Source code for gpytorch.likelihoods.gaussian_likelihood

#!/usr/bin/env python3

import math
import warnings
from copy import deepcopy
from typing import Any, Optional

import torch
from torch import Tensor

from ..distributions import MultivariateNormal, base_distributions
from ..lazy import ZeroLazyTensor
from ..utils.warnings import GPInputWarning
from .likelihood import Likelihood
from .noise_models import FixedGaussianNoise, HomoskedasticNoise, Noise


class _GaussianLikelihoodBase(Likelihood):
    """Base class for Gaussian Likelihoods, supporting general heteroskedastic noise models."""

    def __init__(self, noise_covar: Noise, **kwargs: Any) -> None:

        super().__init__()
        param_transform = kwargs.get("param_transform")
        if param_transform is not None:
            warnings.warn(
                "The 'param_transform' argument is now deprecated. If you want to use a different "
                "transformaton, specify a different 'noise_constraint' instead.",
                DeprecationWarning,
            )

        self.noise_covar = noise_covar

    def _shaped_noise_covar(self, base_shape: torch.Size, *params: Any, **kwargs: Any):
        return self.noise_covar(*params, shape=base_shape, **kwargs)

    def expected_log_prob(self, target: Tensor, input: MultivariateNormal, *params: Any, **kwargs: Any) -> Tensor:
        mean, variance = input.mean, input.variance
        num_event_dim = len(input.event_shape)

        noise = self._shaped_noise_covar(mean.shape, *params, **kwargs).diag()
        # Potentially reshape the noise to deal with the multitask case
        noise = noise.view(*noise.shape[:-1], *input.event_shape)

        res = ((target - mean) ** 2 + variance) / noise + noise.log() + math.log(2 * math.pi)
        res = res.mul(-0.5)
        if num_event_dim > 1:  # Do appropriate summation for multitask Gaussian likelihoods
            res = res.sum(list(range(-1, -num_event_dim, -1)))
        return res

    def forward(self, function_samples: Tensor, *params: Any, **kwargs: Any) -> base_distributions.Normal:
        noise = self._shaped_noise_covar(function_samples.shape, *params, **kwargs).diag()
        return base_distributions.Normal(function_samples, noise.sqrt())

    def log_marginal(
        self, observations: Tensor, function_dist: MultivariateNormal, *params: Any, **kwargs: Any
    ) -> Tensor:
        marginal = self.marginal(function_dist, *params, **kwargs)
        # We're making everything conditionally independent
        indep_dist = base_distributions.Normal(marginal.mean, marginal.variance.clamp_min(1e-8).sqrt())
        res = indep_dist.log_prob(observations)

        # Do appropriate summation for multitask Gaussian likelihoods
        num_event_dim = len(function_dist.event_shape)
        if num_event_dim > 1:
            res = res.sum(list(range(-1, -num_event_dim, -1)))
        return res

    def marginal(self, function_dist: MultivariateNormal, *params: Any, **kwargs: Any) -> MultivariateNormal:
        mean, covar = function_dist.mean, function_dist.lazy_covariance_matrix
        noise_covar = self._shaped_noise_covar(mean.shape, *params, **kwargs)
        full_covar = covar + noise_covar
        return function_dist.__class__(mean, full_covar)


