# Copyright 2016-2020 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 numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
from ..base import InputData, MeanAndVariance, Parameter, RegressionData
from ..conditionals import conditional
from ..experimental.check_shapes import check_shapes, inherit_check_shapes
from ..kernels import Kernel
from ..likelihoods import Likelihood
from ..mean_functions import MeanFunction
from ..utilities import to_default_float
from .model import GPModel
from .training_mixins import InternalDataTrainingLossMixin
from .util import InducingPointsLike, data_input_to_tensor, inducingpoint_wrapper
[docs]class SGPMC(GPModel, InternalDataTrainingLossMixin):
r"""
This is the Sparse Variational GP using MCMC (SGPMC).
The key reference is :cite:t:`hensman2015mcmc`.
The latent function values are represented by centered
(whitened) variables, so
.. math::
:nowrap:
\begin{align}
\mathbf v & \sim N(0, \mathbf I) \\
\mathbf u &= \mathbf L\mathbf v
\end{align}
with
.. math::
\mathbf L \mathbf L^\top = \mathbf K
"""
@check_shapes(
"data[0]: [N, D]",
"data[1]: [N, P]",
)
def __init__(
self,
data: RegressionData,
kernel: Kernel,
likelihood: Likelihood,
mean_function: Optional[MeanFunction] = None,
num_latent_gps: Optional[int] = None,
inducing_variable: Optional[InducingPointsLike] = None,
):
"""
data is a tuple of X, Y with X, a data matrix, size [N, D] and Y, a data matrix, size [N, R]
Z is a data matrix, of inducing inputs, size [M, D]
kernel, likelihood, mean_function are appropriate GPflow objects
"""
if num_latent_gps is None:
num_latent_gps = self.calc_num_latent_gps_from_data(data, kernel, likelihood)
super().__init__(kernel, likelihood, mean_function, num_latent_gps=num_latent_gps)
self.data = data_input_to_tensor(data)
self.num_data = data[0].shape[0]
self.inducing_variable = inducingpoint_wrapper(inducing_variable)
self.V = Parameter(np.zeros((self.inducing_variable.num_inducing, self.num_latent_gps)))
self.V.prior = tfp.distributions.Normal(
loc=to_default_float(0.0), scale=to_default_float(1.0)
)
# type-ignore is because of changed method signature:
[docs] @inherit_check_shapes
def log_posterior_density(self) -> tf.Tensor: # type: ignore[override]
return self.log_likelihood_lower_bound() + self.log_prior_density()
# type-ignore is because of changed method signature:
@inherit_check_shapes
def _training_loss(self) -> tf.Tensor: # type: ignore[override]
return -self.log_posterior_density()
# type-ignore is because of changed method signature:
[docs] @inherit_check_shapes
def maximum_log_likelihood_objective(self) -> tf.Tensor: # type: ignore[override]
return self.log_likelihood_lower_bound()
[docs] def log_likelihood_lower_bound(self) -> tf.Tensor:
"""
This function computes the optimal density for v, q*(v), up to a constant
"""
# get the (marginals of) q(f): exactly predicting!
X_data, Y_data = self.data
fmean, fvar = self.predict_f(X_data, full_cov=False)
return tf.reduce_sum(self.likelihood.variational_expectations(X_data, fmean, fvar, Y_data))
[docs] @inherit_check_shapes
def predict_f(
self, Xnew: InputData, full_cov: bool = False, full_output_cov: bool = False
) -> MeanAndVariance:
"""
Xnew is a data matrix of the points at which we want to predict
This method computes
p(F* | (U=LV) )
where F* are points on the GP at Xnew, F=LV are points on the GP at Z,
"""
mu, var = conditional(
Xnew,
self.inducing_variable,
self.kernel,
self.V,
full_cov=full_cov,
q_sqrt=None,
white=True,
full_output_cov=full_output_cov,
)
return mu + self.mean_function(Xnew), var