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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
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import abc
from typing import Optional
import tensorflow as tf
import tensorflow_probability as tfp
from deprecated import deprecated
from ..base import Module, Parameter, TensorData, TensorType
from ..utilities import positive
class InducingVariables(Module):
"""
Abstract base class for inducing variables.
"""
@property
@abc.abstractmethod
def num_inducing(self) -> tf.Tensor:
"""
Returns the number of inducing variables, relevant for example to determine the size of the
variational distribution.
"""
raise NotImplementedError
@deprecated(
reason="len(iv) should return an `int`, but this actually returns a `tf.Tensor`."
" Use `iv.num_inducing` instead."
)
def __len__(self) -> tf.Tensor:
return self.num_inducing
class InducingPointsBase(InducingVariables):
def __init__(self, Z: TensorData, name: Optional[str] = None):
"""
:param Z: the initial positions of the inducing points, size [M, D]
"""
super().__init__(name=name)
if not isinstance(Z, (tf.Variable, tfp.util.TransformedVariable)):
Z = Parameter(Z)
self.Z = Z
@property
def num_inducing(self) -> Optional[tf.Tensor]:
return tf.shape(self.Z)[0]
class InducingPoints(InducingPointsBase):
"""
Real-space inducing points
"""
class Multiscale(InducingPointsBase):
r"""
Multi-scale inducing variables
Originally proposed in
::
@incollection{NIPS2009_3876,
title = {Inter-domain Gaussian Processes for Sparse Inference using Inducing Features},
author = {Miguel L\'{a}zaro-Gredilla and An\'{\i}bal Figueiras-Vidal},
booktitle = {Advances in Neural Information Processing Systems 22},
year = {2009},
}
"""
def __init__(self, Z: TensorData, scales: TensorData):
super().__init__(Z)
# Multi-scale inducing_variable widths (std. dev. of Gaussian)
self.scales = Parameter(scales, transform=positive())
if self.Z.shape != self.scales.shape:
raise ValueError(
"Input locations `Z` and `scales` must have the same shape."
) # pragma: no cover
@staticmethod
def _cust_square_dist(A: TensorType, B: TensorType, sc: TensorType) -> tf.Tensor:
"""
Custom version of _square_dist that allows sc to provide per-datapoint length
scales. sc: [N, M, D].
"""
return tf.reduce_sum(tf.square((tf.expand_dims(A, 1) - tf.expand_dims(B, 0)) / sc), 2)