def eager_subs(self, subs):
assert isinstance(subs, tuple)
subs = tuple(
(k, v if isinstance(v, (Variable, Slice)) else materialize(v))
for k, v in subs if k in self.inputs)
if not subs:
return self
# Constants and Affine funsors are eagerly substituted;
# everything else is lazily substituted.
lazy_subs = tuple(
(k, v) for k, v in subs
if not isinstance(v, (Number, Tensor, Variable, Slice))
and not (is_affine(v) and affine_inputs(v)))
var_subs = tuple((k, v) for k, v in subs if isinstance(v, Variable))
int_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor, Slice))
if v.dtype != 'real')
real_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor))
if v.dtype == 'real')
affine_subs = tuple((k, v) for k, v in subs
if is_affine(v) and affine_inputs(v)
and not isinstance(v, Variable))
if var_subs:
return self._eager_subs_var(
var_subs, int_subs + real_subs + affine_subs + lazy_subs)
if int_subs:
return self._eager_subs_int(int_subs,
real_subs + affine_subs + lazy_subs)
if real_subs:
return self._eager_subs_real(real_subs, affine_subs + lazy_subs)
if affine_subs:
return self._eager_subs_affine(affine_subs, lazy_subs)
return reflect(Subs, self, lazy_subs)
def test_gaussian_mixture_distribution(batch_inputs, event_inputs):
num_samples = 100000
sample_inputs = OrderedDict(particle=bint(num_samples))
be_inputs = OrderedDict(batch_inputs + event_inputs)
int_inputs = OrderedDict(
(k, d) for k, d in be_inputs.items() if d.dtype != 'real')
batch_inputs = OrderedDict(batch_inputs)
event_inputs = OrderedDict(event_inputs)
sampled_vars = frozenset(['f'])
p = random_gaussian(be_inputs) + 0.5 * random_tensor(int_inputs)
p_marginal = p.reduce(ops.logaddexp, 'e')
assert isinstance(p_marginal, Tensor)
q = p.sample(sampled_vars, sample_inputs)
q_marginal = q.reduce(ops.logaddexp, 'e')
q_marginal = materialize(q_marginal).reduce(ops.logaddexp, 'particle')
assert isinstance(q_marginal, Tensor)
q_marginal = q_marginal.align(tuple(p_marginal.inputs))
assert_close(q_marginal, p_marginal, atol=0.1, rtol=None)
def test_tensor_distribution(event_inputs, batch_inputs, test_grad):
num_samples = 50000
sample_inputs = OrderedDict(n=bint(num_samples))
be_inputs = OrderedDict(batch_inputs + event_inputs)
batch_inputs = OrderedDict(batch_inputs)
event_inputs = OrderedDict(event_inputs)
sampled_vars = frozenset(event_inputs)
p = random_tensor(be_inputs)
p.data.requires_grad_(test_grad)
q = p.sample(sampled_vars, sample_inputs)
mq = materialize(q).reduce(ops.logaddexp, 'n')
mq = mq.align(tuple(p.inputs))
assert_close(mq, p, atol=0.1, rtol=None)
if test_grad:
_, (p_data, mq_data) = align_tensors(p, mq)
assert p_data.shape == mq_data.shape
probe = torch.randn(p_data.shape)
expected = grad((p_data.exp() * probe).sum(), [p.data])[0]
actual = grad((mq_data.exp() * probe).sum(), [p.data])[0]
assert_close(actual, expected, atol=0.1, rtol=None)
def eager_categorical(probs, value):
value = materialize(value)
return Categorical.eager_log_prob(probs=probs, value=value)
def _scatter(src, res, subs):
# inverse of advanced indexing
# TODO check types of subs, in case some logic from eager_subs was accidentally left out?
# use advanced indexing logic copied from Tensor.eager_subs:
# materialize after checking for renaming case
subs = OrderedDict((k, materialize(v)) for k, v in subs)
# Compute result shapes.
inputs = OrderedDict()
for k, domain in res.inputs.items():
inputs[k] = domain
# Construct a dict with each input's positional dim,
# counting from the right so as to support broadcasting.
total_size = len(inputs) + len(res.output.shape) # Assumes only scalar indices.
