#!/usr/bin/env python3
from typing import Optional, Tuple
from .kernel import Kernel
[docs]class AdditiveStructureKernel(Kernel):
r"""
A Kernel decorator for kernels with additive structure. If a kernel decomposes
additively, then this module will be much more computationally efficient.
A kernel function `k` decomposes additively 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 a subset of dimensions.
Given a `b x n x d` input, `AdditiveStructureKernel` computes `d` one-dimensional kernels
(using the supplied base_kernel), and then adds the component kernels together.
Unlike :class:`~gpytorch.kernels.AdditiveKernel`, `AdditiveStructureKernel` computes each
of the additive terms in batch, making it very fast.
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`.
"""
@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(AdditiveStructureKernel, 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("AdditiveStructureKernel 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.sum(-2 if diag else -3)
return res
def prediction_strategy(self, train_inputs, train_prior_dist, train_labels, likelihood):
return self.base_kernel.prediction_strategy(train_inputs, train_prior_dist, train_labels, likelihood)
def num_outputs_per_input(self, x1, x2):
return self.base_kernel.num_outputs_per_input(x1, x2)