Source code for gpytorch.kernels.rq_kernel

from __future__ import absolute_import, division, print_function, unicode_literals

import torch

from ..constraints import Positive
from .kernel import Kernel


[docs]class RQKernel(Kernel): r""" Computes a covariance matrix based on the rational quadratic kernel between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`: .. math:: \begin{equation*} k_{\text{RQ}}(\mathbf{x_1}, \mathbf{x_2}) = \left(1 + \frac{1}{2\alpha} (\mathbf{x_1} - \mathbf{x_2})^\top \Theta^{-2} (\mathbf{x_1} - \mathbf{x_2}) \right)^{-\alpha} \end{equation*} where :math:`\Theta` is a :attr:`lengthscale` parameter, and :math:`\alpha` is the rational quadratic relative weighting parameter. See :class:`gpytorch.kernels.Kernel` for descriptions of the lengthscale options. .. note:: This kernel does not have an `outputscale` parameter. To add a scaling parameter, decorate this kernel with a :class:`gpytorch.kernels.ScaleKernel`. Args: :attr:`ard_num_dims` (int, optional): Set this if you want a separate lengthscale for each input dimension. It should be `d` if :attr:`x1` is a `n x d` matrix. Default: `None` :attr:`batch_shape` (torch.Size, optional): Set this if you want a separate lengthscale for each batch of input data. It should be `b` if :attr:`x1` is a `b x n x d` tensor. Default: `torch.Size([])`. :attr:`active_dims` (tuple of ints, optional): Set this if you want to compute the covariance of only a few input dimensions. The ints corresponds to the indices of the dimensions. Default: `None`. :attr:`lengthscale_prior` (Prior, optional): Set this if you want to apply a prior to the lengthscale parameter. Default: `None`. :attr:`lengthscale_constraint` (Constraint, optional): Set this if you want to apply a constraint to the lengthscale parameter. Default: `Positive`. :attr:`alpha_constraint` (Constraint, optional): Set this if you want to apply a constraint to the alpha parameter. Default: `Positive`. :attr:`eps` (float): The minimum value that the lengthscale can take (prevents divide by zero errors). Default: `1e-6`. Attributes: :attr:`lengthscale` (Tensor): The lengthscale parameter. Size/shape of parameter depends on the :attr:`ard_num_dims` and :attr:`batch_shape` arguments. :attr:`alpha` (Tensor): The rational quadratic relative weighting parameter. Size/shape of parameter depends on the :attr:`batch_shape` argument """ has_lengthscale = True def __init__(self, alpha_constraint=None, **kwargs): super(RQKernel, self).__init__(**kwargs) self.register_parameter(name="raw_alpha", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1))) if alpha_constraint is None: alpha_constraint = Positive() self.register_constraint("raw_alpha", alpha_constraint) def forward(self, x1, x2, diag=False, **params): def postprocess_rq(dist): alpha = self.alpha for _ in range(1, len(dist.shape) - len(self.batch_shape)): alpha = alpha.unsqueeze(-1) return (1 + dist.div(2 * alpha)).pow(-alpha) x1_ = x1.div(self.lengthscale) x2_ = x2.div(self.lengthscale) return self.covar_dist( x1_, x2_, square_dist=True, diag=diag, dist_postprocess_func=postprocess_rq, postprocess=True, **params ) @property def alpha(self): return self.raw_alpha_constraint.transform(self.raw_alpha) @alpha.setter def alpha(self, value): if not torch.is_tensor(value): value = torch.as_tensor(value).to(self.raw_lengthscale) self.initialize(raw_alpha=self.raw_alpha_constraint.inverse_transform(value))