Extend lift rewrites to multivariate RVs

[ricardoV94]

Please describe the purpose of filing this issue

We have two rewrites than move Dimshuffles and Subtensor operations up to the inputs of RVs.

DimShuffle lifting facilitates pattern matching of some graphs, while the Subtensor lifting allows more efficient graphs to be obtained from a general one, when we only compute some of the indepedent dimensions of batched RVs.

We already make use of the later in auto-imputation of univariate RVs in PyMC: pymc-devs/pymc#5260, and I can imagine even more uses for efficient posterior predictive sampling.

pytensor/pytensor/tensor/random/rewriting.py

Lines 112 to 411 in 19e1a98

	@node_rewriter([DimShuffle])
	def local_dimshuffle_rv_lift(fgraph, node):
	"""Lift a ``DimShuffle`` through ``RandomVariable`` inputs.
	For example, ``normal(mu, std).T == normal(mu.T, std.T)``.
	The basic idea behind this rewrite is that we need to separate the
	``DimShuffle``-ing into distinct ``DimShuffle``s that each occur in two
	distinct sub-spaces: the (set of independent) parameters and ``size``
	(i.e. replications) sub-spaces.
	If a ``DimShuffle`` exchanges dimensions across those two sub-spaces, then we
	don't do anything.
	Otherwise, if the ``DimShuffle`` only exchanges dimensions within each of
	those sub-spaces, we can break it apart and apply the parameter-space
	``DimShuffle`` to the distribution parameters, and then apply the
	replications-space ``DimShuffle`` to the ``size`` tuple. The latter is a
	particularly simple rearranging of a tuple, but the former requires a
	little more work.
	TODO: Currently, multivariate support for this rewrite is disabled.
	"""
	ds_op = node.op
	if not isinstance(ds_op, DimShuffle):
	return False
	base_rv = node.inputs[0]
	rv_node = base_rv.owner
	if not (
	rv_node and isinstance(rv_node.op, RandomVariable) and rv_node.op.ndim_supp == 0
	):
	return False
	# If no one else is using the underlying `RandomVariable`, then we can
	# do this; otherwise, the graph would be internally inconsistent.
	if is_rv_used_in_graph(base_rv, node, fgraph):
	return False
	rv_op = rv_node.op
	rng, size, dtype, *dist_params = rv_node.inputs
	# We need to know the dimensions that were *not* added by the `size`
	# parameter (i.e. the dimensions corresponding to independent variates with
	# different parameter values)
	num_ind_dims = None
	if len(dist_params) == 1:
	num_ind_dims = dist_params[0].ndim
	else:
	# When there is more than one distribution parameter, assume that all
	# of them will broadcast to the maximum number of dimensions
	num_ind_dims = max(d.ndim for d in dist_params)
	# If the indices in `ds_new_order` are entirely within the replication
	# indices group or the independent variates indices group, then we can apply
	# this rewrite.
	ds_new_order = ds_op.new_order
	# Create a map from old index order to new/`DimShuffled` index order
	dim_orders = [(n, d) for n, d in enumerate(ds_new_order) if isinstance(d, int)]
	# Find the index at which the replications/independents split occurs
	reps_ind_split_idx = len(dim_orders) - (num_ind_dims + rv_op.ndim_supp)
	ds_reps_new_dims = dim_orders[:reps_ind_split_idx]
	ds_ind_new_dims = dim_orders[reps_ind_split_idx:]
	ds_in_ind_space = ds_ind_new_dims and all(
	d >= reps_ind_split_idx for n, d in ds_ind_new_dims
	)
	if ds_in_ind_space or (not ds_ind_new_dims and not ds_reps_new_dims):
	# Update the `size` array to reflect the `DimShuffle`d dimensions,
	# since the trailing dimensions in `size` represent the independent
	# variates dimensions (for univariate distributions, at least)
	has_size = get_vector_length(size) > 0
	new_size = (
	[constant(1, dtype="int64") if o == "x" else size[o] for o in ds_new_order]
	if has_size
	else size
	)
