#!/usr/bin/env python3
from linear_operator.operators import MaskedLinearOperator
from .. import settings
from ..distributions import MultivariateNormal, MultivariateQExponential
from ..likelihoods import _GaussianLikelihoodBase, _QExponentialLikelihoodBase
from .marginal_log_likelihood import MarginalLogLikelihood
[docs]class ExactMarginalLogLikelihood(MarginalLogLikelihood):
"""
The exact marginal log likelihood (MLL) for an exact Gaussian (Q-Exponential) process with a
Gaussian (Q-Exponential) likelihood.
.. note::
This module will not work with anything other than a :obj:`~qpytorch.likelihoods.GaussianLikelihood`
(:obj:`~qpytorch.likelihoods.QExponentialLikelihood`) and a :obj:`~gpytorch.models.ExactGP` (:obj:`~qpytorch.models.ExactQEP`).
It also cannot be used in conjunction with stochastic optimization.
:param ~qpytorch.likelihoods.GaussianLikelihood (~qpytorch.likelihoods.QExponentialLikelihood) likelihood: The Gaussian (Q-Exponential) likelihood for the model
:param ~gpytorch.models.ExactGP (~qpytorch.models.ExactQEP) model: The exact GP (QEP) model
Example:
>>> # model is a qpytorch.models.ExactGP or qpytorch.models.ExactQEP
>>> # likelihood is a qpytorch.likelihoods.Likelihood
>>> mll = qpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
>>>
>>> output = model(train_x)
>>> loss = -mll(output, train_y)
>>> loss.backward()
"""
def __init__(self, likelihood, model):
if not isinstance(likelihood, (_GaussianLikelihoodBase, _QExponentialLikelihoodBase)):
raise RuntimeError("Likelihood must be Gaussian or Q-Exponential for exact inference")
super(ExactMarginalLogLikelihood, self).__init__(likelihood, model)
def _add_other_terms(self, res, params):
# Add additional terms (SGPR / learned inducing points, heteroskedastic likelihood models)
for added_loss_term in self.model.added_loss_terms():
res = res.add(added_loss_term.loss(*params))
# Add log probs of priors on the (functions of) parameters
res_ndim = res.ndim
for name, module, prior, closure, _ in self.model.named_priors():
prior_term = prior.log_prob(closure(module))
res.add_(prior_term.view(*prior_term.shape[:res_ndim], -1).sum(dim=-1))
return res
[docs] def forward(self, function_dist, target, *params, **kwargs):
r"""
Computes the MLL given :math:`p(\mathbf f)` and :math:`\mathbf y`.
:param ~gpytorch.distributions.MultivariateNormal or ~qpytorch.distributions.MultivariateQExponential function_dist: :math:`p(\mathbf f)`
the outputs of the latent function (the :obj:`gpytorch.models.ExactGP` or :obj:`qpytorch.models.ExactQEP`)
:param torch.Tensor target: :math:`\mathbf y` The target values
:rtype: torch.Tensor
:return: Exact MLL. Output shape corresponds to batch shape of the model/input data.
"""
if not isinstance(function_dist, (MultivariateNormal, MultivariateQExponential)):
raise RuntimeError("ExactMarginalLogLikelihood can only operate on Gaussian or Q-Exponential random variables")
# Determine output likelihood
output = self.likelihood(function_dist, *params, **kwargs)
# Remove NaN values if enabled
if settings.observation_nan_policy.value() == "mask":
observed = settings.observation_nan_policy._get_observed(target, output.event_shape)
if isinstance(function_dist, MultivariateNormal):
output = MultivariateNormal(
mean=output.mean[..., observed],
covariance_matrix=MaskedLinearOperator(
output.lazy_covariance_matrix, observed.reshape(-1), observed.reshape(-1)
),
)
elif isinstance(function_dist, MultivariateQExponential):
output = MultivariateQExponential(
mean=output.mean[..., observed],
covariance_matrix=MaskedLinearOperator(
output.lazy_covariance_matrix, observed.reshape(-1), observed.reshape(-1)
),
power=output.power
)
target = target[..., observed]
elif settings.observation_nan_policy.value() == "fill":
raise ValueError("NaN observation policy 'fill' is not supported by ExactMarginalLogLikelihood!")
# Get the log prob of the marginal distribution
res = output.log_prob(target)
res = self._add_other_terms(res, params)
# Scale by the amount of data we have
num_data = function_dist.event_shape.numel()
return res.div_(num_data)