})
assert_close(actual, expected, atol=1e-3, rtol=1e-3)
actual = Integrate(approx, x, 'x')
expected = Integrate(gaussian, x, {'j', 'x'})
assert_close(actual, expected, atol=1e-2, rtol=1e-2)
actual = Integrate(approx, x * x, 'x')
expected = Integrate(gaussian, x * x, {'j', 'x'})
assert_close(actual, expected, atol=1e-2, rtol=1e-2)