Source code for gpytorch.kernels.rbf_kernel_grad

#!/usr/bin/env python3
import torch

from ..lazy.kronecker_product_lazy_tensor import KroneckerProductLazyTensor
from .rbf_kernel import RBFKernel, postprocess_rbf


[docs]class RBFKernelGrad(RBFKernel): r""" Computes a covariance matrix of the RBF kernel that models the covariance between the values and partial derivatives for inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`. 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:`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:`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. Example: >>> x = torch.randn(10, 5) >>> # Non-batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernelGrad()) >>> covar = covar_module(x) # Output: LazyTensor of size (60 x 60), where 60 = n * (d + 1) >>> >>> batch_x = torch.randn(2, 10, 5) >>> # Batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernelGrad()) >>> # Batch: different lengthscale for each batch >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernelGrad(batch_shape=torch.Size([2]))) >>> covar = covar_module(x) # Output: LazyTensor of size (2 x 60 x 60) """ def forward(self, x1, x2, diag=False, **params): batch_shape = x1.shape[:-2] n_batch_dims = len(batch_shape) n1, d = x1.shape[-2:] n2 = x2.shape[-2] K = torch.zeros(*batch_shape, n1 * (d + 1), n2 * (d + 1), device=x1.device, dtype=x1.dtype) if not diag: # Scale the inputs by the lengthscale (for stability) x1_ = x1.div(self.lengthscale) x2_ = x2.div(self.lengthscale) # Form all possible rank-1 products for the gradient and Hessian blocks outer = x1_.view(*batch_shape, n1, 1, d) - x2_.view(*batch_shape, 1, n2, d) outer = outer / self.lengthscale.unsqueeze(-2) outer = torch.transpose(outer, -1, -2).contiguous() # 1) Kernel block diff = self.covar_dist(x1_, x2_, square_dist=True, dist_postprocess_func=postprocess_rbf, **params) K_11 = diff K[..., :n1, :n2] = K_11 # 2) First gradient block outer1 = outer.view(*batch_shape, n1, n2 * d) K[..., :n1, n2:] = outer1 * K_11.repeat([*([1] * (n_batch_dims + 1)), d]) # 3) Second gradient block outer2 = outer.transpose(-1, -3).reshape(*batch_shape, n2, n1 * d) outer2 = outer2.transpose(-1, -2) K[..., n1:, :n2] = -outer2 * K_11.repeat([*([1] * n_batch_dims), d, 1]) # 4) Hessian block outer3 = outer1.repeat([*([1] * n_batch_dims), d, 1]) * outer2.repeat([*([1] * (n_batch_dims + 1)), d]) kp = KroneckerProductLazyTensor( torch.eye(d, d, device=x1.device, dtype=x1.dtype).repeat(*batch_shape, 1, 1) / self.lengthscale.pow(2), torch.ones(n1, n2, device=x1.device, dtype=x1.dtype).repeat(*batch_shape, 1, 1), ) chain_rule = kp.evaluate() - outer3 K[..., n1:, n2:] = chain_rule * K_11.repeat([*([1] * n_batch_dims), d, d]) # Symmetrize for stability if n1 == n2 and torch.eq(x1, x2).all(): K = 0.5 * (K.transpose(-1, -2) + K) # Apply a perfect shuffle permutation to match the MutiTask ordering pi1 = torch.arange(n1 * (d + 1)).view(d + 1, n1).t().reshape((n1 * (d + 1))) pi2 = torch.arange(n2 * (d + 1)).view(d + 1, n2).t().reshape((n2 * (d + 1))) K = K[..., pi1, :][..., :, pi2] return K else: if not (n1 == n2 and torch.eq(x1, x2).all()): raise RuntimeError("diag=True only works when x1 == x2") kernel_diag = super(RBFKernelGrad, self).forward(x1, x2, diag=True) grad_diag = torch.ones(*batch_shape, n2, d, device=x1.device, dtype=x1.dtype) / self.lengthscale.pow_(2) grad_diag = grad_diag.transpose(-1, -2).reshape(*batch_shape, n2 * d) k_diag = torch.cat((kernel_diag, grad_diag), dim=-1) pi = torch.arange(n2 * (d + 1)).view(d + 1, n2).t().reshape((n2 * (d + 1))) return k_diag[..., pi] def num_outputs_per_input(self, x1, x2): return x1.size(-1) + 1