def testTriL(self):
with self.cached_session():
shift = np.array([-1, 0, 1], dtype=np.float32)
tril = np.array([[[3, 0, 0], [2, -1, 0], [3, 2, 1]],
[[2, 0, 0], [3, -2, 0], [4, 3, 2]]],
dtype=np.float32)
scale = linalg.LinearOperatorLowerTriangular(tril,
is_non_singular=True)
affine = AffineLinearOperator(shift=shift,
scale=scale,
validate_args=True)
x = np.array([[[1, 0, -1], [2, 3, 4]], [[4, 1, -7], [6, 9, 8]]],
dtype=np.float32)
# If we made the bijector do x*A+b then this would be simplified to:
# y = np.matmul(x, tril) + shift.
y = np.squeeze(np.matmul(tril, np.expand_dims(x, -1)), -1) + shift
ildj = -np.sum(
np.log(np.abs(np.diagonal(tril, axis1=-2, axis2=-1))))
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(
ildj,
affine.inverse_log_det_jacobian(y, event_ndims=2).eval())
self.assertAllClose(
-affine.inverse_log_det_jacobian(y, event_ndims=2).eval(),
affine.forward_log_det_jacobian(x, event_ndims=2).eval())
def testTriL(self):
with self.test_session():
shift = np.array([-1, 0, 1], dtype=np.float32)
tril = np.array([[[1, 0, 0],
[2, -1, 0],
[3, 2, 1]],
[[2, 0, 0],
[3, -2, 0],
[4, 3, 2]]],
dtype=np.float32)
scale = linalg.LinearOperatorLowerTriangular(tril, is_non_singular=True)
affine = AffineLinearOperator(
shift=shift, scale=scale, validate_args=True)
x = np.array([[[1, 0, -1],
[2, 3, 4]],
[[4, 1, -7],
[6, 9, 8]]],
dtype=np.float32)
# If we made the bijector do x*A+b then this would be simplified to:
# y = np.matmul(x, tril) + shift.
y = np.squeeze(np.matmul(tril, np.expand_dims(x, -1)), -1) + shift
ildj = -np.sum(np.log(np.abs(np.diagonal(
tril, axis1=-2, axis2=-1))),
axis=-1)
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(ildj, affine.inverse_log_det_jacobian(y).eval())
self.assertAllClose(-affine.inverse_log_det_jacobian(y).eval(),
affine.forward_log_det_jacobian(x).eval())
def testIdentity(self):
with self.test_session():
affine = AffineLinearOperator(validate_args=True)
x = np.array([[1, 0, -1], [2, 3, 4]], dtype=np.float32)
y = x
ildj = 0.
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(ildj,
affine.inverse_log_det_jacobian(y).eval())
self.assertAllClose(-affine.inverse_log_det_jacobian(y).eval(),
affine.forward_log_det_jacobian(x).eval())
def testIdentity(self):
with self.test_session():
affine = AffineLinearOperator(
validate_args=True)
x = np.array([[1, 0, -1], [2, 3, 4]], dtype=np.float32)
y = x
ildj = 0.
