def _compute_moments(self, *u_parents):
# Compute the number of plate axes for each node
plate_counts0 = [(np.ndim(u_parent[0]) - len(keys))
for (keys,u_parent) in zip(self.in_keys, u_parents)]
plate_counts1 = [(np.ndim(u_parent[1]) - 2*len(keys))
for (keys,u_parent) in zip(self.in_keys, u_parents)]
# The number of plate axes for the output
N0 = max(plate_counts0)
N1 = max(plate_counts1)
# The total number of unique keys used (keys are 0,1,...,N_keys-1)
D = self.N_keys
#
# Compute the mean
#
out_all_keys = list(range(D+N0-1, D-1, -1)) + self.out_keys
#nodes_dim_keys = self.nodes_dim_keys
in_all_keys = [list(range(D+plate_count-1, D-1, -1)) + keys
for (plate_count, keys) in zip(plate_counts0,
self.in_keys)]
u0 = [u[0] for u in u_parents]
args = misc.zipper_merge(u0, in_all_keys) + [out_all_keys]
x0 = np.einsum(*args)
#
# Compute the covariance
#
out_all_keys = (list(range(2*D+N1-1, 2*D-1, -1))
+ [D+key for key in self.out_keys]
+ self.out_keys)
in_all_keys = [list(range(2*D+plate_count-1, 2*D-1, -1))
+ [D+key for key in node_keys]
+ node_keys
for (plate_count, node_keys) in zip(plate_counts1,
self.in_keys)]
u1 = [u[1] for u in u_parents]
args = misc.zipper_merge(u1, in_all_keys) + [out_all_keys]
x1 = np.einsum(*args)
if not self.gaussian_gamma:
return [x0, x1]
# Compute Gaussian-gamma specific moments
x2 = 1
x3 = 0
for i in range(len(u_parents)):
x2 = x2 * u_parents[i][2]
x3 = x3 + u_parents[i][3]
return [x0, x1, x2, x3]
def MultiMixture(thetas, *mixture_args, **kwargs):
"""Creates a mixture over several axes using as many categorical variables.
The mixings are assumed to be separate, that is, inner mixings don't affect
the parameters of outer mixings.
"""
thetas = list(thetas)
N = len(thetas)
# Add trailing plate axes to thetas because you assume that each
# mixed axis is separate from the others.
thetas = [
theta[(Ellipsis, ) + i * (None, )] for (i, theta) in enumerate(thetas)
]
args = (thetas[:1] +
list(misc.zipper_merge(
(N - 1) * [Mixture], thetas[1:])) + list(mixture_args))
return Mixture(*args, **kwargs)
def MultiMixture(thetas, *mixture_args, **kwargs):
"""Creates a mixture over several axes using as many categorical variables.
The mixings are assumed to be separate, that is, inner mixings don't affect
the parameters of outer mixings.
"""
thetas = list(thetas)
N = len(thetas)
# Add trailing plate axes to thetas because you assume that each
# mixed axis is separate from the others.
thetas = [theta[(Ellipsis,) + i*(None,)]
for (i, theta) in enumerate(thetas)]
args = (
thetas[:1]
+ list(misc.zipper_merge((N-1) * [Mixture], thetas[1:]))
+ list(mixture_args)
)
return Mixture(*args, **kwargs)
def _compute_function(self, *x_parents):
# TODO: Add unit tests for this function
(xs, alphas) = (
(x_parents, 1) if not self.gaussian_gamma else
zip(*x_parents)
)
# Add Ellipsis for the plates
in_keys = [[Ellipsis] + k for k in self.in_keys]
out_keys = [Ellipsis] + self.out_keys
samples_and_keys = misc.zipper_merge(xs, in_keys)
y = np.einsum(*(samples_and_keys + [out_keys]))
return (
y if not self.gaussian_gamma else
(y, misc.multiply(*alphas))
)
def _compute_message(*arrays, plates_from=(), plates_to=(), ndim=0):
"""
A general function for computing messages by sum-multiply
The function computes the product of the input arrays and then sums to
the requested plates.
"""
# Check that the plates broadcast properly
if not misc.is_shape_subset(plates_to, plates_from):
raise ValueError("plates_to must be broadcastable to plates_from")
# Compute the explicit shape of the product
shapes = [np.shape(array) for array in arrays]
arrays_shape = misc.broadcasted_shape(*shapes)
# Compute plates and dims that are present
if ndim == 0:
arrays_plates = arrays_shape
dims = ()
else:
arrays_plates = arrays_shape[:-ndim]
dims = arrays_shape[-ndim:]
# Compute the correction term. If some of the plates that should be
# summed are actually broadcasted, one must multiply by the size of the
# corresponding plate
r = Node.broadcasting_multiplier(plates_from, arrays_plates, plates_to)
# For simplicity, make the arrays equal ndim
arrays = misc.make_equal_ndim(*arrays)
# Keys for the input plates: (N-1, N-2, ..., 0)
nplates = len(arrays_plates)
in_plate_keys = list(range(nplates))
# Keys for the output plates
out_plate_keys = [key
for key in in_plate_keys
if key < len(plates_to) and plates_to[-key-1] != 1]
# Keys for the dims
dim_keys = list(range(nplates, nplates+ndim))
# Total input and output keys
in_keys = len(arrays) * [in_plate_keys + dim_keys]
out_keys = out_plate_keys + dim_keys
# Compute the sum-product with correction
einsum_args = misc.zipper_merge(arrays, in_keys) + [out_keys]
y = r * np.einsum(*einsum_args)
# Reshape the result and apply correction
nplates_result = min(len(plates_to), len(arrays_plates))
if nplates_result == 0:
plates_result = []
else:
plates_result = [min(plates_to[ind], arrays_plates[ind])
for ind in range(-nplates_result, 0)]
y = np.reshape(y, plates_result + list(dims))
return y
def _compute_message(*arrays, plates_from=(), plates_to=(), ndim=0):
"""
A general function for computing messages by sum-multiply
The function computes the product of the input arrays and then sums to
the requested plates.
