# Source code for gpytorch.kernels.polynomial_kernel

#!/usr/bin/env python3

from typing import Optional

import torch

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

[docs]class PolynomialKernel(Kernel): r""" Computes a covariance matrix based on the Polynomial kernel between inputs :math:\mathbf{x_1} and :math:\mathbf{x_2}: .. math:: \begin{equation*} k_\text{Poly}(\mathbf{x_1}, \mathbf{x_2}) = (\mathbf{x_1}^\top \mathbf{x_2} + c)^{d}. \end{equation*} where * :math:c is an :attr:offset parameter. Args: :attr:offset_prior (:class:gpytorch.priors.Prior): Prior over the offset parameter (default None). :attr:offset_constraint (Constraint, optional): Constraint to place on offset parameter. Default: Positive. :attr:active_dims (list): List of data dimensions to operate on. len(active_dims) should equal num_dimensions. """ def __init__( self, power: int, offset_prior: Optional[Prior] = None, offset_constraint: Optional[Interval] = None, **kwargs ): super().__init__(**kwargs) if offset_constraint is None: offset_constraint = Positive() self.register_parameter(name="raw_offset", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1))) # We want the power to be a float so we dont have to worry about its device / dtype. if torch.is_tensor(power): if power.numel() > 1: raise RuntimeError("Cant create a Polynomial kernel with more than one power") else: power = power.item() self.power = power if offset_prior is not None: self.register_prior("offset_prior", offset_prior, lambda: self.offset, lambda v: self._set_offset(v)) self.register_constraint("raw_offset", offset_constraint) @property def offset(self) -> torch.Tensor: return self.raw_offset_constraint.transform(self.raw_offset) @offset.setter def offset(self, value: torch.Tensor) -> None: self._set_offset(value) def _set_offset(self, value: torch.Tensor) -> None: if not torch.is_tensor(value): value = torch.as_tensor(value).to(self.raw_offset) self.initialize(raw_offset=self.raw_offset_constraint.inverse_transform(value)) def forward( self, x1: torch.Tensor, x2: torch.Tensor, diag: Optional[bool] = False, last_dim_is_batch: Optional[bool] = False, **params, ) -> torch.Tensor: offset = self.offset.view(*self.batch_shape, 1, 1) if last_dim_is_batch: x1 = x1.transpose(-1, -2).unsqueeze(-1) x2 = x2.transpose(-1, -2).unsqueeze(-1) if diag: return ((x1 * x2).sum(dim=-1) + self.offset).pow(self.power) if x1.dim() == 2 and x2.dim() == 2: return torch.addmm(offset, x1, x2.transpose(-2, -1)).pow(self.power) else: return (torch.matmul(x1, x2.transpose(-2, -1)) + offset).pow(self.power)