def model(data):
log_prob = funsor.Number(0.)
# s is the discrete latent state,
# x is the continuous latent state,
# y is the observed state.
s_curr = funsor.Tensor(torch.tensor(0), dtype=2)
x_curr = funsor.Tensor(torch.tensor(0.))
for t, y in enumerate(data):
s_prev = s_curr
x_prev = x_curr
# A delayed sample statement.
s_curr = funsor.Variable('s_{}'.format(t), funsor.bint(2))
log_prob += dist.Categorical(trans_probs[s_prev], value=s_curr)
# A delayed sample statement.
x_curr = funsor.Variable('x_{}'.format(t), funsor.reals())
log_prob += dist.Normal(x_prev, trans_noise[s_curr], value=x_curr)
# Marginalize out previous delayed sample statements.
if t > 0:
log_prob = log_prob.reduce(ops.logaddexp,
{s_prev.name, x_prev.name})
# An observe statement.
log_prob += dist.Normal(x_curr, emit_noise, value=y)
log_prob = log_prob.reduce(ops.logaddexp)
return log_prob
def log_prob(self, data):
trans_logits, trans_probs, trans_mvn, obs_mvn, x_trans_dist, y_dist = self.get_tensors_and_dists(
)
log_prob = funsor.Number(0.)
s_vars = {
-1: funsor.Tensor(torch.tensor(0), dtype=self.num_components)
}
x_vars = {}
for t, y in enumerate(data):
# construct free variables for s_t and x_t
s_vars[t] = funsor.Variable(f's_{t}',
funsor.bint(self.num_components))
x_vars[t] = funsor.Variable(f'x_{t}',
funsor.reals(self.hidden_dim))
# incorporate the discrete switching dynamics
log_prob += dist.Categorical(trans_probs(s=s_vars[t - 1]),
value=s_vars[t])
# incorporate the prior term p(x_t | x_{t-1})
if t == 0:
log_prob += self.x_init_mvn(value=x_vars[t])
else:
log_prob += x_trans_dist(s=s_vars[t],
x=x_vars[t - 1],
y=x_vars[t])
# do a moment-matching reduction. at this point log_prob depends on (moment_matching_lag + 1)-many
# pairs of free variables.
if t > self.moment_matching_lag - 1:
log_prob = log_prob.reduce(
ops.logaddexp,
frozenset([
s_vars[t - self.moment_matching_lag].name,
x_vars[t - self.moment_matching_lag].name
]))
# incorporate the observation p(y_t | x_t, s_t)
log_prob += y_dist(s=s_vars[t], x=x_vars[t], y=y)
T = data.shape[0]
# reduce any remaining free variables
for t in range(self.moment_matching_lag):
log_prob = log_prob.reduce(
ops.logaddexp,
frozenset([
s_vars[T - self.moment_matching_lag + t].name,
x_vars[T - self.moment_matching_lag + t].name
]))
# assert that we've reduced all the free variables in log_prob
assert not log_prob.inputs, 'unexpected free variables remain'
# return the PyTorch tensor behind log_prob (which we can directly differentiate)
return log_prob.data
def model(data):
log_prob = funsor.to_funsor(0.)
trans = dist.Categorical(probs=funsor.Tensor(
trans_probs,
inputs=OrderedDict([('prev', funsor.bint(args.hidden_dim))]),
))
emit = dist.Categorical(probs=funsor.Tensor(
emit_probs,
inputs=OrderedDict([('latent', funsor.bint(args.hidden_dim))]),
))
x_curr = funsor.Number(0, args.hidden_dim)
for t, y in enumerate(data):
