def _sample_posterior(model, first_available_dim, temperature, rng_key, *args,
**kwargs):
if temperature == 0:
sum_op, prod_op = funsor.ops.max, funsor.ops.add
approx = funsor.approximations.argmax_approximate
elif temperature == 1:
sum_op, prod_op = funsor.ops.logaddexp, funsor.ops.add
rng_key, sub_key = random.split(rng_key)
approx = funsor.montecarlo.MonteCarlo(rng_key=sub_key)
else:
raise ValueError("temperature must be 0 (map) or 1 (sample) for now")
if first_available_dim is None:
with block():
model_trace = trace(seed(model,
rng_key)).get_trace(*args, **kwargs)
first_available_dim = -_guess_max_plate_nesting(model_trace) - 1
with block(), enum(first_available_dim=first_available_dim):
with plate_to_enum_plate():
model_tr = packed_trace(model).get_trace(*args, **kwargs)
terms = terms_from_trace(model_tr)
# terms["log_factors"] = [log p(x) for each observed or latent sample site x]
# terms["log_measures"] = [log p(z) or other Dice factor
# for each latent sample site z]
with funsor.interpretations.lazy:
log_prob = funsor.sum_product.sum_product(
sum_op,
prod_op,
list(terms["log_factors"].values()) +
list(terms["log_measures"].values()),
eliminate=terms["measure_vars"] | terms["plate_vars"],
plates=terms["plate_vars"],
)
log_prob = funsor.optimizer.apply_optimizer(log_prob)
with approx:
approx_factors = funsor.adjoint.adjoint(sum_op, prod_op, log_prob)
# construct a result trace to replay against the model
sample_tr = model_tr.copy()
sample_subs = {}
for name, node in sample_tr.items():
if node["type"] != "sample":
continue
if node["is_observed"]:
# "observed" values may be collapsed samples that depend on enumerated
# values, so we have to slice them down
# TODO this should really be handled entirely under the hood by adjoint
output = funsor.Reals[node["fn"].event_shape]
value = funsor.to_funsor(node["value"],
output,
dim_to_name=node["infer"]["dim_to_name"])
value = value(**sample_subs)
node["value"] = funsor.to_data(
value, name_to_dim=node["infer"]["name_to_dim"])
else:
log_measure = approx_factors[terms["log_measures"][name]]
sample_subs[name] = _get_support_value(log_measure, name)
node["value"] = funsor.to_data(
sample_subs[name], name_to_dim=node["infer"]["name_to_dim"])
with replay(guide_trace=sample_tr):
return model(*args, **kwargs)
def log_density(model, model_args, model_kwargs, params):
"""
Similar to :func:`numpyro.infer.util.log_density` but works for models
with discrete latent variables. Internally, this uses :mod:`funsor`
to marginalize discrete latent sites and evaluate the joint log probability.
:param model: Python callable containing NumPyro primitives. Typically,
the model has been enumerated by using
:class:`~numpyro.contrib.funsor.enum_messenger.enum` handler::
def model(*args, **kwargs):
...
log_joint = log_density(enum(config_enumerate(model)), args, kwargs, params)
:param tuple model_args: args provided to the model.
:param dict model_kwargs: kwargs provided to the model.
:param dict params: dictionary of current parameter values keyed by site
name.
:return: log of joint density and a corresponding model trace
"""
model = substitute(model, data=params)
with plate_to_enum_plate():
model_trace = packed_trace(model).get_trace(*model_args,
**model_kwargs)
log_factors = []
time_to_factors = defaultdict(list) # log prob factors
time_to_init_vars = defaultdict(frozenset) # _init/... variables
time_to_markov_dims = defaultdict(frozenset) # dimensions at markov sites
sum_vars, prod_vars = frozenset(), frozenset()
for site in model_trace.values():
if site['type'] == 'sample':
value = site['value']
intermediates = site['intermediates']
scale = site['scale']
if intermediates:
log_prob = site['fn'].log_prob(value, intermediates)
else:
log_prob = site['fn'].log_prob(value)
if (scale is not None) and (not is_identically_one(scale)):
log_prob = scale * log_prob
dim_to_name = site["infer"]["dim_to_name"]
log_prob = funsor.to_funsor(log_prob,
output=funsor.reals(),
dim_to_name=dim_to_name)
time_dim = None
for dim, name in dim_to_name.items():
if name.startswith("_time"):
time_dim = funsor.Variable(
name, funsor.domains.bint(site["value"].shape[dim]))
time_to_factors[time_dim].append(log_prob)
time_to_init_vars[time_dim] |= frozenset(
s for s in dim_to_name.values()
if s.startswith("_init"))
break
if time_dim is None:
log_factors.append(log_prob)
if not site['is_observed']:
sum_vars |= frozenset({site['name']})
prod_vars |= frozenset(f.name for f in site['cond_indep_stack']
if f.dim is not None)
for time_dim, init_vars in time_to_init_vars.items():
for var in init_vars:
curr_var = "/".join(var.split("/")[1:])
dim_to_name = model_trace[curr_var]["infer"]["dim_to_name"]
if var in dim_to_name.values(
): # i.e. _init (i.e. prev) in dim_to_name
time_to_markov_dims[time_dim] |= frozenset(
name for name in dim_to_name.values())
if len(time_to_factors) > 0:
markov_factors = compute_markov_factors(time_to_factors,
time_to_init_vars,
time_to_markov_dims, sum_vars,
prod_vars)
log_factors = log_factors + markov_factors
with funsor.interpreter.interpretation(funsor.terms.lazy):
lazy_result = funsor.sum_product.sum_product(funsor.ops.logaddexp,
funsor.ops.add,
log_factors,
eliminate=sum_vars
| prod_vars,
plates=prod_vars)
result = funsor.optimizer.apply_optimizer(lazy_result)
if len(result.inputs) > 0:
raise ValueError(
"Expected the joint log density is a scalar, but got {}. "
"There seems to be something wrong at the following sites: {}.".