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(ildj, affine.inverse_log_det_jacobian(y).eval())
self.assertAllClose(-affine.inverse_log_det_jacobian(y).eval(),
affine.forward_log_det_jacobian(x).eval())
def testDiag(self):
with self.test_session():
shift = np.array([-1, 0, 1], dtype=np.float32)
diag = np.array([[1, 2, 3], [2, 5, 6]], dtype=np.float32)
scale = linalg.LinearOperatorDiag(diag, is_non_singular=True)
affine = AffineLinearOperator(shift=shift,
scale=scale,
validate_args=True)
x = np.array([[1, 0, -1], [2, 3, 4]], dtype=np.float32)
y = diag * x + shift
ildj = -np.sum(np.log(np.abs(diag)), axis=-1)
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(ildj,
affine.inverse_log_det_jacobian(y).eval())
self.assertAllClose(-affine.inverse_log_det_jacobian(y).eval(),
affine.forward_log_det_jacobian(x).eval())
def testDiag(self):
with self.test_session():
shift = np.array([-1, 0, 1], dtype=np.float32)
diag = np.array([[1, 2, 3],
[2, 5, 6]], dtype=np.float32)
scale = linalg.LinearOperatorDiag(diag, is_non_singular=True)
affine = AffineLinearOperator(
shift=shift, scale=scale, validate_args=True)
x = np.array([[1, 0, -1], [2, 3, 4]], dtype=np.float32)
y = diag * x + shift
ildj = -np.sum(np.log(np.abs(diag)), axis=-1)
self.assertEqual(affine.name, "affine_linear_operator")
self.assertAllClose(y, affine.forward(x).eval())
self.assertAllClose(x, affine.inverse(y).eval())
self.assertAllClose(ildj, affine.inverse_log_det_jacobian(y).eval())
self.assertAllClose(-affine.inverse_log_det_jacobian(y).eval(),
affine.forward_log_det_jacobian(x).eval())
def __init__(self,
mix_loc,
temperature,
distribution,
loc=None,
scale=None,
quadrature_size=8,
quadrature_fn=quadrature_scheme_softmaxnormal_quantiles,
validate_args=False,
allow_nan_stats=True,
name="VectorDiffeomixture"):
"""Constructs the VectorDiffeomixture on `R^d`.
The vector diffeomixture (VDM) approximates the compound distribution
```none
p(x) = int p(x | z) p(z) dz,
where z is in the K-simplex, and
p(x | z) := p(x | loc=sum_k z[k] loc[k], scale=sum_k z[k] scale[k])
```
Args:
mix_loc: `float`-like `Tensor` with shape `[b1, ..., bB, K-1]`.
In terms of samples, larger `mix_loc[..., k]` ==>
`Z` is more likely to put more weight on its `kth` component.
temperature: `float`-like `Tensor`. Broadcastable with `mix_loc`.
In terms of samples, smaller `temperature` means one component is more
likely to dominate. I.e., smaller `temperature` makes the VDM look more
like a standard mixture of `K` components.
distribution: `tf.Distribution`-like instance. Distribution from which `d`
iid samples are used as input to the selected affine transformation.
Must be a scalar-batch, scalar-event distribution. Typically
`distribution.reparameterization_type = FULLY_REPARAMETERIZED` or it is
a function of non-trainable parameters. WARNING: If you backprop through
a VectorDiffeomixture sample and the `distribution` is not
`FULLY_REPARAMETERIZED` yet is a function of trainable variables, then
the gradient will be incorrect!
loc: Length-`K` list of `float`-type `Tensor`s. The `k`-th element
represents the `shift` used for the `k`-th affine transformation. If
the `k`-th item is `None`, `loc` is implicitly `0`. When specified,
must have shape `[B1, ..., Bb, d]` where `b >= 0` and `d` is the event
size.
scale: Length-`K` list of `LinearOperator`s. Each should be
positive-definite and operate on a `d`-dimensional vector space. The
`k`-th element represents the `scale` used for the `k`-th affine
transformation. `LinearOperator`s must have shape `[B1, ..., Bb, d, d]`,
`b >= 0`, i.e., characterizes `b`-batches of `d x d` matrices
quadrature_size: Python `int` scalar representing number of
quadrature points. Larger `quadrature_size` means `q_N(x)` better
approximates `p(x)`.
quadrature_fn: Python callable taking `normal_loc`, `normal_scale`,
`quadrature_size`, `validate_args` and returning `tuple(grid, probs)`
representing the SoftmaxNormal grid and corresponding normalized weight.
normalized) weight.
Default value: `quadrature_scheme_softmaxnormal_quantiles`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: if `not scale or len(scale) < 2`.