x_prev = x_curr
# A delayed sample statement.
x_curr = funsor.Variable('x_{}'.format(t),
funsor.bint(args.hidden_dim))
log_prob += trans(prev=x_prev, value=x_curr)
if not args.lazy and isinstance(x_prev, funsor.Variable):
log_prob = log_prob.reduce(ops.logaddexp, x_prev.name)
log_prob += emit(latent=x_curr, value=funsor.Tensor(y, dtype=2))
log_prob = log_prob.reduce(ops.logaddexp)
return log_prob
def one_step_prediction(p_x_tp1, t, var_names, emit_eq, emit_noise):
"""Computes p(y_{t+1}) from p(x_{t+1}). We assume y_t is scalar, so only one emit_eq"""
log_prob = p_x_tp1
x_tp1s = [
funsor.Variable(name + '_{}'.format(t + 1), funsor.reals())
for name in var_names
]
y_tp1 = funsor.Variable('y_{}'.format(t + 1), funsor.reals())
log_prob += dist.Normal(emit_eq(x_tp1s),
torch.exp(emit_noise),
value=y_tp1)
log_prob = log_prob.reduce(ops.logaddexp,
frozenset([x_tp1.name for x_tp1 in x_tp1s]))
return log_prob
def model(data):
log_prob = funsor.to_funsor(0.)
xs_curr = [funsor.Tensor(torch.tensor(0.)) for var in var_names]
for t, y in enumerate(data):
xs_prev = xs_curr
# A delayed sample statement.
xs_curr = [
funsor.Variable(name + '_{}'.format(t), funsor.reals())
for name in var_names
]
for i, x_curr in enumerate(xs_curr):
log_prob += dist.Normal(trans_eqs[var_names[i]](xs_prev),
torch.exp(trans_noises[i]),
value=x_curr)
if t > 0:
log_prob = log_prob.reduce(
ops.logaddexp,
frozenset([x_prev.name for x_prev in xs_prev]))
# An observe statement.
log_prob += dist.Normal(emit_eq(xs_curr),
torch.exp(emit_noise),
value=y)
# Marginalize out all remaining delayed variables.
return log_prob.reduce(ops.logaddexp), log_prob.gaussian
def next_state(p_x_t, t, var_names, trans_eqs, trans_noises):
"""Computes p(x_{t+1}) from p(x_t)"""
log_prob = p_x_t
x_ts = [
funsor.Variable(name + '_{}'.format(t), funsor.reals())
for name in var_names
]
x_tp1s = [
funsor.Variable(name + '_{}'.format(t + 1), funsor.reals())
for name in var_names
]
for i, x_tp1 in enumerate(x_tp1s):
log_prob += dist.Normal(trans_eqs[var_names[i]](x_ts),
torch.exp(trans_noises[i]),
value=x_tp1)
log_prob = log_prob.reduce(ops.logaddexp,
frozenset([x_t.name for x_t in x_ts]))
return log_prob
def _pyro_sample(self, msg):
# Eagerly convert fn and value to Funsor.
dim_to_name = {f.dim: f.name for f in msg["cond_indep_stack"]}
dim_to_name.update(self.preserved_plates)
msg["fn"] = funsor.to_funsor(msg["fn"], funsor.Real, dim_to_name)
domain = msg["fn"].inputs["value"]
if msg["value"] is None:
msg["value"] = funsor.Variable(msg["name"], domain)
else:
msg["value"] = funsor.to_funsor(msg["value"], domain, dim_to_name)
msg["done"] = True
msg["stop"] = True
def _forward_funsor(self, features, trip_counts):
total_hours = len(features)
observed_hours, num_origins, num_destins = trip_counts.shape
assert observed_hours == total_hours
assert num_origins == self.num_stations
assert num_destins == self.num_stations
n = self.num_stations
gate_rate = funsor.Variable("gate_rate_t",
reals(observed_hours, 2 * n * n))["time"]
@funsor.torch.function(reals(2 * n * n), (reals(n, n, 2), reals(n, n)))
def unpack_gate_rate(gate_rate):
batch_shape = gate_rate.shape[:-1]
gate, rate = gate_rate.reshape(batch_shape + (2, n, n)).unbind(-3)
gate = gate.sigmoid().clamp(min=0.01, max=0.99)
rate = bounded_exp(rate, bound=1e4)
gate = torch.stack((1 - gate, gate), dim=-1)