format(result.data.shape,
{k.split("__BOUND")[0]
for k in result.inputs}))
return result.data, model_trace
def _enum_log_density(model, model_args, model_kwargs, params, sum_op, prod_op):
"""Helper function to compute elbo and extract its components from execution traces."""
model = substitute(model, data=params)
with plate_to_enum_plate():
model_trace = packed_trace(model).get_trace(*model_args, **model_kwargs)
log_factors = []
time_to_factors = defaultdict(list) # log prob factors
time_to_init_vars = defaultdict(frozenset) # PP... variables
time_to_markov_dims = defaultdict(frozenset) # dimensions at markov sites
sum_vars, prod_vars = frozenset(), frozenset()
history = 1
log_measures = {}
for site in model_trace.values():
if site["type"] == "sample":
value = site["value"]
intermediates = site["intermediates"]
scale = site["scale"]
if intermediates:
log_prob = site["fn"].log_prob(value, intermediates)
else:
log_prob = site["fn"].log_prob(value)
if (scale is not None) and (not is_identically_one(scale)):
log_prob = scale * log_prob
dim_to_name = site["infer"]["dim_to_name"]
log_prob_factor = funsor.to_funsor(
log_prob, output=funsor.Real, dim_to_name=dim_to_name
)
time_dim = None
for dim, name in dim_to_name.items():
if name.startswith("_time"):
time_dim = funsor.Variable(name, funsor.Bint[log_prob.shape[dim]])
time_to_factors[time_dim].append(log_prob_factor)
history = max(
history, max(_get_shift(s) for s in dim_to_name.values())
)
time_to_init_vars[time_dim] |= frozenset(
s for s in dim_to_name.values() if s.startswith("_PREV_")
)
break
if time_dim is None:
log_factors.append(log_prob_factor)
if not site["is_observed"]:
log_measures[site["name"]] = log_prob_factor
sum_vars |= frozenset({site["name"]})
prod_vars |= frozenset(
f.name for f in site["cond_indep_stack"] if f.dim is not None
)
for time_dim, init_vars in time_to_init_vars.items():
for var in init_vars:
curr_var = _shift_name(var, -_get_shift(var))
dim_to_name = model_trace[curr_var]["infer"]["dim_to_name"]
if var in dim_to_name.values(): # i.e. _PREV_* (i.e. prev) in dim_to_name
time_to_markov_dims[time_dim] |= frozenset(
name for name in dim_to_name.values()
)
if len(time_to_factors) > 0:
markov_factors = compute_markov_factors(
time_to_factors,
time_to_init_vars,
time_to_markov_dims,
sum_vars,
prod_vars,
history,
sum_op,
prod_op,
)
log_factors = log_factors + markov_factors
with funsor.interpretations.lazy:
lazy_result = funsor.sum_product.sum_product(
sum_op,
prod_op,
log_factors,
eliminate=sum_vars | prod_vars,
plates=prod_vars,
)
result = funsor.optimizer.apply_optimizer(lazy_result)
if len(result.inputs) > 0:
raise ValueError(
"Expected the joint log density is a scalar, but got {}. "
"There seems to be something wrong at the following sites: {}.".format(
result.data.shape, {k.split("__BOUND")[0] for k in result.inputs}
)
)
return result, model_trace, log_measures