ValueError: if `len(loc) != len(scale)`
ValueError: if `quadrature_grid_and_probs is not None` and
`len(quadrature_grid_and_probs[0]) != len(quadrature_grid_and_probs[1])`
ValueError: if `validate_args` and any not scale.is_positive_definite.
TypeError: if any scale.dtype != scale[0].dtype.
TypeError: if any loc.dtype != scale[0].dtype.
NotImplementedError: if `len(scale) != 2`.
ValueError: if `not distribution.is_scalar_batch`.
ValueError: if `not distribution.is_scalar_event`.
"""
parameters = dict(locals())
with ops.name_scope(name, values=[mix_loc, temperature]) as name:
if not scale or len(scale) < 2:
raise ValueError(
"Must specify list (or list-like object) of scale "
"LinearOperators, one for each component with "
"num_component >= 2.")
if loc is None:
loc = [None] * len(scale)
if len(loc) != len(scale):
raise ValueError("loc/scale must be same-length lists "
"(or same-length list-like objects).")
dtype = scale[0].dtype.base_dtype
loc = [
ops.convert_to_tensor(
loc_, dtype=dtype, name="loc{}".format(k))
if loc_ is not None else None for k, loc_ in enumerate(loc)
]
for k, scale_ in enumerate(scale):
if validate_args and not scale_.is_positive_definite:
raise ValueError(
"scale[{}].is_positive_definite = {} != True".format(
k, scale_.is_positive_definite))
if scale_.dtype.base_dtype != dtype:
raise TypeError(
"dtype mismatch; scale[{}].base_dtype=\"{}\" != \"{}\""
.format(k, scale_.dtype.base_dtype.name, dtype.name))
self._endpoint_affine = [
AffineLinearOperator(shift=loc_,
scale=scale_,
validate_args=validate_args,
name="endpoint_affine_{}".format(k))
for k, (loc_, scale_) in enumerate(zip(loc, scale))
]
# TODO(jvdillon): Remove once we support k-mixtures.
# We make this assertion here because otherwise `grid` would need to be a
# vector not a scalar.
if len(scale) != 2:
raise NotImplementedError(
"Currently only bimixtures are supported; "
"len(scale)={} is not 2.".format(len(scale)))
mix_loc = ops.convert_to_tensor(mix_loc,
dtype=dtype,
name="mix_loc")
temperature = ops.convert_to_tensor(temperature,
dtype=dtype,
name="temperature")
self._grid, probs = tuple(
quadrature_fn(mix_loc / temperature, 1. / temperature,
quadrature_size, validate_args))
# Note: by creating the logits as `log(prob)` we ensure that
# `self.mixture_distribution.logits` is equivalent to
# `math_ops.log(self.mixture_distribution.probs)`.
self._mixture_distribution = categorical_lib.Categorical(
logits=math_ops.log(probs),
validate_args=validate_args,
allow_nan_stats=allow_nan_stats)
asserts = distribution_util.maybe_check_scalar_distribution(
distribution, dtype, validate_args)
if asserts:
self._grid = control_flow_ops.with_dependencies(
asserts, self._grid)
self._distribution = distribution
self._interpolated_affine = [
AffineLinearOperator(shift=loc_,
scale=scale_,
validate_args=validate_args,
name="interpolated_affine_{}".format(k))
for k, (loc_, scale_) in enumerate(
zip(interpolate_loc(self._grid, loc),
interpolate_scale(self._grid, scale)))
]
[
self._batch_shape_,
self._batch_shape_tensor_,
self._event_shape_,
self._event_shape_tensor_,
] = determine_batch_event_shapes(self._grid, self._endpoint_affine)
