def forward(self, input):
"""
Adds the log task noises to the diagonal of the covariance matrix of the supplied
:obj:`gpytorch.random_variables.GaussianRandomVariable` or
:obj:`gpytorch.random_variables.MultitaskGaussianRandomVariable`.
To accomplish this, we form a new :obj:`gpytorch.lazy.KroneckerProductLazyVariable` between :math:`I_{n}`,
an identity matrix with size equal to the data and a diagonal matrix containing the task noises :math:`D_{t}`.
We also incorporate a shared `log_noise` parameter from the base
:class:`gpytorch.likelihoods.GaussianLikelihood` that we extend.
The final covariance matrix after this method is then :math:`K + D_{t} \otimes I_{n} + \sigma^{2}I_{nt}`.
Args:
input (:obj:`gpytorch.random_variables.MultitaskGaussianRandomVariable`): Random variable whose covariance
matrix is a :obj:`gpytorch.lazy.LazyVariable` we intend to augment.
Returns:
:obj:`gpytorch.random_variables.MultitaskGaussianRandomVariable`: A new random variable whose covariance
matrix is a :obj:`gpytorch.lazy.LazyVariable` with :math:`D_{t} \otimes I_{n}` and :math:`\sigma^{2}I_{nt}`
added.
"""
mean, covar = input.representation()
eye_lv = DiagLazyVariable(
torch.ones(covar.size(-1) // self.n_tasks,
device=self.log_noise.device))
task_var_lv = DiagLazyVariable(self.log_task_noises.exp())
diag_kron_lv = KroneckerProductLazyVariable(task_var_lv, eye_lv)
noise = covar + diag_kron_lv
noise = add_diag(noise, self.log_noise.exp())
return input.__class__(mean, noise)
def forward(self, input):
assert isinstance(input, GaussianRandomVariable)
mean, covar = input.representation()
noise = add_diag(covar, self.log_noise.exp())
return input.__class__(mean, noise)
