# 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.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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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 ..config import default_float, default_jitter
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 data_input_to_tensor
[docs]class GPMC(GPModel, InternalDataTrainingLossMixin):
def __init__(
self,
data: RegressionData,
kernel: Kernel,
likelihood: Likelihood,
mean_function: Optional[MeanFunction] = None,
num_latent_gps: Optional[int] = None,
):
"""
data is a tuple of X, Y with X, a data matrix, size [N, D] and Y, a data matrix, size [N, R]
kernel, likelihood, mean_function are appropriate GPflow objects
This is a vanilla implementation of a GP with a non-Gaussian
likelihood. The latent function values are represented by centered
(whitened) variables, so
v ~ N(0, I)
f = Lv + m(x)
with
L L^T = K
"""
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)
self.data = data_input_to_tensor(data)
self.num_data = self.data[0].shape[0]
self.V = Parameter(np.zeros((self.num_data, self.num_latent_gps)))
self.V.prior = tfp.distributions.Normal(
loc=to_default_float(0.0), scale=to_default_float(1.0)
)
[docs] def log_posterior_density(self) -> tf.Tensor:
return self.log_likelihood() + self.log_prior_density()
def _training_loss(self) -> tf.Tensor:
return -self.log_posterior_density()
[docs] def maximum_log_likelihood_objective(self) -> tf.Tensor:
return self.log_likelihood()
[docs] def log_likelihood(self) -> tf.Tensor:
r"""
Construct a tf function to compute the likelihood of a general GP
model.
\log p(Y | V, theta).
"""
X_data, Y_data = self.data
K = self.kernel(X_data)
L = tf.linalg.cholesky(
K + tf.eye(tf.shape(X_data)[0], dtype=default_float()) * default_jitter()
)
F = tf.linalg.matmul(L, self.V) + self.mean_function(X_data)
return tf.reduce_sum(self.likelihood.log_prob(F, Y_data))
[docs] def predict_f(self, Xnew: InputData, full_cov=False, full_output_cov=False) -> MeanAndVariance:
"""
Xnew is a data matrix, point at which we want to predict
This method computes
p(F* | (F=LV) )
where F* are points on the GP at Xnew, F=LV are points on the GP at X.
"""
X_data, Y_data = self.data
mu, var = conditional(
Xnew, X_data, self.kernel, self.V, full_cov=full_cov, q_sqrt=None, white=True
)
return mu + self.mean_function(Xnew), var