# Source code for botorch.models.gp_regression

```
#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
r"""
Gaussian Process Regression models based on GPyTorch models.
These models are often a good starting point and are further documented in the
tutorials.
`SingleTaskGP`, `FixedNoiseGP`, and `HeteroskedasticSingleTaskGP` are all
single-task exact GP models, differing in how they treat noise. They use
relatively strong priors on the Kernel hyperparameters, which work best when
covariates are normalized to the unit cube and outcomes are standardized (zero
mean, unit variance).
These models all work in batch mode (each batch having its own hyperparameters).
When the training observations include multiple outputs, these models use
batching to model outputs independently.
These models all support multiple outputs. However, as single-task models,
`SingleTaskGP`, `FixedNoiseGP`, and `HeteroskedasticSingleTaskGP` should be
used only when the outputs are independent and all use the same training data.
If outputs are independent and outputs have different training data, use the
`ModelListGP`. When modeling correlations between outputs, use a multi-task
model like `MultiTaskGP`.
"""
from __future__ import annotations
import warnings
from typing import NoReturn, Optional
import torch
from botorch.models.gpytorch import BatchedMultiOutputGPyTorchModel
from botorch.models.model import FantasizeMixin
from botorch.models.transforms.input import InputTransform
from botorch.models.transforms.outcome import Log, OutcomeTransform
from botorch.models.utils import validate_input_scaling
from botorch.models.utils.gpytorch_modules import (
get_gaussian_likelihood_with_gamma_prior,
get_matern_kernel_with_gamma_prior,
MIN_INFERRED_NOISE_LEVEL,
)
from gpytorch.constraints.constraints import GreaterThan
from gpytorch.distributions.multivariate_normal import MultivariateNormal
from gpytorch.likelihoods.gaussian_likelihood import (
_GaussianLikelihoodBase,
FixedNoiseGaussianLikelihood,
GaussianLikelihood,
)
from gpytorch.likelihoods.likelihood import Likelihood
from gpytorch.likelihoods.noise_models import HeteroskedasticNoise
from gpytorch.means.constant_mean import ConstantMean
from gpytorch.means.mean import Mean
from gpytorch.mlls.noise_model_added_loss_term import NoiseModelAddedLossTerm
from gpytorch.models.exact_gp import ExactGP
from gpytorch.module import Module
from gpytorch.priors.smoothed_box_prior import SmoothedBoxPrior
from torch import Tensor
[docs]class SingleTaskGP(BatchedMultiOutputGPyTorchModel, ExactGP, FantasizeMixin):
r"""A single-task exact GP model, supporting both known and inferred noise levels.
A single-task exact GP using relatively strong priors on the Kernel
hyperparameters, which work best when covariates are normalized to the unit
cube and outcomes are standardized (zero mean, unit variance).
This model works in batch mode (each batch having its own hyperparameters).
When the training observations include multiple outputs, this model will use
batching to model outputs independently.
Use this model when you have independent output(s) and all outputs use the
same training data. If outputs are independent and outputs have different
training data, use the ModelListGP. When modeling correlations between
outputs, use the MultiTaskGP.
An example of a case in which noise levels are known is online
experimentation, where noise can be measured using the variability of
different observations from the same arm, or provided by outside software.
Another use case is simulation optimization, where the evaluation can
provide variance estimates, perhaps from bootstrapping. In any case, these
noise levels can be provided to `SingleTaskGP` as `train_Yvar`.
`SingleTaskGP` can also be used when the observations are known to be
noise-free. Noise-free observations can be modeled using arbitrarily small
noise values, such as `train_Yvar=torch.full_like(train_Y, 1e-6)`.
