def rv_op(cls, rhos, sigma, init_dist, steps, ar_order, constant_term, size=None):
# Init dist should have shape (*size, ar_order)
if size is not None:
batch_size = size
else:
# In this case the size of the init_dist depends on the parameters shape
# The last dimension of rho and init_dist does not matter
batch_size = at.broadcast_shape(sigma, rhos[..., 0], init_dist[..., 0])
if init_dist.owner.op.ndim_supp == 0:
init_dist_size = (*batch_size, ar_order)
else:
# In this case the support dimension must cover for ar_order
init_dist_size = batch_size
init_dist = change_rv_size(init_dist, init_dist_size)
# Create OpFromGraph representing random draws form AR process
# Variables with underscore suffix are dummy inputs into the OpFromGraph
init_ = init_dist.type()
rhos_ = rhos.type()
sigma_ = sigma.type()
steps_ = steps.type()
rhos_bcast_shape_ = init_.shape
if constant_term:
# In this case init shape is one unit smaller than rhos in the last dimension
rhos_bcast_shape_ = (*rhos_bcast_shape_[:-1], rhos_bcast_shape_[-1] + 1)
rhos_bcast_ = at.broadcast_to(rhos_, rhos_bcast_shape_)
noise_rng = aesara.shared(np.random.default_rng())
def step(*args):
*prev_xs, reversed_rhos, sigma, rng = args
if constant_term:
mu = reversed_rhos[-1] + at.sum(prev_xs * reversed_rhos[:-1], axis=0)
else:
mu = at.sum(prev_xs * reversed_rhos, axis=0)
next_rng, new_x = Normal.dist(mu=mu, sigma=sigma, rng=rng).owner.outputs
return new_x, {rng: next_rng}
# We transpose inputs as scan iterates over first dimension
innov_, innov_updates_ = aesara.scan(
fn=step,
outputs_info=[{"initial": init_.T, "taps": range(-ar_order, 0)}],
non_sequences=[rhos_bcast_.T[::-1], sigma_.T, noise_rng],
n_steps=steps_,
strict=True,
)
(noise_next_rng,) = tuple(innov_updates_.values())
ar_ = at.concatenate([init_, innov_.T], axis=-1)
ar_op = AutoRegressiveRV(
inputs=[rhos_, sigma_, init_, steps_],
outputs=[noise_next_rng, ar_],
ar_order=ar_order,
constant_term=constant_term,
inline=True,
)
ar = ar_op(rhos, sigma, init_dist, steps)
return ar
def rv_op(cls, dist, lower=None, upper=None, size=None, rngs=None):
lower = at.constant(
-np.inf) if lower is None else at.as_tensor_variable(lower)
upper = at.constant(
np.inf) if upper is None else at.as_tensor_variable(upper)
# When size is not specified, dist may have to be broadcasted according to lower/upper
dist_shape = size if size is not None else at.broadcast_shape(
dist, lower, upper)
dist = change_rv_size(dist, dist_shape)
# Censoring is achieved by clipping the base distribution between lower and upper
rv_out = at.clip(dist, lower, upper)
# Reference nodes to facilitate identification in other classmethods, without
# worring about possible dimshuffles
rv_out.tag.dist = dist
rv_out.tag.lower = lower
rv_out.tag.upper = upper
if rngs is not None:
rv_out = cls._change_rngs(rv_out, rngs)
return rv_out
def make_node(self, rng, size, dtype, mu, sigma, init, steps):
steps = at.as_tensor_variable(steps)
if not steps.ndim == 0 or not steps.dtype.startswith("int"):
raise ValueError("steps must be an integer scalar (ndim=0).")
mu = at.as_tensor_variable(mu)
sigma = at.as_tensor_variable(sigma)
init = at.as_tensor_variable(init)
# Resize init distribution
size = normalize_size_param(size)
# If not explicit, size is determined by the shapes of mu, sigma, and init
init_size = size if not rv_size_is_none(size) else at.broadcast_shape(mu, sigma, init)
init = change_rv_size(init, init_size)
return super().make_node(rng, size, dtype, mu, sigma, init, steps)
def rv_op(cls, weights, *components, size=None):
# Create new rng for the mix_indexes internal RV
mix_indexes_rng = aesara.shared(np.random.default_rng())
single_component = len(components) == 1
ndim_supp = components[0].owner.op.ndim_supp
if size is not None:
components = cls._resize_components(size, *components)
elif not single_component:
# We might need to broadcast components when size is not specified
shape = tuple(at.broadcast_shape(*components))
size = shape[:len(shape) - ndim_supp]
components = cls._resize_components(size, *components)
# Extract replication ndims from components and weights
ndim_batch = components[0].ndim - ndim_supp
if single_component:
# One dimension is taken by the mixture axis in the single component case
ndim_batch -= 1
# The weights may imply extra batch dimensions that go beyond what is already
# implied by the component dimensions (ndim_batch)
weights_ndim_batch = max(0, weights.ndim - ndim_batch - 1)
# If weights are large enough that they would broadcast the component distributions
# we try to resize them. This in necessary to avoid duplicated values in the
# random method and for equivalency with the logp method
if weights_ndim_batch:
new_size = at.concatenate([
weights.shape[:weights_ndim_batch],
components[0].shape[:ndim_batch],
])
components = cls._resize_components(new_size, *components)
# Extract support and batch ndims from components and weights
ndim_batch = components[0].ndim - ndim_supp
if single_component:
ndim_batch -= 1
weights_ndim_batch = max(0, weights.ndim - ndim_batch - 1)
assert weights_ndim_batch == 0
# Component RVs terms are accounted by the Mixture logprob, so they can be
# safely ignored by Aeppl
components = [ignore_logprob(component) for component in components]
# Create a OpFromGraph that encapsulates the random generating process
# Create dummy input variables with the same type as the ones provided
weights_ = weights.type()
components_ = [component.type() for component in components]
mix_indexes_rng_ = mix_indexes_rng.type()
mix_axis = -ndim_supp - 1
# Stack components across mixture axis
if single_component:
# If single component, we consider it as being already "stacked"
stacked_components_ = components_[0]
else:
stacked_components_ = at.stack(components_, axis=mix_axis)
# Broadcast weights to (*batched dimensions, stack dimension), ignoring support dimensions
weights_broadcast_shape_ = stacked_components_.shape[:ndim_batch + 1]
weights_broadcasted_ = at.broadcast_to(weights_,
weights_broadcast_shape_)
# Draw mixture indexes and append (stack + ndim_supp) broadcastable dimensions to the right
mix_indexes_ = at.random.categorical(weights_broadcasted_,
rng=mix_indexes_rng_)
mix_indexes_padded_ = at.shape_padright(mix_indexes_, ndim_supp + 1)
# Index components and squeeze mixture dimension
mix_out_ = at.take_along_axis(stacked_components_,
mix_indexes_padded_,
axis=mix_axis)
mix_out_ = at.squeeze(mix_out_, axis=mix_axis)
# Output mix_indexes rng update so that it can be updated in place
mix_indexes_rng_next_ = mix_indexes_.owner.outputs[0]
mix_op = MarginalMixtureRV(
inputs=[mix_indexes_rng_, weights_, *components_],
outputs=[mix_indexes_rng_next_, mix_out_],
)
# Create the actual MarginalMixture variable
mix_out = mix_op(mix_indexes_rng, weights, *components)
# Reference nodes to facilitate identification in other classmethods
mix_out.tag.weights = weights
mix_out.tag.components = components
mix_out.tag.choices_rng = mix_indexes_rng
return mix_out
