Source code for gpflow.models.sgpmc

# 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 check_shapes import check_shapes, inherit_check_shapes

from ..base import InputData, MeanAndVariance, Parameter, RegressionData
from ..conditionals import conditional
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