def differentiable_loss(self, model, guide, *args, **kwargs):
with enum(), plate(
size=self.num_particles
) if self.num_particles > 1 else contextlib.ExitStack():
guide_tr = trace(config_enumerate(
default="flat")(guide)).get_trace(*args, **kwargs)
model_tr = trace(replay(model, trace=guide_tr)).get_trace(
*args, **kwargs)
model_terms = terms_from_trace(model_tr)
guide_terms = terms_from_trace(guide_tr)
log_measures = guide_terms["log_measures"] + model_terms["log_measures"]
log_factors = model_terms["log_factors"] + [
-f for f in guide_terms["log_factors"]
]
plate_vars = model_terms["plate_vars"] | guide_terms["plate_vars"]
measure_vars = model_terms["measure_vars"] | guide_terms["measure_vars"]
elbo = funsor.Integrate(
sum(log_measures, to_funsor(0.0)),
sum(log_factors, to_funsor(0.0)),
measure_vars,
)
elbo = elbo.reduce(funsor.ops.add, plate_vars)
return -to_data(elbo)
def differentiable_loss(self, model, guide, *args, **kwargs):
# get batched, enumerated, to_funsor-ed traces from the guide and model
with plate(size=self.num_particles) if self.num_particles > 1 else contextlib.ExitStack(), \
enum(first_available_dim=(-self.max_plate_nesting-1) if self.max_plate_nesting else None):
guide_tr = trace(guide).get_trace(*args, **kwargs)
model_tr = trace(replay(model, trace=guide_tr)).get_trace(
*args, **kwargs)
# extract from traces all metadata that we will need to compute the elbo
guide_terms = terms_from_trace(guide_tr)
model_terms = terms_from_trace(model_tr)
# build up a lazy expression for the elbo
with funsor.interpreter.interpretation(funsor.terms.lazy):
# identify and contract out auxiliary variables in the model with partial_sum_product
contracted_factors, uncontracted_factors = [], []
for f in model_terms["log_factors"]:
if model_terms["measure_vars"].intersection(f.inputs):
contracted_factors.append(f)
else:
uncontracted_factors.append(f)
# incorporate the effects of subsampling and handlers.scale through a common scale factor
contracted_costs = [
model_terms["scale"] * f
for f in funsor.sum_product.partial_sum_product(
funsor.ops.logaddexp,
funsor.ops.add,
model_terms["log_measures"] + contracted_factors,
plates=model_terms["plate_vars"],
eliminate=model_terms["measure_vars"])
]
costs = contracted_costs + uncontracted_factors # model costs: logp
costs += [-f for f in guide_terms["log_factors"]
] # guide costs: -logq
# finally, integrate out guide variables in the elbo and all plates
plate_vars = guide_terms["plate_vars"] | model_terms["plate_vars"]
elbo = to_funsor(0, output=funsor.Real)
for cost in costs:
# compute the marginal logq in the guide corresponding to this cost term
log_prob = funsor.sum_product.sum_product(
funsor.ops.logaddexp,
funsor.ops.add,
guide_terms["log_measures"],
plates=plate_vars,
eliminate=(plate_vars | guide_terms["measure_vars"]) -
frozenset(cost.inputs))
# compute the expected cost term E_q[logp] or E_q[-logq] using the marginal logq for q
elbo_term = funsor.Integrate(
log_prob, cost,
guide_terms["measure_vars"] & frozenset(cost.inputs))
elbo += elbo_term.reduce(funsor.ops.add,
plate_vars & frozenset(cost.inputs))
# evaluate the elbo, using memoize to share tensor computation where possible
with funsor.memoize.memoize():
return -to_data(funsor.optimizer.apply_optimizer(elbo))
def terms_from_trace(tr):
"""Helper function to extract elbo components from execution traces."""
# data structure containing densities, measures, scales, and identification
# of free variables as either product (plate) variables or sum (measure) variables
terms = {
"log_factors": [],
"log_measures": [],
"scale": to_funsor(1.0),
"plate_vars": frozenset(),
"measure_vars": frozenset(),
"plate_to_step": dict(),
}
for name, node in tr.nodes.items():
# add markov dimensions to the plate_to_step dictionary
if node["type"] == "markov_chain":
terms["plate_to_step"][node["name"]] = node["value"]
# ensure previous step variables are added to measure_vars
for step in node["value"]:
terms["measure_vars"] |= frozenset({
var
for var in step[1:-1] if tr.nodes[var]["funsor"].get(
"log_measure", None) is not None
})
if (node["type"] != "sample"
or type(node["fn"]).__name__ == "_Subsample"
or node["infer"].get("_do_not_score", False)):
continue
# grab plate dimensions from the cond_indep_stack
terms["plate_vars"] |= frozenset(f.name
for f in node["cond_indep_stack"]
if f.vectorized)
# grab the log-measure, found only at sites that are not replayed or observed
if node["funsor"].get("log_measure", None) is not None:
terms["log_measures"].append(node["funsor"]["log_measure"])
# sum (measure) variables: the fresh non-plate variables at a site
terms["measure_vars"] |= (frozenset(node["funsor"]["value"].inputs)
| {name}) - terms["plate_vars"]
# grab the scale, assuming a common subsampling scale
if (node.get("replay_active", False) and
set(node["funsor"]["log_prob"].inputs) & terms["measure_vars"]
and float(to_data(node["funsor"]["scale"])) != 1.0):
# model site that depends on enumerated variable: common scale
terms["scale"] = node["funsor"]["scale"]
else: # otherwise: default scale behavior
node["funsor"]["log_prob"] = (node["funsor"]["log_prob"] *
node["funsor"]["scale"])
# grab the log-density, found at all sites except those that are not replayed
if node["is_observed"] or not node.get("replay_skipped", False):
terms["log_factors"].append(node["funsor"]["log_prob"])
# add plate dimensions to the plate_to_step dictionary
terms["plate_to_step"].update({
plate: terms["plate_to_step"].get(plate, {})
for plate in terms["plate_vars"]
})
return terms
def terms_from_trace(tr):
"""Helper function to extract elbo components from execution traces."""