	# Compute the new axes parameter(s) for the `DimShuffle` that will be
	# applied to the `RandomVariable` parameters (they need to be offset)
	if ds_ind_new_dims:
	rv_params_new_order = [
	d - reps_ind_split_idx if isinstance(d, int) else d
	for d in ds_new_order[ds_ind_new_dims[0][0] :]
	]
	if not has_size and len(ds_new_order[: ds_ind_new_dims[0][0]]) > 0:
	# Additional broadcast dimensions need to be added to the
	# independent dimensions (i.e. parameters), since there's no
	# `size` to which they can be added
	rv_params_new_order = (
	list(ds_new_order[: ds_ind_new_dims[0][0]]) + rv_params_new_order
	)
	else:
	# This case is reached when, for example, `ds_new_order` only
	# consists of new broadcastable dimensions (i.e. `"x"`s)
	rv_params_new_order = ds_new_order
	# Lift the `DimShuffle`s into the parameters
	# NOTE: The parameters might not be broadcasted against each other, so
	# we can only apply the parts of the `DimShuffle` that are relevant.
	new_dist_params = []
	for d in dist_params:
	if d.ndim < len(ds_ind_new_dims):
	_rv_params_new_order = [
	o
	for o in rv_params_new_order
	if (isinstance(o, int) and o < d.ndim) or o == "x"
	]
	else:
	_rv_params_new_order = rv_params_new_order
	new_dist_params.append(
	type(ds_op)(d.type.broadcastable, _rv_params_new_order)(d)
	)
	new_node = rv_op.make_node(rng, new_size, dtype, *new_dist_params)
	if config.compute_test_value != "off":
	compute_test_value(new_node)
	out = new_node.outputs[1]
	if base_rv.name:
	out.name = f"{base_rv.name}_lifted"
	return [out]
	ds_in_reps_space = ds_reps_new_dims and all(
	d < reps_ind_split_idx for n, d in ds_reps_new_dims
	)
	if ds_in_reps_space:
	# Update the `size` array to reflect the `DimShuffle`d dimensions.
	# There should be no need to `DimShuffle` now.
	new_size = [
	constant(1, dtype="int64") if o == "x" else size[o] for o in ds_new_order
	]
	new_node = rv_op.make_node(rng, new_size, dtype, *dist_params)
	if config.compute_test_value != "off":
	compute_test_value(new_node)
	out = new_node.outputs[1]
	if base_rv.name:
	out.name = f"{base_rv.name}_lifted"
	return [out]
	return False
	@node_rewriter([Subtensor, AdvancedSubtensor1, AdvancedSubtensor])
	def local_subtensor_rv_lift(fgraph, node):
	"""Lift a ``*Subtensor`` through ``RandomVariable`` inputs.
	In a fashion similar to ``local_dimshuffle_rv_lift``, the indexed dimensions
	need to be separated into distinct replication-space and (independent)
	parameter-space ``*Subtensor``s.
	The replication-space ``*Subtensor`` can be used to determine a
	sub/super-set of the replication-space and, thus, a "smaller"/"larger"
	``size`` tuple. The parameter-space ``*Subtensor`` is simply lifted and
	applied to the distribution parameters.
	Consider the following example graph:
	``normal(mu, std, size=(d1, d2, d3))[idx1, idx2, idx3]``. The
	``*Subtensor`` ``Op`` requests indices ``idx1``, ``idx2``, and ``idx3``,
	which correspond to all three ``size`` dimensions. Now, depending on the
	broadcasted dimensions of ``mu`` and ``std``, this ``*Subtensor`` ``Op``
	could be reducing the ``size`` parameter and/or sub-setting the independent
	``mu`` and ``std`` parameters. Only once the dimensions are properly
	separated into the two replication/parameter subspaces can we determine how
	the ``*Subtensor`` indices are distributed.
	For instance, ``normal(mu, std, size=(d1, d2, d3))[idx1, idx2, idx3]``
	could become
	``normal(mu[idx1], std[idx2], size=np.shape(idx1) + np.shape(idx2) + np.shape(idx3))``
	if ``mu.shape == std.shape == ()``
	``normal`` is a rather simple case, because it's univariate. Multivariate
	cases require a mapping between the parameter space and the image of the
	random variable. This may not always be possible, but for many common
