Source code for gpytorch.kernels.linear_kernel

#!/usr/bin/env python3

import warnings
from typing import Optional, Union

import torch
from linear_operator.operators import LinearOperator, MatmulLinearOperator, RootLinearOperator
from torch import Tensor

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

[docs]class LinearKernel(Kernel): r""" Computes a covariance matrix based on the Linear kernel between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`: .. math:: \begin{equation*} k_\text{Linear}(\mathbf{x_1}, \mathbf{x_2}) = v\mathbf{x_1}^\top \mathbf{x_2}. \end{equation*} where * :math:`v` is a variance parameter. .. note:: To implement this efficiently, we use a :obj:`~linear_operator.operators.RootLinearOperator` during training and a :class:`~linear_operator.operators.MatmulLinearOperator` during test. These lazy tensors represent matrices of the form :math:`\mathbf K = \mathbf X \mathbf X^{\prime \top}`. This makes inference efficient because a matrix-vector product :math:`\mathbf K \mathbf v` can be computed as :math:`\mathbf K \mathbf v = \mathbf X( \mathbf X^{\prime \top} \mathbf v)`, where the base multiply :math:`\mathbf X \mathbf v` takes only :math:`\mathcal O(ND)` time and space. :param variance_prior: Prior over the variance parameter. (Default `None`.) :param variance_constraint: Constraint to place on variance parameter. (Default: `Positive`.) :param active_dims: List of data dimensions to operate on. `len(active_dims)` should equal `num_dimensions`. """ def __init__( self, num_dimensions: Optional[int] = None, offset_prior: Optional[Prior] = None, variance_prior: Optional[Prior] = None, variance_constraint: Optional[Interval] = None, **kwargs, ): super(LinearKernel, self).__init__(**kwargs) if variance_constraint is None: variance_constraint = Positive() if num_dimensions is not None: # Remove after 1.0 warnings.warn("The `num_dimensions` argument is deprecated and no longer used.", DeprecationWarning) self.register_parameter(name="offset", parameter=torch.nn.Parameter(torch.zeros(1, 1, num_dimensions))) if offset_prior is not None: # Remove after 1.0 warnings.warn("The `offset_prior` argument is deprecated and no longer used.", DeprecationWarning) self.register_parameter(name="raw_variance", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1, 1))) if variance_prior is not None: if not isinstance(variance_prior, Prior): raise TypeError("Expected gpytorch.priors.Prior but got " + type(variance_prior).__name__) self.register_prior("variance_prior", variance_prior, lambda m: m.variance, lambda m, v: m._set_variance(v)) self.register_constraint("raw_variance", variance_constraint) @property def variance(self) -> Tensor: return self.raw_variance_constraint.transform(self.raw_variance) @variance.setter def variance(self, value: Union[float, Tensor]): self._set_variance(value) def _set_variance(self, value: Union[float, Tensor]): if not torch.is_tensor(value): value = torch.as_tensor(value).to(self.raw_variance) self.initialize(raw_variance=self.raw_variance_constraint.inverse_transform(value)) def forward( self, x1: Tensor, x2: Tensor, diag: Optional[bool] = False, last_dim_is_batch: Optional[bool] = False, **params ) -> LinearOperator: x1_ = x1 * self.variance.sqrt() if last_dim_is_batch: x1_ = x1_.transpose(-1, -2).unsqueeze(-1) if x1.size() == x2.size() and torch.equal(x1, x2): # Use RootLinearOperator when x1 == x2 for efficiency when composing # with other kernels prod = RootLinearOperator(x1_) else: x2_ = x2 * self.variance.sqrt() if last_dim_is_batch: x2_ = x2_.transpose(-1, -2).unsqueeze(-1) prod = MatmulLinearOperator(x1_, x2_.transpose(-2, -1)) if diag: return prod.diagonal(dim1=-1, dim2=-2) else: return prod