def test_expand(extra_shape, log_normalizer_shape, info_vec_shape,
precision_shape, dim):
rank = dim + dim
log_normalizer = torch.randn(log_normalizer_shape)
info_vec = torch.randn(info_vec_shape + (dim, ))
precision = torch.randn(precision_shape + (dim, rank))
precision = precision.matmul(precision.transpose(-1, -2))
gaussian = Gaussian(log_normalizer, info_vec, precision)
expected_shape = extra_shape + broadcast_shape(
log_normalizer_shape, info_vec_shape, precision_shape)
actual = gaussian.expand(expected_shape)
assert actual.batch_shape == expected_shape
def random_gaussian(batch_shape, dim, rank=None):
"""
Generate a random Gaussian for testing.
"""
if rank is None:
rank = dim + dim
log_normalizer = torch.randn(batch_shape)
info_vec = torch.randn(batch_shape + (dim, ))
samples = torch.randn(batch_shape + (dim, rank))
precision = torch.matmul(samples, samples.transpose(-2, -1))
result = Gaussian(log_normalizer, info_vec, precision)
assert result.dim() == dim
assert result.batch_shape == batch_shape
return result
def log_prob(self, value):
# We compute a normalized distribution as p(obs,hidden) / p(hidden).
logp_oh = self._trans
logp_h = self._trans
# Combine observation and transition factors.
logp_oh += self._obs.condition(value).event_pad(left=self.hidden_dim)
logp_h += self._obs.marginalize(right=self.obs_dim).event_pad(
left=self.hidden_dim)
# Concatenate p(obs,hidden) and p(hidden) into a single Gaussian.
batch_dim = 1 + max(
len(self._init.batch_shape) + 1, len(logp_oh.batch_shape))
batch_shape = (1, ) * (batch_dim -
len(logp_oh.batch_shape)) + logp_oh.batch_shape
logp = Gaussian.cat(
[logp_oh.expand(batch_shape),
logp_h.expand(batch_shape)])
# Eliminate time dimension.
logp = _sequential_gaussian_tensordot(logp)
# Combine initial factor.
logp = gaussian_tensordot(self._init, logp, dims=self.hidden_dim)
# Marginalize out final state.
logp_oh, logp_h = logp.event_logsumexp()
return logp_oh - logp_h # = log( p(obs,hidden) / p(hidden) )
def test_cat(shape, cat_dim, split, dim):
assert sum(split) == shape[cat_dim]
gaussian = random_gaussian(shape, dim)
parts = []
end = 0
for size in split:
beg, end = end, end + size
if cat_dim == -1:
part = gaussian[..., beg:end]
elif cat_dim == -2:
part = gaussian[..., beg:end, :]
elif cat_dim == 1:
part = gaussian[:, beg:end]
else:
raise ValueError
parts.append(part)
actual = Gaussian.cat(parts, cat_dim)
assert_close_gaussian(actual, gaussian)
def _sequential_gaussian_tensordot(gaussian):
"""
Integrates a Gaussian ``x`` whose rightmost batch dimension is time, computes::
x[..., 0] @ x[..., 1] @ ... @ x[..., T-1]
"""
assert isinstance(gaussian, Gaussian)
assert gaussian.dim() % 2 == 0, "dim is not even"
batch_shape = gaussian.batch_shape[:-1]
state_dim = gaussian.dim() // 2
while gaussian.batch_shape[-1] > 1:
time = gaussian.batch_shape[-1]
even_time = time // 2 * 2
even_part = gaussian[..., :even_time]
x_y = even_part.reshape(batch_shape + (even_time // 2, 2))
x, y = x_y[..., 0], x_y[..., 1]
contracted = gaussian_tensordot(x, y, state_dim)
if time > even_time:
contracted = Gaussian.cat((contracted, gaussian[..., -1:]), dim=-1)
gaussian = contracted
return gaussian[..., 0]
def test_gaussian_funsor(batch_shape):
# This tests sample distribution, rsample gradients, log_prob, and log_prob
# gradients for both Pyro's and Funsor's Gaussian.
import funsor
funsor.set_backend("torch")
num_samples = 100000
# Declare unconstrained parameters.
loc = torch.randn(batch_shape + (3, )).requires_grad_()
t = transform_to(constraints.positive_definite)
m = torch.randn(batch_shape + (3, 3))
precision_unconstrained = t.inv(m @ m.transpose(-1, -2)).requires_grad_()
# Transform to constrained space.
log_normalizer = torch.zeros(batch_shape)
precision = t(precision_unconstrained)
info_vec = (precision @ loc[..., None])[..., 0]
def check_equal(actual, expected, atol=0.01, rtol=0):
assert_close(actual.data, expected.data, atol=atol, rtol=rtol)
grads = torch.autograd.grad(
(actual - expected).abs().sum(),
[loc, precision_unconstrained],
retain_graph=True,
)
for grad in grads:
assert grad.abs().max() < atol
entropy = dist.MultivariateNormal(loc,
precision_matrix=precision).entropy()
# Monte carlo estimate entropy via pyro.
p_gaussian = Gaussian(log_normalizer, info_vec, precision)
p_log_Z = p_gaussian.event_logsumexp()
p_rsamples = p_gaussian.rsample((num_samples, ))
pp_entropy = (p_log_Z - p_gaussian.log_density(p_rsamples)).mean(0)
check_equal(pp_entropy, entropy)
# Monte carlo estimate entropy via funsor.
inputs = OrderedDict([(k, funsor.Bint[v])
for k, v in zip("ij", batch_shape)])
inputs["x"] = funsor.Reals[3]
f_gaussian = funsor.gaussian.Gaussian(mean=loc,
precision=precision,
inputs=inputs)
f_log_Z = f_gaussian.reduce(funsor.ops.logaddexp, "x")
sample_inputs = OrderedDict(particle=funsor.Bint[num_samples])
deltas = f_gaussian.sample("x", sample_inputs)
f_rsamples = funsor.montecarlo.extract_samples(deltas)["x"]
ff_entropy = (f_log_Z - f_gaussian(x=f_rsamples)).reduce(
funsor.ops.mean, "particle")
check_equal(ff_entropy.data, entropy)
# Check Funsor's .rsample against Pyro's .log_prob.
pf_entropy = (p_log_Z - p_gaussian.log_density(f_rsamples.data)).mean(0)
check_equal(pf_entropy, entropy)
# Check Pyro's .rsample against Funsor's .log_prob.
fp_rsamples = funsor.Tensor(p_rsamples)["particle"]
for i in "ij"[:len(batch_shape)]:
fp_rsamples = fp_rsamples[i]
fp_entropy = (f_log_Z - f_gaussian(x=fp_rsamples)).reduce(
funsor.ops.mean, "particle")
check_equal(fp_entropy.data, entropy)
