Source code for gpytorch.kernels.cylindrical_kernel

#!/usr/bin/env python3

from typing import Optional

import torch

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


[docs]class CylindricalKernel(Kernel): r""" Computes a covariance matrix based on the Cylindrical Kernel between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`. It was proposed in `BOCK: Bayesian Optimization with Cylindrical Kernels`. See http://proceedings.mlr.press/v80/oh18a.html for more details .. note:: The data must lie completely within the unit ball. Args: :attr:`num_angular_weights` (int): The number of components in the angular kernel :attr:`radial_base_kernel` (gpytorch.kernel): The base kernel for computing the radial kernel :attr:`batch_size` (int, optional): Set this if the data is batch of input data. It should be `b` if :attr:`x1` is a `b x n x d` tensor. Default: `1` :attr:`eps` (float): Small floating point number used to improve numerical stability in kernel computations. Default: `1e-6` :attr:`param_transform` (function, optional): Set this if you want to use something other than softplus to ensure positiveness of parameters. :attr:`inv_param_transform` (function, optional): Set this to allow setting parameters directly in transformed space and sampling from priors. Automatically inferred for common transformations such as torch.exp or torch.nn.functional.softplus. """ def __init__( self, num_angular_weights: int, radial_base_kernel: Kernel, eps: Optional[int] = 1e-6, angular_weights_prior: Optional[Prior] = None, angular_weights_constraint: Optional[Interval] = None, alpha_prior: Optional[Prior] = None, alpha_constraint: Optional[Interval] = None, beta_prior: Optional[Prior] = None, beta_constraint: Optional[Interval] = None, **kwargs, ): if angular_weights_constraint is None: angular_weights_constraint = Positive() if alpha_constraint is None: alpha_constraint = Positive() if beta_constraint is None: beta_constraint = Positive() super().__init__(**kwargs) self.num_angular_weights = num_angular_weights self.radial_base_kernel = radial_base_kernel self.eps = eps self.register_parameter( name="raw_angular_weights", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, num_angular_weights)), ) self.register_constraint("raw_angular_weights", angular_weights_constraint) self.register_parameter(name="raw_alpha", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1))) self.register_constraint("raw_alpha", alpha_constraint) self.register_parameter(name="raw_beta", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1))) self.register_constraint("raw_beta", beta_constraint) if angular_weights_prior is not None: self.register_prior( "angular_weights_prior", angular_weights_prior, lambda: self.angular_weights, lambda v: self._set_angular_weights(v), ) if alpha_prior is not None: self.register_prior("alpha_prior", alpha_prior, lambda: self.alpha, lambda v: self._set_alpha(v)) if beta_prior is not None: self.register_prior("beta_prior", beta_prior, lambda: self.beta, lambda v: self._set_beta(v)) @property def angular_weights(self) -> torch.Tensor: return self.raw_angular_weights_constraint.transform(self.raw_angular_weights) @angular_weights.setter def angular_weights(self, value: torch.Tensor) -> None: if not torch.is_tensor(value): value = torch.tensor(value) self.initialize(raw_angular_weights=self.raw_angular_weights_constraint.inverse_transform(value)) @property def alpha(self) -> torch.Tensor: return self.raw_alpha_constraint.transform(self.raw_alpha) @alpha.setter def alpha(self, value: torch.Tensor) -> None: if not torch.is_tensor(value): value = torch.tensor(value) self.initialize(raw_alpha=self.raw_alpha_constraint.inverse_transform(value)) @property def beta(self) -> torch.Tensor: return self.raw_beta_constraint.transform(self.raw_beta) @beta.setter def beta(self, value: torch.Tensor) -> None: if not torch.is_tensor(value): value = torch.tensor(value) self.initialize(raw_beta=self.raw_beta_constraint.inverse_transform(value)) def forward(self, x1: torch.Tensor, x2: torch.Tensor, diag: Optional[bool] = False, **params) -> torch.Tensor: x1_, x2_ = x1.clone(), x2.clone() # Jitter datapoints that are exactly 0 x1_[x1_ == 0], x2_[x2_ == 0] = x1_[x1_ == 0] + self.eps, x2_[x2_ == 0] + self.eps r1, r2 = x1_.norm(dim=-1, keepdim=True), x2_.norm(dim=-1, keepdim=True) if torch.any(r1 > 1.0) or torch.any(r2 > 1.0): raise RuntimeError("Cylindrical kernel not defined for data points with radius > 1. Scale your data!") a1, a2 = x1.div(r1), x2.div(r2) if not diag: gram_mat = a1.matmul(a2.transpose(-2, -1)) for p in range(self.num_angular_weights): if p == 0: angular_kernel = self.angular_weights[..., 0, None, None] else: angular_kernel = angular_kernel + self.angular_weights[..., p, None, None].mul(gram_mat.pow(p)) else: gram_mat = a1.mul(a2).sum(-1) for p in range(self.num_angular_weights): if p == 0: angular_kernel = self.angular_weights[..., 0, None] else: angular_kernel = angular_kernel + self.angular_weights[..., p, None].mul(gram_mat.pow(p)) with settings.lazily_evaluate_kernels(False): radial_kernel = self.radial_base_kernel(self.kuma(r1), self.kuma(r2), diag=diag, **params) return radial_kernel.mul(angular_kernel) def kuma(self, x: torch.Tensor) -> torch.Tensor: alpha = self.alpha.view(*self.batch_shape, 1, 1) beta = self.beta.view(*self.batch_shape, 1, 1) res = 1 - (1 - x.pow(alpha) + self.eps).pow(beta) return res def num_outputs_per_input(self, x1: torch.Tensor, x2: torch.Tensor) -> int: return self.radial_base_kernel.num_outputs_per_input(x1, x2)