https://github.com/GPflow/GPflow
Tip revision: b819db324fb3c64cab4db52c8f618ab8ff0f5778 authored by st-- on 14 September 2020, 17:03:08 UTC
Merge pull request #1565 from GPflow/develop
Merge pull request #1565 from GPflow/develop
Tip revision: b819db3
gpr.py
# 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, Tuple
import tensorflow as tf
import gpflow
from ..kernels import Kernel
from ..logdensities import multivariate_normal
from ..mean_functions import MeanFunction
from .model import GPModel, InputData, MeanAndVariance, RegressionData
from .training_mixins import InternalDataTrainingLossMixin
from .util import data_input_to_tensor
class GPR(GPModel, InternalDataTrainingLossMixin):
r"""
Gaussian Process Regression.
This is a vanilla implementation of GP regression with a Gaussian
likelihood. Multiple columns of Y are treated independently.
The log likelihood of this model is given by
.. math::
\log p(Y \,|\, \mathbf f) =
\mathcal N(Y \,|\, 0, \sigma_n^2 \mathbf{I})
To train the model, we maximise the log _marginal_ likelihood
w.r.t. the likelihood variance and kernel hyperparameters theta.
The marginal likelihood is found by integrating the likelihood
over the prior, and has the form
.. math::
\log p(Y \,|\, \sigma_n, \theta) =
\mathcal N(Y \,|\, 0, \mathbf{K} + \sigma_n^2 \mathbf{I})
"""
def __init__(
self,
data: RegressionData,
kernel: Kernel,
mean_function: Optional[MeanFunction] = None,
noise_variance: float = 1.0,
):
likelihood = gpflow.likelihoods.Gaussian(noise_variance)
_, Y_data = data
super().__init__(kernel, likelihood, mean_function, num_latent_gps=Y_data.shape[-1])
self.data = data_input_to_tensor(data)
def maximum_log_likelihood_objective(self) -> tf.Tensor:
return self.log_marginal_likelihood()
def log_marginal_likelihood(self) -> tf.Tensor:
r"""
Computes the log marginal likelihood.
.. math::
\log p(Y | \theta).
"""
X, Y = self.data
K = self.kernel(X)
num_data = tf.shape(X)[0]
k_diag = tf.linalg.diag_part(K)
s_diag = tf.fill([num_data], self.likelihood.variance)
ks = tf.linalg.set_diag(K, k_diag + s_diag)
L = tf.linalg.cholesky(ks)
m = self.mean_function(X)
# [R,] log-likelihoods for each independent dimension of Y
log_prob = multivariate_normal(Y, m, L)
return tf.reduce_sum(log_prob)
def predict_f(
self, Xnew: InputData, full_cov: bool = False, full_output_cov: bool = False
) -> MeanAndVariance:
r"""
This method computes predictions at X \in R^{N \x D} input points
.. math::
p(F* | Y)
where F* are points on the GP at new data points, Y are noisy observations at training data points.
"""
X_data, Y_data = self.data
err = Y_data - self.mean_function(X_data)
kmm = self.kernel(X_data)
knn = self.kernel(Xnew, full_cov=full_cov)
kmn = self.kernel(X_data, Xnew)
num_data = X_data.shape[0]
s = tf.linalg.diag(tf.fill([num_data], self.likelihood.variance))
conditional = gpflow.conditionals.base_conditional
f_mean_zero, f_var = conditional(
kmn, kmm + s, knn, err, full_cov=full_cov, white=False
) # [N, P], [N, P] or [P, N, N]
f_mean = f_mean_zero + self.mean_function(Xnew)
return f_mean, f_var