Example:
Model with inferred noise levels:
>>> import torch
>>> from botorch.models.gp_regression import SingleTaskGP
>>> from botorch.models.transforms.outcome import Standardize
>>>
>>> train_X = torch.rand(20, 2, dtype=torch.float64)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)
>>> outcome_transform = Standardize(m=1)
>>> inferred_noise_model = SingleTaskGP(
... train_X, train_Y, outcome_transform=outcome_transform,
... )
Model with a known observation variance of 0.2:
>>> train_Yvar = torch.full_like(train_Y, 0.2)
>>> observed_noise_model = SingleTaskGP(
... train_X, train_Y, train_Yvar,
... outcome_transform=outcome_transform,
... )
With noise-free observations:
>>> train_Yvar = torch.full_like(train_Y, 1e-6)
>>> noise_free_model = SingleTaskGP(
... train_X, train_Y, train_Yvar,
... outcome_transform=outcome_transform,
... )
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
train_Yvar: Optional[Tensor] = None,
likelihood: Optional[Likelihood] = None,
covar_module: Optional[Module] = None,
mean_module: Optional[Mean] = None,
outcome_transform: Optional[OutcomeTransform] = None,
input_transform: Optional[InputTransform] = None,
) -> None:
r"""
Args:
train_X: A `batch_shape x n x d` tensor of training features.
train_Y: A `batch_shape x n x m` tensor of training observations.
train_Yvar: An optional `batch_shape x n x m` tensor of observed
measurement noise.
likelihood: A likelihood. If omitted, use a standard
`GaussianLikelihood` with inferred noise level if `train_Yvar`
is None, and a `FixedNoiseGaussianLikelihood` with the given
noise observations if `train_Yvar` is not None.
covar_module: The module computing the covariance (Kernel) matrix.
If omitted, use a `MaternKernel`.
mean_module: The mean function to be used. If omitted, use a
`ConstantMean`.
outcome_transform: An outcome transform that is applied to the
training data during instantiation and to the posterior during
inference (that is, the `Posterior` obtained by calling
`.posterior` on the model will be on the original scale).
input_transform: An input transform that is applied in the model's
forward pass.
"""
with torch.no_grad():
transformed_X = self.transform_inputs(
X=train_X, input_transform=input_transform
)
if outcome_transform is not None:
train_Y, train_Yvar = outcome_transform(train_Y, train_Yvar)
self._validate_tensor_args(X=transformed_X, Y=train_Y, Yvar=train_Yvar)
ignore_X_dims = getattr(self, "_ignore_X_dims_scaling_check", None)
validate_input_scaling(
train_X=transformed_X,
train_Y=train_Y,
train_Yvar=train_Yvar,
ignore_X_dims=ignore_X_dims,
)
self._set_dimensions(train_X=train_X, train_Y=train_Y)
train_X, train_Y, train_Yvar = self._transform_tensor_args(
X=train_X, Y=train_Y, Yvar=train_Yvar
)
if likelihood is None:
if train_Yvar is None:
likelihood = get_gaussian_likelihood_with_gamma_prior(
batch_shape=self._aug_batch_shape
)
else:
likelihood = FixedNoiseGaussianLikelihood(
noise=train_Yvar, batch_shape=self._aug_batch_shape
)
else:
self._is_custom_likelihood = True
ExactGP.__init__(
self, train_inputs=train_X, train_targets=train_Y, likelihood=likelihood
)
if mean_module is None:
mean_module = ConstantMean(batch_shape=self._aug_batch_shape)
self.mean_module = mean_module
if covar_module is None:
covar_module = get_matern_kernel_with_gamma_prior(
ard_num_dims=transformed_X.shape[-1],
batch_shape=self._aug_batch_shape,
)
self._subset_batch_dict = {
"mean_module.raw_constant": -1,
"covar_module.raw_outputscale": -1,
"covar_module.base_kernel.raw_lengthscale": -3,
}
if train_Yvar is None:
self._subset_batch_dict["likelihood.noise_covar.raw_noise"] = -2
self.covar_module = covar_module
# TODO: Allow subsetting of other covar modules
if outcome_transform is not None:
self.outcome_transform = outcome_transform
if input_transform is not None:
self.input_transform = input_transform
self.to(train_X)
[docs] def forward(self, x: Tensor) -> MultivariateNormal:
if self.training:
x = self.transform_inputs(x)
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return MultivariateNormal(mean_x, covar_x)
[docs]class FixedNoiseGP(SingleTaskGP):
r"""A single-task exact GP model using fixed noise levels.
DEPRECATED: `FixedNoiseGP` has been merged into `SingleTaskGP`. Please use
`SingleTaskGP` with `train_Yvar` instead.
Will be removed in a future release (~v0.12).
