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Rewrite Tensor._sample to handle dice_factor as Delta's log_density #569

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Rewrite Tensor._sample to handle dice_factor as Delta's log_density #569

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126 changes: 45 additions & 81 deletions funsor/tensor.py
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Original file line number Diff line number Diff line change
Expand Up @@ -335,94 +335,58 @@ def _sample(self, sampled_vars, sample_inputs, rng_key):
if not sampled_vars:
return self

# Partition inputs into sample_inputs + batch_inputs + event_inputs.
sample_inputs = OrderedDict(
(k, d) for k, d in sample_inputs.items() if k not in self.inputs
)
sample_shape = tuple(int(d.dtype) for d in sample_inputs.values())
results = []
backend = get_backend()
remaining_vars = set(sampled_vars)
term = self
shape = tuple(d.size for k, d in sample_inputs.items() if k not in self.inputs)
shape += tuple(d.size for k, d in self.inputs.items() if k not in sampled_vars)
batch_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if k not in sampled_vars
(k, v) for k, v in sample_inputs.items() if k not in self.inputs
)
event_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if k in sampled_vars
batch_inputs.update(
(k, v) for k, v in self.inputs.items() if k not in sampled_vars
)
be_inputs = batch_inputs.copy()
be_inputs.update(event_inputs)
sb_inputs = sample_inputs.copy()
sb_inputs.update(batch_inputs)

# Sample all variables in a single Categorical call.
logits = align_tensor(be_inputs, self)
batch_shape = logits.shape[: len(batch_inputs)]
flat_logits = logits.reshape(batch_shape + (-1,))
sample_shape = tuple(d.dtype for d in sample_inputs.values())
while remaining_vars:
name = remaining_vars.pop()
domain = self.inputs[name]
logits = funsor.Lambda(
Variable(name, domain), term.reduce(ops.logaddexp, remaining_vars)
)

backend = get_backend()
if backend != "numpy":
from importlib import import_module
if backend != "numpy":
from importlib import import_module

dist = import_module(
funsor.distribution.BACKEND_TO_DISTRIBUTIONS_BACKEND[backend]
)
sample_args = (
(sample_shape,) if rng_key is None else (rng_key, sample_shape)
)
flat_sample = dist.CategoricalLogits.dist_class(logits=flat_logits).sample(
*sample_args
)
else: # default numpy backend
assert backend == "numpy"
shape = sample_shape + flat_logits.shape[:-1]
logit_max = np.amax(flat_logits, -1, keepdims=True)
probs = np.exp(flat_logits - logit_max)
probs = probs / np.sum(probs, -1, keepdims=True)
s = np.cumsum(probs, -1)
r = np.random.rand(*shape)
flat_sample = np.sum(s < np.expand_dims(r, -1), axis=-1)

assert flat_sample.shape == sample_shape + batch_shape
results = []
mod_sample = flat_sample
for name, domain in reversed(list(event_inputs.items())):
size = domain.dtype
point = Tensor(mod_sample % size, sb_inputs, size)
mod_sample = mod_sample // size
results.append(Delta(name, point))

# Account for the log normalizer factor.
# Derivation: Let f be a nonnormalized distribution (a funsor), and
# consider operations in linear space (source code is in log space).
# Let x0 ~ f/|f| be a monte carlo sample from a normalized f/|f|.
# f(x0) / |f| # dice numerator
# Let g = delta(x=x0) |f| -----------------
# detach(f(x0)/|f|) # dice denominator
# |detach(f)| f(x0)
# = delta(x=x0) ----------------- be a dice approximation of f.
# detach(f(x0))
# Then g is an unbiased estimator of f in value and all derivatives.
# In the special case f = detach(f), we can simplify to
# g = delta(x=x0) |f|.
if (backend == "torch" and flat_logits.requires_grad) or backend == "jax":
# Apply a dice factor to preserve differentiability.
index = [
ops.new_arange(self.data, n).reshape(
(n,) + (1,) * (len(flat_logits.shape) - i - 2)
dist = import_module(
funsor.distribution.BACKEND_TO_DISTRIBUTIONS_BACKEND[backend]
)
for i, n in enumerate(flat_logits.shape[:-1])
]
index.append(flat_sample)
log_prob = flat_logits[tuple(index)]
assert log_prob.shape == flat_sample.shape
results.append(
Tensor(
ops.logsumexp(ops.detach(flat_logits), -1)
+ (log_prob - ops.detach(log_prob)),
sb_inputs,
sample_inputs = OrderedDict(
(k, v) for k, v in sample_inputs.items() if k not in logits.inputs
)
)
else:
# This is the special case f = detach(f).
results.append(Tensor(ops.logsumexp(flat_logits, -1), batch_inputs))
delta = dist.CategoricalLogits(logits=logits, value=name)._sample(
frozenset({name}), sample_inputs, rng_key
)
point = delta.terms[0][1][0]
log_density = delta.terms[0][1][1] + self.reduce(
ops.logaddexp, sampled_vars
) / len(sampled_vars)
term = term(**{name: point})
sample = Delta(name, point, log_density)
results.append(sample)
else: # default numpy backend
assert backend == "numpy"
probs = (logits - ops.logsumexp(logits)).exp().data
# shape = sample_shape + flat_logits.shape[:-1]
# logit_max = np.amax(flat_logits, -1, keepdims=True)
# probs = np.exp(flat_logits - logit_max)
# probs = probs / np.sum(probs, -1, keepdims=True)
s = np.cumsum(probs, -1)
r = np.random.rand(*shape)
flat_sample = np.sum(s < np.expand_dims(r, -1), axis=-1)
point = Tensor(flat_sample, batch_inputs, domain.dtype)
term = term(**{name: point})
sample = Delta(name, point)
results.append(sample)

return reduce(ops.add, results)

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