return gate, rate
# Create a Gaussian latent dynamical system.
init_dist, trans_matrix, trans_dist, obs_matrix, obs_dist = \
self._dynamics(features[:observed_hours])
init = dist_to_funsor(init_dist)(value="state")
trans = matrix_and_mvn_to_funsor(trans_matrix, trans_dist, ("time", ),
"state", "state(time=1)")
obs = matrix_and_mvn_to_funsor(obs_matrix, obs_dist, ("time", ),
"state(time=1)", "gate_rate")
# Compute dynamic prior over gate_rate.
prior = trans + obs(gate_rate=gate_rate)
prior = MarkovProduct(ops.logaddexp, ops.add, prior, "time",
{"state": "state(time=1)"})
prior += init
prior = prior.reduce(ops.logaddexp, {"state", "state(time=1)"})
# Compute zero-inflated Poisson likelihood.
gate, rate = unpack_gate_rate(gate_rate)
likelihood = fdist.Categorical(gate["origin", "destin"], value="gated")
trip_counts = tensor_to_funsor(trip_counts,
("time", "origin", "destin"))
likelihood += funsor.Stack(
"gated",
(fdist.Poisson(rate["origin", "destin"], value=trip_counts),
fdist.Delta(0, value=trip_counts)))
likelihood = likelihood.reduce(ops.logaddexp, "gated")
likelihood = likelihood.reduce(ops.add, {"time", "origin", "destin"})
assert set(prior.inputs) == {"gate_rate_t"}, prior.inputs
assert set(likelihood.inputs) == {"gate_rate_t"}, likelihood.inputs
return prior, likelihood
def update(p_x_tp1, t, y, var_names, emit_eq, emit_noise):
"""Computes p(x_{t+1} | y_{t+1}) from p(x_{t+1}). This is useful for iterating 1-step ahead predictions"""
log_prob = p_x_tp1
x_tp1s = [
funsor.Variable(name + '_{}'.format(t + 1), funsor.reals())
for name in var_names
]
log_p_x = log_prob
log_prob += dist.Normal(emit_eq(x_tp1s), emit_noise, value=y)
log_p_y = log_prob.reduce(ops.logaddexp,
frozenset([x_tp1.name for x_tp1 in x_tp1s]))
log_p_x_y = log_prob + log_p_x - log_p_y
return log_p_x_y
def generate_HMM_dataset(model, args):
""" Generates a sequence of observations from a given funsor model
"""
data = [
funsor.Variable('y_{}'.format(t), funsor.bint(args.hidden_dim))
for t in range(args.time_steps)
]
log_prob = model(data)
var = [key for key, value in log_prob.inputs.items()]
# TODO: move sample to model definition, to avoid memory explosion
r = log_prob.sample(frozenset(var))
data = torch.tensor([
r.deltas[i].point.data for i in range(len(r.deltas))
if r.deltas[i].name.startswith('y')
])
return data
def model(data):
log_prob = funsor.to_funsor(0.)
x_curr = funsor.Tensor(torch.tensor(0.))
for t, y in enumerate(data):
x_prev = x_curr
# A delayed sample statement.
x_curr = funsor.Variable('x_{}'.format(t), funsor.reals())
log_prob += dist.Normal(1 + x_prev / 2., trans_noise, value=x_curr)
# Optionally marginalize out the previous state.
if t > 0 and not args.lazy:
log_prob = log_prob.reduce(ops.logaddexp, x_prev.name)
# An observe statement.
log_prob += dist.Normal(0.5 + 3 * x_curr, emit_noise, value=y)
# Marginalize out all remaining delayed variables.
log_prob = log_prob.reduce(ops.logaddexp)
return log_prob
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 filter_and_predict(self, data, smoothing=False):
trans_logits, trans_probs, trans_mvn, obs_mvn, x_trans_dist, y_dist = self.get_tensors_and_dists(
)
log_prob = funsor.Number(0.)
