Source code for gpytorch.kernels.product_structure_kernel

#!/usr/bin/env python3

from ..lazy import lazify
from .kernel import Kernel


[docs]class ProductStructureKernel(Kernel): r""" A Kernel decorator for kernels with product structure. If a kernel decomposes multiplicatively, then this module will be much more computationally efficient. A kernel function `k` has product structure if it can be written as .. math:: \begin{equation*} k(\mathbf{x_1}, \mathbf{x_2}) = k'(x_1^{(1)}, x_2^{(1)}) * \ldots * k'(x_1^{(d)}, x_2^{(d)}) \end{equation*} for some kernel :math:`k'` that operates on each dimension. Given a `b x n x d` input, `ProductStructureKernel` computes `d` one-dimensional kernels (using the supplied base_kernel), and then multiplies the component kernels together. Unlike :class:`~gpytorch.kernels.ProductKernel`, `ProductStructureKernel` computes each of the product terms in batch, making it very fast. See `Product Kernel Interpolation for Scalable Gaussian Processes`_ for more detail. Args: - :attr:`base_kernel` (Kernel): The kernel to approximate with KISS-GP - :attr:`num_dims` (int): The dimension of the input data. - :attr:`active_dims` (tuple of ints, optional): Passed down to the `base_kernel`. .. _Product Kernel Interpolation for Scalable Gaussian Processes: https://arxiv.org/pdf/1802.08903 """ @property def is_stationary(self) -> bool: """ Kernel is stationary if the base kernel is stationary. """ return self.base_kernel.is_stationary def __init__(self, base_kernel, num_dims, active_dims=None): super(ProductStructureKernel, self).__init__(active_dims=active_dims) self.base_kernel = base_kernel self.num_dims = num_dims def forward(self, x1, x2, diag=False, last_dim_is_batch=False, **params): if last_dim_is_batch: raise RuntimeError("ProductStructureKernel does not accept the last_dim_is_batch argument.") res = self.base_kernel(x1, x2, diag=diag, last_dim_is_batch=True, **params) res = res.prod(-2 if diag else -3) return res def num_outputs_per_input(self, x1, x2): return self.base_kernel.num_outputs_per_input(x1, x2) def __call__(self, x1_, x2_=None, diag=False, last_dim_is_batch=False, **params): """ We cannot lazily evaluate actual kernel calls when using SKIP, because we cannot root decompose rectangular matrices. Because we slice in to the kernel during prediction to get the test x train covar before calling evaluate_kernel, the order of operations would mean we would get a MulLazyTensor representing a rectangular matrix, which we cannot matmul with because we cannot root decompose it. Thus, SKIP actually *requires* that we work with the full (train + test) x (train + test) kernel matrix. """ res = super().__call__(x1_, x2_, diag=diag, last_dim_is_batch=last_dim_is_batch, **params) res = lazify(res).evaluate_kernel() return res