Source code for gpytorch.kernels.cosine_kernel

#!/usr/bin/env python3

import math
from typing import Optional

import torch

from ..constraints import Interval, Positive
from ..priors import Prior
from .kernel import Kernel

[docs]class CosineKernel(Kernel):
r"""
Computes a covariance matrix based on the cosine kernel
between inputs :math:\mathbf{x_1} and :math:\mathbf{x_2}:

.. math::

\begin{equation*}
k_{\text{Cosine}}(\mathbf{x_1}, \mathbf{x_2}) = \cos \left(
\pi \Vert \mathbf{x_1} - \mathbf{x_2} \Vert_2 / p \right)
\end{equation*}

where :math:p is the period length parameter.

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:period_length_prior (Prior, optional):
Set this if you want to apply a prior to the period length parameter.  Default: None
:attr:period_length_constraint (Constraint, optional):
Set this if you want to apply a constraint to the period length parameter. Default: Positive.
:attr:eps (float):
The minimum value that the lengthscale/period length can take
(prevents divide by zero errors). Default: 1e-6.

Attributes:
:attr:period_length (Tensor):
The period length parameter. Size = *batch_shape x 1 x 1.

Example:
>>> x = torch.randn(10, 5)
>>> # Non-batch: Simple option
>>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.CosineKernel())
>>>
>>> batch_x = torch.randn(2, 10, 5)
>>> # Batch: Simple option
>>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.CosineKernel())
>>> # Batch: different lengthscale for each batch
>>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.CosineKernel(batch_shape=torch.Size([2])))
>>> covar = covar_module(x)  # Output: LazyVariable of size (2 x 10 x 10)
"""

is_stationary = True

def __init__(
self,
period_length_prior: Optional[Prior] = None,
period_length_constraint: Optional[Interval] = None,
**kwargs,
):
super(CosineKernel, self).__init__(**kwargs)

self.register_parameter(
name="raw_period_length", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1, 1))
)

if period_length_constraint is None:
period_length_constraint = Positive()

if period_length_prior is not None:
if not isinstance(period_length_prior, Prior):
raise TypeError("Expected gpytorch.priors.Prior but got " + type(period_length_prior).__name__)
self.register_prior(
"period_length_prior",
period_length_prior,
lambda m: m.period_length,
lambda m, v: m._set_period_length(v),
)

self.register_constraint("raw_period_length", period_length_constraint)

@property
def period_length(self):
return self.raw_period_length_constraint.transform(self.raw_period_length)

@period_length.setter
def period_length(self, value):
return self._set_period_length(value)

def _set_period_length(self, value):
if not torch.is_tensor(value):
value = torch.as_tensor(value).to(self.raw_period_length)

self.initialize(raw_period_length=self.raw_period_length_constraint.inverse_transform(value))

def forward(self, x1, x2, **params):
x1_ = x1.div(self.period_length)
x2_ = x2.div(self.period_length)
diff = self.covar_dist(x1_, x2_, **params)
res = torch.cos(diff.mul(math.pi))
return res