Revision e48d5b438d4b2dd61f702d26a509d02f106593ea authored by James Hensman on 28 January 2019, 13:26:33 UTC, committed by James Hensman on 28 January 2019, 13:26:33 UTC
1 parent 56bb9b1
features.py
# Copyright 2017 st--, Mark van der Wilk
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from abc import abstractmethod
import warnings
import numpy as np
import tensorflow as tf
from . import transforms, kernels, settings
from .decors import params_as_tensors, params_as_tensors_for
from .params import Parameter, Parameterized
from .dispatch import dispatch
logger = settings.logger()
class InducingFeature(Parameterized):
"""
Abstract base class for inducing features.
"""
@abstractmethod
def __len__(self) -> int:
"""
Returns the number of features, relevant for example to determine the
size of the variational distribution.
"""
raise NotImplementedError()
def Kuu(self, kern, jitter=0.0):
"""
Calculates the covariance matrix between features for kernel `kern`.
Return shape M x M
M = len(feat)
"""
warnings.warn('Please replace feature.Kuu(kernel) with Kuu(feature, kernel)',
DeprecationWarning)
return Kuu(self, kern, jitter=jitter)
def Kuf(self, kern, Xnew):
"""
Calculates the covariance matrix with function values at new points
`Xnew` for kernel `kern`.
Return shape M x N
M = len(feat)
N = len(Xnew)
"""
warnings.warn('Please replace feature.Kuf(kernel, Xnew) with Kuf(feature, kernel, Xnew)',
DeprecationWarning)
return Kuf(self, kern, Xnew)
class InducingPointsBase(InducingFeature):
"""
Real-space inducing points
"""
def __init__(self, Z):
"""
:param Z: the initial positions of the inducing points, size M x D
"""
super().__init__()
self.Z = Parameter(Z, dtype=settings.float_type)
def __len__(self):
return self.Z.shape[0]
class InducingPoints(InducingPointsBase):
pass
@dispatch(InducingPoints, kernels.Kernel)
def Kuu(feat, kern, *, jitter=0.0):
with params_as_tensors_for(feat):
Kzz = kern.K(feat.Z)
Kzz += jitter * tf.eye(len(feat), dtype=settings.dtypes.float_type)
return Kzz
@dispatch(InducingPoints, kernels.Kernel, object)
def Kuf(feat, kern, Xnew):
with params_as_tensors_for(feat):
Kzx = kern.K(feat.Z, Xnew)
return Kzx
class Multiscale(InducingPointsBase):
"""
Multi-scale inducing features
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, scales):
super().__init__(Z)
self.scales = Parameter(scales,
transform=transforms.positive) # Multi-scale feature widths (std. dev. of Gaussian)
if self.Z.shape != scales.shape:
raise ValueError("Input locations `Z` and `scales` must have the same shape.") # pragma: no cover
@staticmethod
def _cust_square_dist(A, B, sc):
"""
Custom version of _square_dist that allows sc to provide per-datapoint length
scales. sc: N x M x D.
"""
return tf.reduce_sum(tf.square((tf.expand_dims(A, 1) - tf.expand_dims(B, 0)) / sc), 2)
@dispatch(Multiscale, kernels.RBF, object)
def Kuf(feat, kern, Xnew):
with params_as_tensors_for(feat, kern):
Xnew, _ = kern._slice(Xnew, None)
Zmu, Zlen = kern._slice(feat.Z, feat.scales)
idlengthscales = kern.lengthscales + Zlen
d = feat._cust_square_dist(Xnew, Zmu, idlengthscales)
Kuf = tf.transpose(kern.variance * tf.exp(-d / 2) *
tf.reshape(tf.reduce_prod(kern.lengthscales / idlengthscales, 1),
(1, -1)))
return Kuf
@dispatch(Multiscale, kernels.RBF)
def Kuu(feat, kern, *, jitter=0.0):
with params_as_tensors_for(feat, kern):
Zmu, Zlen = kern._slice(feat.Z, feat.scales)
idlengthscales2 = tf.square(kern.lengthscales + Zlen)
sc = tf.sqrt(
tf.expand_dims(idlengthscales2, 0) + tf.expand_dims(idlengthscales2, 1) - tf.square(
kern.lengthscales))
d = feat._cust_square_dist(Zmu, Zmu, sc)
Kzz = kern.variance * tf.exp(-d / 2) * tf.reduce_prod(kern.lengthscales / sc, 2)
Kzz += jitter * tf.eye(len(feat), dtype=settings.float_type)
return Kzz
def inducingpoint_wrapper(feat, Z):
"""
Models which used to take only Z can now pass `feat` and `Z` to this method. This method will
check for consistency and return the correct feature. This allows backwards compatibility in
for the methods.
"""
if feat is not None and Z is not None:
raise ValueError("Cannot pass both an InducingFeature instance and Z values") # pragma: no cover
elif feat is None and Z is None:
raise ValueError("You must pass either an InducingFeature instance or Z values") # pragma: no cover
elif Z is not None:
feat = InducingPoints(Z)
elif isinstance(feat, np.ndarray):
feat = InducingPoints(feat)
else:
assert isinstance(feat, InducingFeature) # pragma: no cover
return feat
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