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
train_Yvar: Tensor,
covar_module: Optional[Module] = None,
mean_module: Optional[Mean] = None,
outcome_transform: Optional[OutcomeTransform] = None,
input_transform: Optional[InputTransform] = None,
) -> None:
r"""DEPRECATED. See SingleTaskGP."""
warnings.warn(
"`FixedNoiseGP` has been merged into `SingleTaskGP`. "
"Please use `SingleTaskGP` with `train_Yvar` instead.",
DeprecationWarning,
)
super().__init__(
train_X=train_X,
train_Y=train_Y,
train_Yvar=train_Yvar,
covar_module=covar_module,
mean_module=mean_module,
outcome_transform=outcome_transform,
input_transform=input_transform,
)
[docs]class HeteroskedasticSingleTaskGP(BatchedMultiOutputGPyTorchModel, ExactGP):
r"""A single-task exact GP model using a heteroskedastic noise model.
This model differs from `SingleTaskGP` in that noise levels are provided
rather than inferred, and differs from `FixedNoiseGP` in that it can
predict noise levels out of sample, because it internally wraps another
GP (a SingleTaskGP) to model the observation noise.
Noise levels must be provided to `HeteroskedasticSingleTaskGP` as `train_Yvar`.
Examples of cases in which noise levels are known include online
experimentation and simulation optimization.
Example:
>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X).sum(dim=1, keepdim=True)
>>> se = torch.linalg.norm(train_X, dim=1, keepdim=True)
>>> train_Yvar = 0.1 + se * torch.rand_like(train_Y)
>>> model = HeteroskedasticSingleTaskGP(train_X, train_Y, train_Yvar)
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
train_Yvar: Tensor,
outcome_transform: Optional[OutcomeTransform] = None,
input_transform: Optional[InputTransform] = None,
) -> None:
r"""
Args:
train_X: A `batch_shape x n x d` tensor of training features.
train_Y: A `batch_shape x n x m` tensor of training observations.
train_Yvar: A `batch_shape x n x m` tensor of observed measurement
noise.
outcome_transform: An outcome transform that is applied to the
training data during instantiation and to the posterior during
inference (that is, the `Posterior` obtained by calling
`.posterior` on the model will be on the original scale).
Note that the noise model internally log-transforms the
variances, which will happen after this transform is applied.
input_transform: An input transfrom that is applied in the model's
forward pass.
"""
if outcome_transform is not None:
train_Y, train_Yvar = outcome_transform(train_Y, train_Yvar)
self._validate_tensor_args(X=train_X, Y=train_Y, Yvar=train_Yvar)
validate_input_scaling(train_X=train_X, train_Y=train_Y, train_Yvar=train_Yvar)
self._set_dimensions(train_X=train_X, train_Y=train_Y)
noise_likelihood = GaussianLikelihood(
noise_prior=SmoothedBoxPrior(-3, 5, 0.5, transform=torch.log),
batch_shape=self._aug_batch_shape,
noise_constraint=GreaterThan(
MIN_INFERRED_NOISE_LEVEL, transform=None, initial_value=1.0
),
)
noise_model = SingleTaskGP(
train_X=train_X,
train_Y=train_Yvar,
likelihood=noise_likelihood,
outcome_transform=Log(),
input_transform=input_transform,
)
likelihood = _GaussianLikelihoodBase(HeteroskedasticNoise(noise_model))
# This is hacky -- this class used to inherit from SingleTaskGP, but it
# shouldn't so this is a quick fix to enable getting rid of that
# inheritance
SingleTaskGP.__init__(
# pyre-fixme[6]: Incompatible parameter type
self,
train_X=train_X,
train_Y=train_Y,
likelihood=likelihood,
input_transform=input_transform,
)
self.register_added_loss_term("noise_added_loss")
self.update_added_loss_term(
"noise_added_loss", NoiseModelAddedLossTerm(noise_model)
)
if outcome_transform is not None:
self.outcome_transform = outcome_transform
self.to(train_X)
# pyre-fixme[15]: Inconsistent override
# pyre-fixme[15]: Inconsistent override
[docs] def forward(self, x: Tensor) -> MultivariateNormal:
if self.training:
x = self.transform_inputs(x)
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return MultivariateNormal(mean_x, covar_x)
```