Source code for gpytorch.kernels.periodic_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 PeriodicKernel(Kernel): r"""Computes a covariance matrix based on the periodic kernel between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`: .. math:: \begin{equation*} k_{\text{Periodic}}(\mathbf{x}, \mathbf{x'}) = \exp \left( -2 \sum_i \frac{\sin ^2 \left( \frac{\pi}{p} ({x_{i}} - {x_{i}'} ) \right)}{\lambda} \right) \end{equation*} where * :math:`p` is the period length parameter. * :math:`\lambda` is a lengthscale parameter. Equation is based on `David Mackay's Introduction to Gaussian Processes equation 47`_ (albeit without feature-specific lengthscales and period lengths). The exponential coefficient was changed and lengthscale is not squared to maintain backwards compatibility .. note:: This kernel does not have an `outputscale` parameter. To add a scaling parameter, decorate this kernel with a :class:`gpytorch.kernels.ScaleKernel`. :param ard_num_dims: (Default: `None`) Set this if you want a separate lengthscale for each input dimension. It should be `d` if x1 is a `... x n x d` matrix. :type ard_num_dims: int, optional :param batch_shape: (Default: `None`) Set this if you want a separate lengthscale for each batch of input data. It should be `torch.Size([b1, b2])` for a `b1 x b2 x n x m` kernel output. :type batch_shape: torch.Size, optional :param active_dims: (Default: `None`) Set this if you want to compute the covariance of only a few input dimensions. The ints corresponds to the indices of the dimensions. :type active_dims: Tuple(int) :param period_length_prior: (Default: `None`) Set this if you want to apply a prior to the period length parameter. :type period_length_prior: ~gpytorch.priors.Prior, optional :param period_length_constraint: (Default: `Positive`) Set this if you want to apply a constraint to the period length parameter. :type period_length_constraint: ~gpytorch.constraints.Interval, optional :param lengthscale_prior: (Default: `None`) Set this if you want to apply a prior to the lengthscale parameter. :type lengthscale_prior: ~gpytorch.priors.Prior, optional :param lengthscale_constraint: (Default: `Positive`) Set this if you want to apply a constraint to the lengthscale parameter. :type lengthscale_constraint: ~gpytorch.constraints.Interval, optional :param eps: (Default: 1e-6) The minimum value that the lengthscale can take (prevents divide by zero errors). :type eps: float, optional :var torch.Tensor period_length: The period length parameter. Size/shape of parameter depends on the ard_num_dims and batch_shape arguments. Example: >>> x = torch.randn(10, 5) >>> # Non-batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel()) >>> >>> batch_x = torch.randn(2, 10, 5) >>> # Batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel()) >>> # Batch: different lengthscale for each batch >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel(batch_size=2)) >>> covar = covar_module(x) # Output: LazyVariable of size (2 x 10 x 10) .. _David Mackay's Introduction to Gaussian Processes equation 47: """ has_lengthscale = True def __init__( self, period_length_prior: Optional[Prior] = None, period_length_constraint: Optional[Interval] = None, **kwargs, ): super(PeriodicKernel, self).__init__(**kwargs) if period_length_constraint is None: period_length_constraint = Positive() ard_num_dims = kwargs.get("ard_num_dims", 1) self.register_parameter( name="raw_period_length", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1, ard_num_dims)) ) 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): 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, diag=False, **params): # Pop this argument so that we can manually sum over dimensions last_dim_is_batch = params.pop("last_dim_is_batch", False) # Get lengthscale lengthscale = self.lengthscale x1_ = x1.div(self.period_length / math.pi) x2_ = x2.div(self.period_length / math.pi) # We are automatically overriding last_dim_is_batch here so that we can manually sum over dimensions. diff = self.covar_dist(x1_, x2_, diag=diag, last_dim_is_batch=True, **params) if diag: lengthscale = lengthscale[..., 0, :, None] else: lengthscale = lengthscale[..., 0, :, None, None] exp_term = diff.sin().pow(2.0).div(lengthscale).mul(-2.0) if not last_dim_is_batch: exp_term = exp_term.sum(dim=(-2 if diag else -3)) return exp_term.exp()