	distributions it is. For example, the dimensions of the multivariate
	normal's image can be mapped directly to each dimension of its parameters.
	We use these mappings to change a graph like ``multivariate_normal(mu, Sigma)[idx1]``
	into ``multivariate_normal(mu[idx1], Sigma[idx1, idx1])``.
	"""
	st_op = node.op
	if not isinstance(st_op, (AdvancedSubtensor, AdvancedSubtensor1, Subtensor)):
	return False
	base_rv = node.inputs[0]
	rv_node = base_rv.owner
	if not (rv_node and isinstance(rv_node.op, RandomVariable)):
	return False
	# If no one else is using the underlying `RandomVariable`, then we can
	# do this; otherwise, the graph would be internally inconsistent.
	if is_rv_used_in_graph(base_rv, node, fgraph):
	return False
	rv_op = rv_node.op
	rng, size, dtype, *dist_params = rv_node.inputs
	# TODO: Remove this once the multi-dimensional changes described below are
	# in place.
	if rv_op.ndim_supp > 0:
	return False
	rv_op = base_rv.owner.op
	rng, size, dtype, *dist_params = base_rv.owner.inputs
	idx_list = getattr(st_op, "idx_list", None)
	if idx_list:
	cdata = get_idx_list(node.inputs, idx_list)
	else:
	cdata = node.inputs[1:]
	st_indices, st_is_bool = zip(
	*tuple(
	(as_index_variable(i), getattr(i, "dtype", None) == "bool") for i in cdata
	)
	)
	# We need to separate dimensions into replications and independents
	num_ind_dims = None
	if len(dist_params) == 1:
	num_ind_dims = dist_params[0].ndim
	else:
	# When there is more than one distribution parameter, assume that all
	# of them will broadcast to the maximum number of dimensions
	num_ind_dims = max(d.ndim for d in dist_params)
	reps_ind_split_idx = base_rv.ndim - (num_ind_dims + rv_op.ndim_supp)
	if len(st_indices) > reps_ind_split_idx:
	# These are the indices that need to be applied to the parameters
	ind_indices = tuple(st_indices[reps_ind_split_idx:])
	# We need to broadcast the parameters before applying the `*Subtensor*`
	# with these indices, because the indices could be referencing broadcast
	# dimensions that don't exist (yet)
	bcast_dist_params = broadcast_params(dist_params, rv_op.ndims_params)
	# TODO: For multidimensional distributions, we need a map that tells us
	# which dimensions of the parameters need to be indexed.
	#
	# For example, `multivariate_normal` would have the following:
	# `RandomVariable.param_to_image_dims = ((0,), (0, 1))`
	#
	# I.e. the first parameter's (i.e. mean's) first dimension maps directly to
	# the dimension of the RV's image, and its second parameter's
	# (i.e. covariance's) first and second dimensions map directly to the
	# dimension of the RV's image.
	args_lifted = tuple(p[ind_indices] for p in bcast_dist_params)
	else:
	# In this case, no indexing is applied to the parameters; only the
	# `size` parameter is affected.
	args_lifted = dist_params
	# TODO: Could use `ShapeFeature` info. We would need to be sure that
	# `node` isn't in the results, though.
	# if hasattr(fgraph, "shape_feature"):
	# output_shape = fgraph.shape_feature.shape_of(node.outputs[0])
	# else:
	output_shape = indexed_result_shape(base_rv.shape, st_indices)
	size_lifted = (
	output_shape if rv_op.ndim_supp == 0 else output_shape[: -rv_op.ndim_supp]
	)
	# Boolean indices can actually change the `size` value (compared to just
	# *which* dimensions of `size` are used).
	if any(st_is_bool):
	size_lifted = tuple(
	at_sum(idx) if is_bool else s
	for s, is_bool, idx in zip(
	size_lifted, st_is_bool, st_indices[: (reps_ind_split_idx + 1)]
	)
	)
	new_node = rv_op.make_node(rng, size_lifted, dtype, *args_lifted)
	_, new_rv = new_node.outputs
	# Calling `Op.make_node` directly circumvents test value computations, so
	# we need to compute the test values manually
	if config.compute_test_value != "off":
	compute_test_value(new_node)
	return [new_rv]