Source code for nubo.models.gaussian_process

from torch import Tensor
from gpytorch.distributions import MultivariateNormal
from gpytorch.means import ConstantMean
from gpytorch.models import ExactGP
from gpytorch.kernels import MaternKernel, ScaleKernel
from gpytorch.likelihoods import Likelihood

[docs] class GaussianProcess(ExactGP): r""" Gaussian process model with constant mean function and Matern 5/2 kernel. Constant mean function: .. math:: \mu (\boldsymbol x) = c, where constant :math:`c` is estimated. Matern 5/2 Kernel: .. math:: \Sigma_0 (\boldsymbol x, \boldsymbol x^\prime) = \sigma_K^2 \left(1 + \sqrt{5}r + \frac{5}{3}r^2 \right) \exp{\left(-\sqrt{5}r \right)}, where :math:`r = \sqrt{\sum_{m=1}^d \frac{(\boldsymbol x_m - \boldsymbol x^\prime_m)^2}{l^2_m}}`, :math:`l` is the length-scale, :math:`\sigma_K^2` is the outputscale, and :math:`m` is the :math:`m`-th dimension of the input points. Attributes ---------- x_train : ``torch.Tensor`` (size n x d) Training inputs. y_train : ``torch.Tensor`` (size n) Training outputs. likelihood : ``gpytorch.likelihoods.Likelihood`` Likelihood. mean_module : ``gpytorch.means`` Zero mean function. covar_module : ``gpytorch.kernels`` Automatic relevance determination Matern 5/2 covariance kernel. """ def __init__(self, x_train: Tensor, y_train: Tensor, likelihood: Likelihood) -> None: """ Parameters ---------- x_train : ``torch.Tensor`` (size n x d) Training inputs. y_train : ``torch.Tensor`` (size n) Training targets. likelihood : ``gpytorch.likelihoods.Likelihood`` Likelihood. """ # initialise ExactGP super(GaussianProcess, self).__init__(x_train, y_train, likelihood) # specify mean function and covariance kernel self.mean_module = ConstantMean() self.covar_module = ScaleKernel( base_kernel=MaternKernel(nu=5/2, ard_num_dims=x_train.shape[-1]) )
[docs] def forward(self, x: Tensor) -> MultivariateNormal: """ Compute the mean vector and covariance matrix for some test points `x` and returns a multivariate normal distribution. Parameters ---------- x : ``torch.Tensor`` (size n x d) Test points. Returns ------- ``gpytorch.distributions.MultivariateNormal`` Predictice multivariate normal distribution. """ mean_x = self.mean_module(x) covar_x = self.covar_module(x) return MultivariateNormal(mean_x, covar_x)