# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
#
# 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 typing import Optional
import tensorflow as tf
from check_shapes import check_shapes
from ..base import MeanAndVariance
from ..inducing_variables import InducingVariables
from ..kernels import Kernel
from ..posteriors import BasePosterior, VGPPosterior, get_posterior_class
from .dispatch import conditional
[docs]
@conditional._gpflow_internal_register(object, InducingVariables, Kernel, object)
@check_shapes(
"Xnew: [batch..., N, D]",
"inducing_variable: [M, D, broadcast R]",
"f: [M, R]",
"q_sqrt: [M_R_or_R_M_M...]",
"return[0]: [batch..., N, R]",
"return[1]: [batch..., N, R] if (not full_cov) and (not full_output_cov)",
"return[1]: [batch..., R, N, N] if full_cov and (not full_output_cov)",
"return[1]: [batch..., N, R, R] if (not full_cov) and full_output_cov",
"return[1]: [batch..., N, R, N, R] if full_cov and full_output_cov",
)
def _sparse_conditional(
Xnew: tf.Tensor,
inducing_variable: InducingVariables,
kernel: Kernel,
f: tf.Tensor,
*,
full_cov: bool = False,
full_output_cov: bool = False,
q_sqrt: Optional[tf.Tensor] = None,
white: bool = False,
) -> MeanAndVariance:
"""
Single-output GP conditional.
The covariance matrices used to calculate the conditional have the following shape:
- Kuu: [M, M]
- Kuf: [M, N]
- Kff: [N, N]
Further reference:
- See `gpflow.conditionals._dense_conditional` (below) for a detailed explanation of
conditional in the single-output case.
- See the multiouput notebook for more information about the multiouput framework.
:param Xnew: data matrix
:param f: data matrix
:param full_cov: return the covariance between the datapoints
:param full_output_cov: return the covariance between the outputs.
NOTE: as we are using a single-output kernel with repetitions
these covariances will be zero.
:param q_sqrt: matrix of standard-deviations or Cholesky matrices,
size [M, R] or [R, M, M].
:param white: boolean of whether to use the whitened representation
:return: mean and variance
"""
posterior_class = get_posterior_class(kernel, inducing_variable)
posterior: BasePosterior = posterior_class(
kernel,
inducing_variable,
f,
q_sqrt,
whiten=white,
mean_function=None,
precompute_cache=None,
)
return posterior.fused_predict_f(Xnew, full_cov=full_cov, full_output_cov=full_output_cov)
[docs]
@conditional._gpflow_internal_register(object, object, Kernel, object)
@check_shapes(
"Xnew: [batch..., N, D]",
"X: [M, D]",
"f: [M, R]",
"return[0]: [batch..., N, R]",
"return[1]: [batch..., N, R] if (not full_cov) and (not full_output_cov)",
"return[1]: [batch..., R, N, N] if full_cov and (not full_output_cov)",
"return[1]: [batch..., N, R, R] if (not full_cov) and full_output_cov",
"return[1]: [batch..., N, R, N, R] if full_cov and full_output_cov",
)
def _dense_conditional(
Xnew: tf.Tensor,
X: tf.Tensor,
kernel: Kernel,
f: tf.Tensor,
*,
full_cov: bool = False,
full_output_cov: bool = False,
q_sqrt: Optional[tf.Tensor] = None,
white: bool = False,
) -> MeanAndVariance:
"""
Given f, representing the GP at the points X, produce the mean and
(co-)variance of the GP at the points Xnew.
Additionally, there may be Gaussian uncertainty about f as represented by
q_sqrt. In this case `f` represents the mean of the distribution and
q_sqrt the square-root of the covariance.
Additionally, the GP may have been centered (whitened) so that::
p(v) = ๐ฉ(๐, ๐)
f = ๐v
thus::
p(f) = ๐ฉ(๐, ๐๐แต) = ๐ฉ(๐, ๐).
In this case `f` represents the values taken by v.
The method can either return the diagonals of the covariance matrix for
each output (default) or the full covariance matrix (full_cov=True).
We assume R independent GPs, represented by the columns of f (and the
first dimension of q_sqrt).
:param Xnew: data matrix. Evaluate the GP at these new points
:param X: data points.
:param kernel: GPflow kernel.
:param f: data matrix, representing the function values at X,
for R functions.
:param q_sqrt: matrix of standard-deviations or Cholesky matrices,
size [M, R] or [R, M, M].
:param white: boolean of whether to use the whitened representation as
described above.
:return: mean and variance
"""
posterior = VGPPosterior(
kernel=kernel,
X=X,
q_mu=f,
q_sqrt=q_sqrt,
white=white,
precompute_cache=None,
)
return posterior.fused_predict_f(Xnew, full_cov=full_cov, full_output_cov=full_output_cov)