[docs]class GaussianLikelihood(_GaussianLikelihoodBase): r""" The standard likelihood for regression. Assumes a standard homoskedastic noise model: .. math:: p(y \mid f) = f + \epsilon, \quad \epsilon \sim \mathcal N (0, \sigma^2) where :math:`\sigma^2` is a noise parameter. .. note:: This likelihood can be used for exact or approximate inference. :param noise_prior: Prior for noise parameter :math:`\sigma^2`. :type noise_prior: ~gpytorch.priors.Prior, optional :param noise_constraint: Constraint for noise parameter :math:`\sigma^2`. :type noise_constraint: ~gpytorch.constraints.Interval, optional :param batch_shape: The batch shape of the learned noise parameter (default: []). :type batch_shape: torch.Size, optional :var torch.Tensor noise: :math:`\sigma^2` parameter (noise) """ def __init__(self, noise_prior=None, noise_constraint=None, batch_shape=torch.Size(), **kwargs): noise_covar = HomoskedasticNoise( noise_prior=noise_prior, noise_constraint=noise_constraint, batch_shape=batch_shape ) super().__init__(noise_covar=noise_covar) @property def noise(self) -> Tensor: return self.noise_covar.noise @noise.setter def noise(self, value: Tensor) -> None: self.noise_covar.initialize(noise=value) @property def raw_noise(self) -> Tensor: return self.noise_covar.raw_noise @raw_noise.setter def raw_noise(self, value: Tensor) -> None: self.noise_covar.initialize(raw_noise=value)
[docs]class FixedNoiseGaussianLikelihood(_GaussianLikelihoodBase): """ A Likelihood that assumes fixed heteroscedastic noise. This is useful when you have fixed, known observation noise for each training example. Note that this likelihood takes an additional argument when you call it, `noise`, that adds a specified amount of noise to the passed MultivariateNormal. This allows for adding known observational noise to test data. .. note:: This likelihood can be used for exact or approximate inference. :param noise: Known observation noise (variance) for each training example. :type noise: torch.Tensor (... x N) :param learn_additional_noise: Set to true if you additionally want to learn added diagonal noise, similar to GaussianLikelihood. :type learn_additional_noise: bool, optional :param batch_shape: The batch shape of the learned noise parameter (default []) if :obj:`learn_additional_noise=True`. :type batch_shape: torch.Size, optional :var torch.Tensor noise: :math:`\sigma^2` parameter (noise) Example: >>> train_x = torch.randn(55, 2) >>> noises = torch.ones(55) * 0.01 >>> likelihood = FixedNoiseGaussianLikelihood(noise=noises, learn_additional_noise=True) >>> pred_y = likelihood(gp_model(train_x)) >>> >>> test_x = torch.randn(21, 2) >>> test_noises = torch.ones(21) * 0.02 >>> pred_y = likelihood(gp_model(test_x), noise=test_noises) """ def __init__( self, noise: Tensor, learn_additional_noise: Optional[bool] = False, batch_shape: Optional[torch.Size] = torch.Size(), **kwargs: Any, ) -> None: super().__init__(noise_covar=FixedGaussianNoise(noise=noise)) if learn_additional_noise: noise_prior = kwargs.get("noise_prior", None) noise_constraint = kwargs.get("noise_constraint", None) self.second_noise_covar = HomoskedasticNoise( noise_prior=noise_prior, noise_constraint=noise_constraint, batch_shape=batch_shape ) else: self.second_noise_covar = None @property def noise(self) -> Tensor: return self.noise_covar.noise + self.second_noise @noise.setter def noise(self, value: Tensor) -> None: self.noise_covar.initialize(noise=value) @property def second_noise(self) -> Tensor: if self.second_noise_covar is None: return 0 else: return self.second_noise_covar.noise @second_noise.setter def second_noise(self, value: Tensor) -> None: if self.second_noise_covar is None: raise RuntimeError( "Attempting to set secondary learned noise for FixedNoiseGaussianLikelihood, " "but learn_additional_noise must have been False!" ) self.second_noise_covar.initialize(noise=value) def get_fantasy_likelihood(self, **kwargs): if "noise" not in kwargs: raise RuntimeError("FixedNoiseGaussianLikelihood.fantasize requires a `noise` kwarg") old_noise_covar = self.noise_covar self.noise_covar = None fantasy_liklihood = deepcopy(self) self.noise_covar = old_noise_covar old_noise = old_noise_covar.noise new_noise = kwargs.get("noise") if old_noise.dim() != new_noise.dim(): old_noise = old_noise.expand(*new_noise.shape[:-1], old_noise.shape[-1]) fantasy_liklihood.noise_covar = FixedGaussianNoise(noise=torch.cat([old_noise, new_noise], -1)) return fantasy_liklihood def _shaped_noise_covar(self, base_shape: torch.Size, *params: Any, **kwargs: Any): if len(params) > 0: # we can infer the shape from the params shape = None else: # here shape[:-1] is the batch shape requested, and shape[-1] is `n`, the number of points shape = base_shape res = self.noise_covar(*params, shape=shape, **kwargs) if self.second_noise_covar is not None: res = res + self.second_noise_covar(*params, shape=shape, **kwargs) elif isinstance(res, ZeroLazyTensor): warnings.warn( "You have passed data through a FixedNoiseGaussianLikelihood that did not match the size " "of the fixed noise, *and* you did not specify noise. This is treated as a no-op.", GPInputWarning, ) return res
[docs]class DirichletClassificationLikelihood(FixedNoiseGaussianLikelihood): """ A classification likelihood that treats the labels as regression targets with fixed heteroscedastic noise. From Milios et al, NeurIPS, 2018 [https://arxiv.org/abs/1805.10915]. .. note:: This likelihood can be used for exact or approximate inference. :param targets: classification labels. :type targets: torch.Tensor (N). :param alpha_epsilon: tuning parameter for the scaling of the likeihood targets. We'd suggest 0.01 or setting via cross-validation. :type alpha_epsilon: int. :param learn_additional_noise: Set to true if you additionally want to learn added diagonal noise, similar to GaussianLikelihood. :type learn_additional_noise: bool, optional :param batch_shape: The batch shape of the learned noise parameter (default []) if :obj:`learn_additional_noise=True`. :type batch_shape: torch.Size, optional Example: >>> train_x = torch.randn(55, 1) >>> labels = torch.round(train_x).long() >>> likelihood = DirichletClassificationLikelihood(targets=labels, learn_additional_noise=True) >>> pred_y = likelihood(gp_model(train_x)) >>> >>> test_x = torch.randn(21, 1) >>> test_labels = torch.round(test_x).long() >>> pred_y = likelihood(gp_model(test_x), targets=labels) """ def _prepare_targets(self, targets, alpha_epsilon=0.01, dtype=torch.float): num_classes = targets.max() + 1 # set alpha = \alpha_\epsilon alpha = alpha_epsilon * torch.ones(targets.shape[-1], num_classes, device=targets.device, dtype=dtype) # alpha[class_labels] = 1 + \alpha_\epsilon alpha[torch.arange(len(targets)), targets] = alpha[torch.arange(len(targets)), targets] + 1.0 # sigma^2 = log(1 / alpha + 1) sigma2_i = torch.log(1 / alpha + 1.0) # y = log(alpha) - 0.5 * sigma^2 transformed_targets = alpha.log() - 0.5 * sigma2_i return sigma2_i.transpose(-2, -1).type(dtype), transformed_targets.type(dtype), num_classes def __init__( self, targets: Tensor, alpha_epsilon: int = 0.01, learn_additional_noise: Optional[bool] = False, batch_shape: Optional[torch.Size] = torch.Size(), dtype: Optional[torch.dtype] = torch.float, **kwargs, ): sigma2_labels, transformed_targets, num_classes = self._prepare_targets( targets, alpha_epsilon=alpha_epsilon, dtype=dtype ) super().__init__( noise=sigma2_labels, learn_additional_noise=learn_additional_noise, batch_shape=torch.Size((num_classes,)), **kwargs, ) self.transformed_targets = transformed_targets.transpose(-2, -1) self.num_classes = num_classes self.targets = targets self.alpha_epsilon = alpha_epsilon def get_fantasy_likelihood(self, **kwargs): # we assume that the number of classes does not change. if "targets" not in kwargs: raise RuntimeError("FixedNoiseGaussianLikelihood.fantasize requires a `targets` kwarg") old_noise_covar = self.noise_covar self.noise_covar = None fantasy_liklihood = deepcopy(self) self.noise_covar = old_noise_covar old_noise = old_noise_covar.noise new_targets = kwargs.get("noise") new_noise, new_targets, _ = fantasy_liklihood._prepare_targets(new_targets, self.alpha_epsilon) fantasy_liklihood.targets = torch.cat([fantasy_liklihood.targets, new_targets], -1) if old_noise.dim() != new_noise.dim(): old_noise = old_noise.expand(*new_noise.shape[:-1], old_noise.shape[-1]) fantasy_liklihood.noise_covar = FixedGaussianNoise(noise=torch.cat([old_noise, new_noise], -1)) return fantasy_liklihood def __call__(self, *args, **kwargs): if "targets" in kwargs: targets = kwargs.pop("targets") dtype = self.transformed_targets.dtype new_noise, _, _ = self._prepare_targets(targets, dtype=dtype) kwargs["noise"] = new_noise return super().__call__(*args, **kwargs)