s_vars = {
-1: funsor.Tensor(torch.tensor(0), dtype=self.num_components)
}
x_vars = {-1: None}
predictive_x_dists, predictive_y_dists, filtering_dists = [], [], []
test_LLs = []
for t, y in enumerate(data):
s_vars[t] = funsor.Variable(f's_{t}',
funsor.bint(self.num_components))
x_vars[t] = funsor.Variable(f'x_{t}',
funsor.reals(self.hidden_dim))
log_prob += dist.Categorical(trans_probs(s=s_vars[t - 1]),
value=s_vars[t])
if t == 0:
log_prob += self.x_init_mvn(value=x_vars[t])
else:
log_prob += x_trans_dist(s=s_vars[t],
x=x_vars[t - 1],
y=x_vars[t])
if t > 0:
log_prob = log_prob.reduce(
ops.logaddexp,
frozenset([s_vars[t - 1].name, x_vars[t - 1].name]))
# do 1-step prediction and compute test LL
if t > 0:
predictive_x_dists.append(log_prob)
_log_prob = log_prob - log_prob.reduce(ops.logaddexp)
predictive_y_dist = y_dist(s=s_vars[t],
x=x_vars[t]) + _log_prob
test_LLs.append(
predictive_y_dist(y=y).reduce(ops.logaddexp).data.item())
predictive_y_dist = predictive_y_dist.reduce(
ops.logaddexp, frozenset([f"x_{t}", f"s_{t}"]))
predictive_y_dists.append(
funsor_to_mvn(predictive_y_dist, 0, ()))
log_prob += y_dist(s=s_vars[t], x=x_vars[t], y=y)
# save filtering dists for forward-backward smoothing
if smoothing:
filtering_dists.append(log_prob)
# do the backward recursion using previously computed ingredients
if smoothing:
# seed the backward recursion with the filtering distribution at t=T
smoothing_dists = [filtering_dists[-1]]
T = data.size(0)
s_vars = {
t: funsor.Variable(f's_{t}', funsor.bint(self.num_components))
for t in range(T)
}
x_vars = {
t: funsor.Variable(f'x_{t}', funsor.reals(self.hidden_dim))
for t in range(T)
}
# do the backward recursion.
# let p[t|t-1] be the predictive distribution at time step t.
# let p[t|t] be the filtering distribution at time step t.
# let f[t] denote the prior (transition) density at time step t.
# then the smoothing distribution p[t|T] at time step t is
# given by the following recursion.
# p[t-1|T] = p[t-1|t-1] <p[t|T] f[t] / p[t|t-1]>
# where <...> denotes integration of the latent variables at time step t.
for t in reversed(range(T - 1)):
integral = smoothing_dists[-1] - predictive_x_dists[t]
integral += dist.Categorical(trans_probs(s=s_vars[t]),
value=s_vars[t + 1])
integral += x_trans_dist(s=s_vars[t],
x=x_vars[t],
y=x_vars[t + 1])
integral = integral.reduce(
ops.logaddexp,
frozenset([s_vars[t + 1].name, x_vars[t + 1].name]))
smoothing_dists.append(filtering_dists[t] + integral)
# compute predictive test MSE and predictive variances
predictive_means = torch.stack([d.mean for d in predictive_y_dists
]) # T-1 ydim
predictive_vars = torch.stack([
d.covariance_matrix.diagonal(dim1=-1, dim2=-2)
for d in predictive_y_dists
])
predictive_mse = (predictive_means - data[1:, :]).pow(2.0).mean(-1)
if smoothing:
# compute smoothed mean function
smoothing_dists = [
funsor_to_cat_and_mvn(d, 0, (f"s_{t}", ))
for t, d in enumerate(reversed(smoothing_dists))
]
means = torch.stack([d[1].mean
for d in smoothing_dists]) # T 2 xdim
means = torch.matmul(means.unsqueeze(-2),
self.observation_matrix).squeeze(
-2) # T 2 ydim
probs = torch.stack([d[0].logits for d in smoothing_dists]).exp()
probs = probs / probs.sum(-1, keepdim=True) # T 2
smoothing_means = (probs.unsqueeze(-1) * means).sum(-2) # T ydim
smoothing_probs = probs[:, 1]
return predictive_mse, torch.tensor(np.array(test_LLs)), predictive_means, predictive_vars, \
smoothing_means, smoothing_probs
else:
return predictive_mse, torch.tensor(np.array(test_LLs))
def process_message(self, msg):
if msg["type"] == "sample":
if msg["value"] is None:
# Create a delayed sample.
msg["value"] = funsor.Variable(msg["name"], msg["fn"].output)
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