new_dims = {}
for k, domain in inputs.items():
assert not domain.shape
new_dims[k] = len(new_dims) - total_size
# Use advanced indexing to construct a simultaneous substitution.
index = []
for k, domain in res.inputs.items():
if k in subs:
v = subs.get(k)
if isinstance(v, Number):
index.append(int(v.data))
else:
# Permute and expand v.data to end up at new_dims.
assert isinstance(v, Tensor)
v = v.align(tuple(k2 for k2 in inputs if k2 in v.inputs))
assert isinstance(v, Tensor)
v_shape = [1] * total_size
for k2, size in zip(v.inputs, v.data.shape):
v_shape[new_dims[k2]] = size
index.append(v.data.reshape(tuple(v_shape)))
else:
# Construct a [:] slice for this preserved input.
offset_from_right = -1 - new_dims[k]
index.append(torch.arange(domain.dtype).reshape(
(-1,) + (1,) * offset_from_right))
# Construct a [:] slice for the output.
for i, size in enumerate(res.output.shape):
offset_from_right = len(res.output.shape) - i - 1
index.append(torch.arange(size).reshape(
(-1,) + (1,) * offset_from_right))
# the only difference from Tensor.eager_subs is here:
# instead of indexing the rhs (lhs = rhs[index]), we index the lhs (lhs[index] = rhs)
# unsqueeze to make broadcasting work
src_inputs, src_data = src.inputs.copy(), src.data
for k, v in res.inputs.items():
if k not in src.inputs and isinstance(subs[k], Number):
src_inputs[k] = bint(1)
src_data = src_data.unsqueeze(-1 - len(src.output.shape))
src = Tensor(src_data, src_inputs, src.output.dtype).align(tuple(res.inputs.keys()))
data = res.data
data[tuple(index)] = src.data
return Tensor(data, inputs, res.dtype)
def eager_subs(self, subs):
assert isinstance(subs, tuple)
subs = tuple((k, materialize(to_funsor(v, self.inputs[k])))
for k, v in subs if k in self.inputs)
if not subs:
return self
# Constants and Variables are eagerly substituted;
# everything else is lazily substituted.
lazy_subs = tuple((k, v) for k, v in subs
if not isinstance(v, (Number, Tensor, Variable)))
var_subs = tuple((k, v) for k, v in subs if isinstance(v, Variable))
int_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor))
if v.dtype != 'real')
real_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor))
if v.dtype == 'real')
if not (var_subs or int_subs or real_subs):
return reflect(Subs, self, lazy_subs)
# First perform any variable substitutions.
if var_subs:
rename = {k: v.name for k, v in var_subs}
inputs = OrderedDict(
(rename.get(k, k), d) for k, d in self.inputs.items())
if len(inputs) != len(self.inputs):
raise ValueError("Variable substitution name conflict")
var_result = Gaussian(self.loc, self.precision, inputs)
return Subs(var_result, int_subs + real_subs + lazy_subs)
# Next perform any integer substitution, i.e. slicing into a batch.
if int_subs:
int_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype != 'real')
real_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype == 'real')
tensors = [self.loc, self.precision]
funsors = [Subs(Tensor(x, int_inputs), int_subs) for x in tensors]
inputs = funsors[0].inputs.copy()
inputs.update(real_inputs)
int_result = Gaussian(funsors[0].data, funsors[1].data, inputs)
return Subs(int_result, real_subs + lazy_subs)
# Try to perform a complete substitution of all real variables, resulting in a Tensor.
real_subs = OrderedDict(subs)
assert real_subs and not int_subs
if all(k in real_subs for k, d in self.inputs.items()
if d.dtype == 'real'):
# Broadcast all component tensors.
int_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype != 'real')
tensors = [
Tensor(self.loc, int_inputs),
Tensor(self.precision, int_inputs)
]
tensors.extend(real_subs.values())
inputs, tensors = align_tensors(*tensors)
batch_dim = tensors[0].dim() - 1
batch_shape = broadcast_shape(*(x.shape[:batch_dim]
for x in tensors))
(loc, precision), values = tensors[:2], tensors[2:]
# Form the concatenated value.
offsets, event_size = _compute_offsets(self.inputs)
value = BlockVector(batch_shape + (event_size, ))
for k, value_k in zip(real_subs, values):
offset = offsets[k]
value_k = value_k.reshape(value_k.shape[:batch_dim] + (-1, ))
if not torch._C._get_tracing_state():
assert value_k.size(-1) == self.inputs[k].num_elements
value_k = value_k.expand(batch_shape + value_k.shape[-1:])
value[...,
offset:offset + self.inputs[k].num_elements] = value_k
value = value.as_tensor()
# Evaluate the non-normalized log density.
result = -0.5 * _vmv(precision, value - loc)
result = Tensor(result, inputs)
assert result.output == reals()
return Subs(result, lazy_subs)
