Source code for gpytorch.kernels.product_structure_kernel

#!/usr/bin/env python3

from typing import Optional, Tuple

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:
base_kernel (Kernel):
The kernel to approximate with KISS-GP
num_dims (int):
The dimension of the input data.
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: Kernel,
num_dims: int,
active_dims: Optional[Tuple[int, ...]] = 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