super(VectorDiffeomixture, self).__init__(
dtype=dtype,
# We hard-code `FULLY_REPARAMETERIZED` because when
# `validate_args=True` we verify that indeed
# `distribution.reparameterization_type == FULLY_REPARAMETERIZED`. A
# distribution which is a function of only non-trainable parameters
# also implies we can use `FULLY_REPARAMETERIZED`. However, we cannot
# easily test for that possibility thus we use `validate_args=False`
# as a "back-door" to allow users a way to use non
# `FULLY_REPARAMETERIZED` distribution. In such cases IT IS THE USERS
# RESPONSIBILITY to verify that the base distribution is a function of
# non-trainable parameters.
reparameterization_type=distribution_lib.FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=(
distribution._graph_parents # pylint: disable=protected-access
+ [loc_ for loc_ in loc if loc_ is not None] +
[p for scale_ in scale for p in scale_.graph_parents]),
name=name)
def __init__(self,
mix_loc,
mix_scale,
distribution,
loc=None,
scale=None,
quadrature_grid_and_probs=None,
validate_args=False,
allow_nan_stats=True,
name="VectorDiffeomixture"):
"""Constructs the VectorDiffeomixture on `R**k`.
Args:
mix_loc: `float`-like `Tensor`. Represents the `location` parameter of the
SoftmaxNormal used for selecting one of the `K` affine transformations.
mix_scale: `float`-like `Tensor`. Represents the `scale` parameter of the
SoftmaxNormal used for selecting one of the `K` affine transformations.
distribution: `tf.Distribution`-like instance. Distribution from which `d`
iid samples are used as input to the selected affine transformation.
Must be a scalar-batch, scalar-event distribution. Typically
`distribution.reparameterization_type = FULLY_REPARAMETERIZED` or it is
a function of non-trainable parameters. WARNING: If you backprop through
a VectorDiffeomixture sample and the `distribution` is not
`FULLY_REPARAMETERIZED` yet is a function of trainable variables, then
the gradient will be incorrect!
loc: Length-`K` list of `float`-type `Tensor`s. The `k`-th element
represents the `shift` used for the `k`-th affine transformation. If
the `k`-th item is `None`, `loc` is implicitly `0`. When specified,
must have shape `[B1, ..., Bb, d]` where `b >= 0` and `d` is the event
size.
scale: Length-`K` list of `LinearOperator`s. Each should be
positive-definite and operate on a `d`-dimensional vector space. The
`k`-th element represents the `scale` used for the `k`-th affine
transformation. `LinearOperator`s must have shape `[B1, ..., Bb, d, d]`,
`b >= 0`, i.e., characterizes `b`-batches of `d x d` matrices
quadrature_grid_and_probs: Python pair of `list`-like objects representing
the sample points and the corresponding (possibly normalized) weight.
When `None`, defaults to: `np.polynomial.hermite.hermgauss(deg=8)`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: if `not scale or len(scale) < 2`.
ValueError: if `len(loc) != len(scale)`
ValueError: if `quadrature_grid_and_probs is not None` and
`len(quadrature_grid_and_probs[0]) != len(quadrature_grid_and_probs[1])`
ValueError: if `validate_args` and any not scale.is_positive_definite.
TypeError: if any scale.dtype != scale[0].dtype.
TypeError: if any loc.dtype != scale[0].dtype.
NotImplementedError: if `len(scale) != 2`.
ValueError: if `not distribution.is_scalar_batch`.
ValueError: if `not distribution.is_scalar_event`.
"""
parameters = locals()
with ops.name_scope(name, values=[mix_loc, mix_scale]):
if not scale or len(scale) < 2:
raise ValueError(
"Must specify list (or list-like object) of scale "
"LinearOperators, one for each component with "
"num_component >= 2.")
if loc is None:
loc = [None] * len(scale)
if len(loc) != len(scale):
raise ValueError("loc/scale must be same-length lists "
"(or same-length list-like objects).")