# Perform a partial substution of a subset of real variables, resulting in a Joint.
# See "The Matrix Cookbook" (November 15, 2012) ss. 8.1.3 eq. 353.
# http://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
raise NotImplementedError(
'TODO implement partial substitution of real variables')
def eager_subs(self, subs):
assert isinstance(subs, tuple)
subs = tuple(
(k, v if isinstance(v, (Variable, Slice)) else materialize(v))
for k, v in subs if k in self.inputs)
if not subs:
return self
# Constants and Variables are eagerly substituted;
# everything else is lazily substituted.
lazy_subs = tuple(
(k, v) for k, v in subs
if not isinstance(v, (Number, Tensor, Variable, Slice)))
var_subs = tuple((k, v) for k, v in subs if isinstance(v, Variable))
int_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor, Slice))
if v.dtype != 'real')
real_subs = tuple((k, v) for k, v in subs
if isinstance(v, (Number, Tensor))
if v.dtype == 'real')
if not (var_subs or int_subs or real_subs):
return reflect(Subs, self, lazy_subs)
# First perform any variable substitutions.
if var_subs:
rename = {k: v.name for k, v in var_subs}
inputs = OrderedDict(
(rename.get(k, k), d) for k, d in self.inputs.items())
if len(inputs) != len(self.inputs):
raise ValueError("Variable substitution name conflict")
var_result = Gaussian(self.info_vec, self.precision, inputs)
return Subs(var_result, int_subs + real_subs + lazy_subs)
# Next perform any integer substitution, i.e. slicing into a batch.
if int_subs:
int_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype != 'real')
real_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype == 'real')
tensors = [self.info_vec, self.precision]
funsors = [Subs(Tensor(x, int_inputs), int_subs) for x in tensors]
inputs = funsors[0].inputs.copy()
inputs.update(real_inputs)
int_result = Gaussian(funsors[0].data, funsors[1].data, inputs)
return Subs(int_result, real_subs + lazy_subs)
# Broadcast all component tensors.
real_subs = OrderedDict(subs)
assert real_subs and not int_subs
int_inputs = OrderedDict(
(k, d) for k, d in self.inputs.items() if d.dtype != 'real')
tensors = [
Tensor(self.info_vec, int_inputs),
Tensor(self.precision, int_inputs)
]
tensors.extend(real_subs.values())
int_inputs, tensors = align_tensors(*tensors)
batch_dim = tensors[0].dim() - 1
batch_shape = broadcast_shape(*(x.shape[:batch_dim] for x in tensors))
(info_vec, precision), values = tensors[:2], tensors[2:]
offsets, event_size = _compute_offsets(self.inputs)
slices = [(k, slice(offset, offset + self.inputs[k].num_elements))
for k, offset in offsets.items()]
# Expand all substituted values.
values = OrderedDict(zip(real_subs, values))
for k, value in values.items():
value = value.reshape(value.shape[:batch_dim] + (-1, ))
if not torch._C._get_tracing_state():
assert value.size(-1) == self.inputs[k].num_elements
values[k] = value.expand(batch_shape + value.shape[-1:])
# Try to perform a complete substitution of all real variables, resulting in a Tensor.
if all(k in real_subs for k, d in self.inputs.items()
if d.dtype == 'real'):
# Form the concatenated value.
value = BlockVector(batch_shape + (event_size, ))
for k, i in slices:
if k in values:
value[..., i] = values[k]
value = value.as_tensor()
# Evaluate the non-normalized log density.
result = _vv(value, info_vec - 0.5 * _mv(precision, value))
result = Tensor(result, int_inputs)
assert result.output == reals()
return Subs(result, lazy_subs)
# Perform a partial substution of a subset of real variables, resulting in a Joint.
# We split real inputs into two sets: a for the preserved and b for the substituted.
b = frozenset(k for k, v in real_subs.items())
a = frozenset(k for k, d in self.inputs.items()
if d.dtype == 'real' and k not in b)
prec_aa = torch.cat([
torch.cat([precision[..., i1, i2] for k2, i2 in slices if k2 in a],
dim=-1) for k1, i1 in slices if k1 in a
],
dim=-2)
prec_ab = torch.cat([
torch.cat([precision[..., i1, i2] for k2, i2 in slices if k2 in b],
dim=-1) for k1, i1 in slices if k1 in a
],
dim=-2)
prec_bb = torch.cat([
torch.cat([precision[..., i1, i2] for k2, i2 in slices if k2 in b],
dim=-1) for k1, i1 in slices if k1 in b
],
dim=-2)
info_a = torch.cat([info_vec[..., i] for k, i in slices if k in a],
dim=-1)
info_b = torch.cat([info_vec[..., i] for k, i in slices if k in b],
dim=-1)
value_b = torch.cat([values[k] for k, i in slices if k in b], dim=-1)
info_vec = info_a - _mv(prec_ab, value_b)
log_scale = _vv(value_b, info_b - 0.5 * _mv(prec_bb, value_b))
precision = prec_aa.expand(info_vec.shape + (-1, ))
inputs = int_inputs.copy()
for k, d in self.inputs.items():
if k not in real_subs:
inputs[k] = d
return Gaussian(info_vec, precision, inputs) + Tensor(
log_scale, int_inputs)
