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from typing import Sequence, Tuple
import tensorflow as tf
from check_shapes import Shape, check_shapes
from ..inducing_variables import InducingVariables
[docs]class MultioutputInducingVariables(InducingVariables):
"""
Multioutput Inducing Variables
Base class for methods which define a collection of inducing variables which
in some way can be grouped. The main example is where the inducing variables
consist of outputs of various independent GPs. This can be because our model
uses multiple independent GPs (SharedIndependent, SeparateIndependent) or
because it is constructed from independent GPs (eg IndependentLatent,
LinearCoregionalization).
"""
@property
def inducing_variables(self) -> Tuple[InducingVariables, ...]:
raise NotImplementedError
[docs]class FallbackSharedIndependentInducingVariables(MultioutputInducingVariables):
"""
Shared definition of inducing variables for each independent latent process.
This class is designated to be used to:
- provide a general interface for multioutput kernels
constructed from independent latent processes,
- only require the specification of Kuu and Kuf.
All multioutput kernels constructed from independent latent processes allow
the inducing variables to be specified in the latent processes, and a
reasonably efficient method (i.e. one that takes advantage of the
independence in the latent processes) can be specified quite generally by
only requiring the following covariances:
- Kuu: [L, M, M],
- Kuf: [L, M, N, P].
In `gpflow/conditionals/multioutput/conditionals.py` we define a conditional() implementation
for this combination. We specify this code path for all kernels which inherit from
`IndependentLatentBase`. This set-up allows inference with any such kernel to be implemented by
specifying only `Kuu()` and `Kuf()`.
We call this the base class, since many multioutput GPs that are constructed
from independent latent processes acutally allow even more efficient
approximations. However, we include this code path, as it does not require
specifying a new `conditional()` implementation.
Here, we share the definition of inducing variables between all latent
processes.
"""
@check_shapes(
"inducing_variable: [M, D, 1]",
)
def __init__(self, inducing_variable: InducingVariables):
super().__init__()
self.inducing_variable = inducing_variable
@property # type: ignore[misc] # mypy doesn't like decorated properties.
@check_shapes(
"return: []",
)
def num_inducing(self) -> tf.Tensor:
return self.inducing_variable.num_inducing
@property
def inducing_variables(self) -> Tuple[InducingVariables]:
return (self.inducing_variable,)
@property
def shape(self) -> Shape:
inner = self.inducing_variable.shape
if inner is None:
return inner
assert inner[2] == 1
return inner[:2] + (None,)
[docs]class FallbackSeparateIndependentInducingVariables(MultioutputInducingVariables):
"""
Separate set of inducing variables for each independent latent process.
This class is designated to be used to:
- provide a general interface for multioutput kernels
constructed from independent latent processes,
- only require the specification of Kuu and Kuf.
All multioutput kernels constructed from independent latent processes allow
the inducing variables to be specified in the latent processes, and a
reasonably efficient method (i.e. one that takes advantage of the
independence in the latent processes) can be specified quite generally by
only requiring the following covariances:
- Kuu: [L, M, M],
- Kuf: [L, M, N, P].
In `gpflow/multioutput/conditionals.py` we define a conditional() implementation for this
combination. We specify this code path for all kernels which inherit from
`IndependentLatentBase`. This set-up allows inference with any such kernel to be implemented by
specifying only `Kuu()` and `Kuf()`.
We call this the base class, since many multioutput GPs that are constructed
from independent latent processes acutally allow even more efficient
approximations. However, we include this code path, as it does not require
specifying a new `conditional()` implementation.
We use a different definition of inducing variables for each latent process.
Note: each object should have the same number of inducing variables, M.
"""
@check_shapes(
"inducing_variable_list[all]: [., D, 1]",
)
def __init__(self, inducing_variable_list: Sequence[InducingVariables]):
super().__init__()
self.inducing_variable_list = inducing_variable_list
@property # type: ignore[misc] # mypy doesn't like decorated properties.
@check_shapes(
"return: []",
)
def num_inducing(self) -> tf.Tensor:
num_inducings = tf.stack([iv.num_inducing for iv in self.inducing_variable_list])
num_inducing, _ = tf.unique(num_inducings)
tf.debugging.assert_equal(
tf.shape(num_inducing),
[1],
message="'num_inducing' does not make sense"
" when children have different numbers of inducing points.",
)
return num_inducing[0]
@property
def inducing_variables(self) -> Tuple[InducingVariables, ...]:
return tuple(self.inducing_variable_list)
@property
def shape(self) -> Shape:
inner = self.inducing_variable_list[0].shape
if inner is None:
return inner
assert inner[2] == 1
for iv in self.inducing_variable_list[1:]:
if inner != iv.shape:
return None
return inner[:2] + (len(self.inducing_variable_list),)
[docs]class SharedIndependentInducingVariables(FallbackSharedIndependentInducingVariables):
"""
Here, we define the same inducing variables as in the base class. However,
this class is intended to be used without the constraints on the shapes that
`Kuu()` and `Kuf()` return. This allows a custom `conditional()` to provide
the most efficient implementation.
"""
[docs]class SeparateIndependentInducingVariables(FallbackSeparateIndependentInducingVariables):
"""
Here, we define the same inducing variables as in the base class. However,
this class is intended to be used without the constraints on the shapes that
`Kuu()` and `Kuf()` return. This allows a custom `conditional()` to provide
the most efficient implementation.
"""