dtype = scale[0].dtype.base_dtype
loc = [
ops.convert_to_tensor(
loc_, dtype=dtype, name="loc{}".format(k))
if loc_ is not None else None for k, loc_ in enumerate(loc)
]
for k, scale_ in enumerate(scale):
if validate_args and not scale_.is_positive_definite:
raise ValueError(
"scale[{}].is_positive_definite = {} != True".format(
k, scale_.is_positive_definite))
if scale_.dtype.base_dtype != dtype:
raise TypeError(
"dtype mismatch; scale[{}].base_dtype=\"{}\" != \"{}\""
.format(k, scale_.dtype.base_dtype.name, dtype.name))
self._endpoint_affine = [
AffineLinearOperator(shift=loc_,
scale=scale_,
event_ndims=1,
validate_args=validate_args,
name="endpoint_affine_{}".format(k))
for k, (loc_, scale_) in enumerate(zip(loc, scale))
]
# TODO(jvdillon): Remove once we support k-mixtures.
# We make this assertion here because otherwise `grid` would need to be a
# vector not a scalar.
if len(scale) != 2:
raise NotImplementedError(
"Currently only bimixtures are supported; "
"len(scale)={} is not 2.".format(len(scale)))
if quadrature_grid_and_probs is None:
grid, probs = np.polynomial.hermite.hermgauss(deg=8)
else:
grid, probs = tuple(quadrature_grid_and_probs)
if len(grid) != len(probs):
raise ValueError(
"`quadrature_grid_and_probs` must be a `tuple` of "
"same-length list-like objects")
grid = grid.astype(dtype.as_numpy_dtype)
probs = probs.astype(dtype.as_numpy_dtype)
probs /= np.linalg.norm(probs, ord=1)
self._quadrature_grid = grid
self._quadrature_probs = probs
# Note: by creating the logits as `log(prob)` we ensure that
# `self.mixture_distribution.logits` is equivalent to
# `math_ops.log(self.mixture_distribution.probs)`.
self._mixture_distribution = categorical_lib.Categorical(
logits=np.log(probs),
validate_args=validate_args,
allow_nan_stats=allow_nan_stats)
mix_loc = maybe_check_mix_param(mix_loc, "mix_loc", dtype,
validate_args)
mix_scale = maybe_check_mix_param(mix_scale, "mix_scale", dtype,
validate_args)
asserts = distribution_util.maybe_check_scalar_distribution(
distribution, dtype, validate_args)
if asserts:
mix_loc = control_flow_ops.with_dependencies(asserts, mix_loc)
self._distribution = distribution
# shape: [B, deg]
self._interpolate_weight = math_ops.sigmoid(mix_loc + np.sqrt(2.) *
mix_scale * grid)
self._interpolated_affine = [
AffineLinearOperator(shift=loc_,
scale=scale_,
event_ndims=1,
validate_args=validate_args,
name="interpolated_affine_{}".format(k))
for k, (loc_, scale_) in enumerate(
zip(
interpolate_loc(len(self._quadrature_grid),
self._interpolate_weight, loc),
interpolate_scale(len(self._quadrature_grid),
self._interpolate_weight, scale)))
]
self._batch_shape_, self._event_shape_ = determine_batch_event_shapes(
mix_loc, mix_scale, self._endpoint_affine)
super(VectorDiffeomixture, self).__init__(
dtype=dtype,
# We hard-code `FULLY_REPARAMETERIZED` because when
# `validate_args=True` we verify that indeed
# `distribution.reparameterization_type == FULLY_REPARAMETERIZED`. A
# distribution which is a function of only non-trainable parameters
# also implies we can use `FULLY_REPARAMETERIZED`. However, we cannot
# easily test for that possibility thus we use `validate_args=False`
# as a "back-door" to allow users a way to use non
# `FULLY_REPARAMETERIZED` distribution. In such cases IT IS THE USERS
# RESPONSIBILITY to verify that the base distribution is a function of
# non-trainable parameters.
reparameterization_type=distribution_lib.FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=(
[mix_loc, mix_scale] + distribution._graph_parents # pylint: disable=protected-access
+ [loc_ for loc_ in loc if loc_ is not None] +
[p for scale_ in scale for p in scale_.graph_parents]),
name=name)