# data structure containing densities, measures, scales, and identification
# of free variables as either product (plate) variables or sum (measure) variables
terms = {
"log_factors": [],
"log_measures": [],
"scale": to_funsor(1.),
"plate_vars": frozenset(),
"measure_vars": frozenset()
}
for name, node in tr.nodes.items():
if node["type"] != "sample" or type(
node["fn"]).__name__ == "_Subsample":
continue
# grab plate dimensions from the cond_indep_stack
terms["plate_vars"] |= frozenset(f.name
for f in node["cond_indep_stack"]
if f.vectorized)
# grab the log-measure, found only at sites that are not replayed or observed
if node["funsor"].get("log_measure", None) is not None:
terms["log_measures"].append(node["funsor"]["log_measure"])
# sum (measure) variables: the fresh non-plate variables at a site
terms["measure_vars"] |= (frozenset(node["funsor"]["value"].inputs)
| {name}) - terms["plate_vars"]
# grab the scale, assuming a common subsampling scale
if node.get("replay_active", False) and set(node["funsor"]["log_prob"].inputs) & terms["measure_vars"] and \
float(to_data(node["funsor"]["scale"])) != 1.:
# model site that depends on enumerated variable: common scale
terms["scale"] = node["funsor"]["scale"]
else: # otherwise: default scale behavior
node["funsor"]["log_prob"] = node["funsor"]["log_prob"] * node[
"funsor"]["scale"]
# grab the log-density, found at all sites except those that are not replayed
if node["is_observed"] or not node.get("replay_skipped", False):
terms["log_factors"].append(node["funsor"]["log_prob"])
return terms
def differentiable_loss(self, model, guide, *args, **kwargs):
# get batched, enumerated, to_funsor-ed traces from the guide and model
with plate(
size=self.num_particles
) if self.num_particles > 1 else contextlib.ExitStack(), enum(
first_available_dim=(-self.max_plate_nesting -
1) if self.max_plate_nesting else None):
guide_tr = trace(guide).get_trace(*args, **kwargs)
model_tr = trace(replay(model, trace=guide_tr)).get_trace(
*args, **kwargs)
# extract from traces all metadata that we will need to compute the elbo
guide_terms = terms_from_trace(guide_tr)
model_terms = terms_from_trace(model_tr)
# build up a lazy expression for the elbo
with funsor.terms.lazy:
# identify and contract out auxiliary variables in the model with partial_sum_product
contracted_factors, uncontracted_factors = [], []
for f in model_terms["log_factors"]:
if model_terms["measure_vars"].intersection(f.inputs):
contracted_factors.append(f)
else:
uncontracted_factors.append(f)
# incorporate the effects of subsampling and handlers.scale through a common scale factor
contracted_costs = [
model_terms["scale"] * f
for f in funsor.sum_product.partial_sum_product(
funsor.ops.logaddexp,
funsor.ops.add,
model_terms["log_measures"] + contracted_factors,
plates=model_terms["plate_vars"],
eliminate=model_terms["measure_vars"],
)
]
# accumulate costs from model (logp) and guide (-logq)
costs = contracted_costs + uncontracted_factors # model costs: logp
costs += [-f for f in guide_terms["log_factors"]
] # guide costs: -logq
# compute expected cost
# Cf. pyro.infer.util.Dice.compute_expectation()
# https://github.com/pyro-ppl/pyro/blob/0.3.0/pyro/infer/util.py#L212
# TODO Replace this with funsor.Expectation
plate_vars = guide_terms["plate_vars"] | model_terms["plate_vars"]
# compute the marginal logq in the guide corresponding to each cost term
targets = dict()
for cost in costs:
input_vars = frozenset(cost.inputs)
if input_vars not in targets:
targets[input_vars] = funsor.Tensor(
funsor.ops.new_zeros(
funsor.tensor.get_default_prototype(),
tuple(v.size for v in cost.inputs.values()),
),
cost.inputs,
cost.dtype,
)
with AdjointTape() as tape:
logzq = funsor.sum_product.sum_product(
funsor.ops.logaddexp,
funsor.ops.add,
guide_terms["log_measures"] + list(targets.values()),
plates=plate_vars,
eliminate=(plate_vars | guide_terms["measure_vars"]),
)
marginals = tape.adjoint(funsor.ops.logaddexp, funsor.ops.add,
logzq, tuple(targets.values()))
# finally, integrate out guide variables in the elbo and all plates
elbo = to_funsor(0, output=funsor.Real)
for cost in costs:
target = targets[frozenset(cost.inputs)]
logzq_local = marginals[target].reduce(
funsor.ops.logaddexp,
frozenset(cost.inputs) - plate_vars)
log_prob = marginals[target] - logzq_local
elbo_term = funsor.Integrate(
log_prob,
cost,
guide_terms["measure_vars"] & frozenset(log_prob.inputs),
)
elbo += elbo_term.reduce(funsor.ops.add,
plate_vars & frozenset(cost.inputs))
# evaluate the elbo, using memoize to share tensor computation where possible
with funsor.interpretations.memoize():
return -to_data(apply_optimizer(elbo))