"""
# Check that the plates broadcast properly
if not misc.is_shape_subset(plates_to, plates_from):
raise ValueError("plates_to must be broadcastable to plates_from")
# Compute the explicit shape of the product
shapes = [np.shape(array) for array in arrays]
arrays_shape = misc.broadcasted_shape(*shapes)
# Compute plates and dims that are present
if ndim == 0:
arrays_plates = arrays_shape
dims = ()
else:
arrays_plates = arrays_shape[:-ndim]
dims = arrays_shape[-ndim:]
# Compute the correction term. If some of the plates that should be
# summed are actually broadcasted, one must multiply by the size of the
# corresponding plate
r = Node.broadcasting_multiplier(plates_from, arrays_plates, plates_to)
# For simplicity, make the arrays equal ndim
arrays = misc.make_equal_ndim(*arrays)
# Keys for the input plates: (N-1, N-2, ..., 0)
nplates = len(arrays_plates)
in_plate_keys = list(range(nplates))
# Keys for the output plates
out_plate_keys = [
key for key in in_plate_keys
if key < len(plates_to) and plates_to[-key - 1] != 1
]
# Keys for the dims
dim_keys = list(range(nplates, nplates + ndim))
# Total input and output keys
in_keys = len(arrays) * [in_plate_keys + dim_keys]
out_keys = out_plate_keys + dim_keys
# Compute the sum-product with correction
einsum_args = misc.zipper_merge(arrays, in_keys) + [out_keys]
y = r * np.einsum(*einsum_args)
# Reshape the result and apply correction
nplates_result = min(len(plates_to), len(arrays_plates))
if nplates_result == 0:
plates_result = []
else:
plates_result = [
min(plates_to[ind], arrays_plates[ind])
for ind in range(-nplates_result, 0)
]
y = np.reshape(y, plates_result + list(dims))
return y
def _compute_moments(self, *u_parents):
# Compute the number of plate axes for each node
plate_counts0 = [
(np.ndim(u_parent[0]) - len(keys))
for (keys,u_parent) in zip(self.in_keys, u_parents)
]
plate_counts1 = [
(
# Gaussian moments: Use second moments "matrix"
(np.ndim(u_parent[1]) - 2*len(keys))
if not is_const else
# Delta moments: Use first moment "vector"
(np.ndim(u_parent[0]) - len(keys))
)
for (keys, u_parent, is_const) in zip(
self.in_keys,
u_parents,
self.is_constant
)
]
# The number of plate axes for the output
N0 = max(plate_counts0)
N1 = max(plate_counts1)
# The total number of unique keys used (keys are 0,1,...,N_keys-1)
D = self.N_keys
#
# Compute the mean
#
out_all_keys = list(range(D+N0-1, D-1, -1)) + self.out_keys
#nodes_dim_keys = self.nodes_dim_keys
in_all_keys = [list(range(D+plate_count-1, D-1, -1)) + keys
for (plate_count, keys) in zip(plate_counts0,
self.in_keys)]
u0 = [u[0] for u in u_parents]
args = misc.zipper_merge(u0, in_all_keys) + [out_all_keys]
x0 = np.einsum(*args)
#
# Compute the covariance
#
out_all_keys = (list(range(2*D+N1-1, 2*D-1, -1))
+ [D+key for key in self.out_keys]
+ self.out_keys)
in_all_keys = [
x
for (plate_count, node_keys, is_const) in zip(
plate_counts1,
self.in_keys,
self.is_constant,
)
for x in (
# Gaussian moments: Use the second moment
[
list(range(2*D+plate_count-1, 2*D-1, -1))
+ [D+key for key in node_keys]
+ node_keys
]
if not is_const else
# Delta moments: Use the first moment tiwce
[
(
list(range(2*D+plate_count-1, 2*D-1, -1))
+ [D+key for key in node_keys]
),
(
list(range(2*D+plate_count-1, 2*D-1, -1))
+ node_keys
),
]
)
]
u1 = [
x
for (u, is_const) in zip(u_parents, self.is_constant)
for x in (
# Gaussian moments: Use the second moment
[u[1]]
if not is_const else
# Delta moments: Use the first moment twice
[u[0], u[0]]
)
]
args = misc.zipper_merge(u1, in_all_keys) + [out_all_keys]
x1 = np.einsum(*args)
if not self.gaussian_gamma:
return [x0, x1]
# Compute Gaussian-gamma specific moments
x2 = 1
x3 = 0
for i in range(len(u_parents)):
x2 = x2 * (1 if self.is_constant[i] else u_parents[i][2])
x3 = x3 + (0 if self.is_constant[i] else u_parents[i][3])
return [x0, x1, x2, x3]
