#!/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"""
Abstract model class for all GPyTorch-based botorch models.
To implement your own, simply inherit from both the provided classes and a
GPyTorch Model class such as an ExactGP.
"""
from __future__ import annotations
import itertools
import warnings
from abc import ABC
from copy import deepcopy
from typing import Any, List, Optional, Tuple, TYPE_CHECKING, Union
import torch
from botorch.acquisition.objective import PosteriorTransform
from botorch.exceptions.errors import (
BotorchTensorDimensionError,
InputDataError,
UnsupportedError,
)
from botorch.exceptions.warnings import (
_get_single_precision_warning,
BotorchTensorDimensionWarning,
InputDataWarning,
)
from botorch.models.model import Model, ModelList
from botorch.models.utils import (
_make_X_full,
add_output_dim,
gpt_posterior_settings,
mod_batch_shape,
multioutput_to_batch_mode_transform,
)
from botorch.models.utils.assorted import fantasize as fantasize_flag
from botorch.posteriors.fully_bayesian import GaussianMixturePosterior
from botorch.posteriors.gpytorch import GPyTorchPosterior
from botorch.utils.multitask import separate_mtmvn
from botorch.utils.transforms import is_ensemble
from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood
from linear_operator.operators import BlockDiagLinearOperator, CatLinearOperator
from torch import Tensor
if TYPE_CHECKING:
from botorch.posteriors.posterior_list import PosteriorList # pragma: no cover
from botorch.posteriors.transformed import TransformedPosterior # pragma: no cover
from gpytorch.likelihoods import Likelihood # pragma: no cover
[docs]
class GPyTorchModel(Model, ABC):
r"""Abstract base class for models based on GPyTorch models.
The easiest way to use this is to subclass a model from a GPyTorch model
class (e.g. an `ExactGP`) and this `GPyTorchModel`. See e.g. `SingleTaskGP`.
"""
likelihood: Likelihood
@staticmethod
def _validate_tensor_args(
X: Tensor, Y: Tensor, Yvar: Optional[Tensor] = None, strict: bool = True
) -> None:
r"""Checks that `Y` and `Yvar` have an explicit output dimension if strict.
Checks that the dtypes of the inputs match, and warns if using float.
This also checks that `Yvar` has the same trailing dimensions as `Y`. Note
we only infer that an explicit output dimension exists when `X` and `Y` have
the same `batch_shape`.
Args:
X: A `batch_shape x n x d`-dim Tensor, where `d` is the dimension of
the feature space, `n` is the number of points per batch, and
`batch_shape` is the batch shape (potentially empty).
Y: A `batch_shape' x n x m`-dim Tensor, where `m` is the number of
model outputs, `n'` is the number of points per batch, and
`batch_shape'` is the batch shape of the observations.
Yvar: A `batch_shape' x n x m` tensor of observed measurement noise.
Note: this will be None when using a model that infers the noise
level (e.g. a `SingleTaskGP`).
strict: A boolean indicating whether to check that `Y` and `Yvar`
have an explicit output dimension.
"""
if X.dim() != Y.dim():
if (X.dim() - Y.dim() == 1) and (X.shape[:-1] == Y.shape):
message = (
"An explicit output dimension is required for targets."
f" Expected Y with dimension {X.dim()} (got {Y.dim()=})."
)
else:
message = (
"Expected X and Y to have the same number of dimensions"
f" (got X with dimension {X.dim()} and Y with dimension"
f" {Y.dim()})."
)
if strict:
raise BotorchTensorDimensionError(message)
else:
warnings.warn(
"Non-strict enforcement of botorch tensor conventions. The "
"following error would have been raised with strict enforcement: "
f"{message}",
BotorchTensorDimensionWarning,
stacklevel=2,
)
# Yvar may not have the same batch dimensions, but the trailing dimensions
# of Yvar should be the same as the trailing dimensions of Y.
if Yvar is not None and Y.shape[-(Yvar.dim()) :] != Yvar.shape:
raise BotorchTensorDimensionError(
"An explicit output dimension is required for observation noise."
f" Expected Yvar with shape: {Y.shape[-Yvar.dim() :]} (got"
f" {Yvar.shape})."
)
# Check the dtypes.
if X.dtype != Y.dtype or (Yvar is not None and Y.dtype != Yvar.dtype):
raise InputDataError(
"Expected all inputs to share the same dtype. Got "
f"{X.dtype} for X, {Y.dtype} for Y, and "
f"{Yvar.dtype if Yvar is not None else None} for Yvar."
)
if X.dtype != torch.float64:
warnings.warn(
_get_single_precision_warning(str(X.dtype)),
InputDataWarning,
stacklevel=3, # Warn at model constructor call.
)
@property
def batch_shape(self) -> torch.Size:
r"""The batch shape of the model.
This is a batch shape from an I/O perspective, independent of the internal
representation of the model (as e.g. in BatchedMultiOutputGPyTorchModel).
For a model with `m` outputs, a `test_batch_shape x q x d`-shaped input `X`
to the `posterior` method returns a Posterior object over an output of
shape `broadcast(test_batch_shape, model.batch_shape) x q x m`.
"""
return self.train_inputs[0].shape[:-2]
@property
def num_outputs(self) -> int:
r"""The number of outputs of the model."""
return self._num_outputs
# pyre-fixme[14]: Inconsistent override.
# `botorch.models.gpytorch.GPyTorchModel.posterior` overrides method defined
# in `Model` inconsistently. Could not find parameter `output_indices` in
# overriding signature.
[docs]
def posterior(
self,
X: Tensor,
observation_noise: Union[bool, Tensor] = False,
posterior_transform: Optional[PosteriorTransform] = None,
**kwargs: Any,
) -> Union[GPyTorchPosterior, TransformedPosterior]:
r"""Computes the posterior over model outputs at the provided points.
Args:
X: A `(batch_shape) x q x d`-dim Tensor, where `d` is the dimension
of the feature space and `q` is the number of points considered
jointly.
observation_noise: If True, add the observation noise from the
likelihood to the posterior. If a Tensor, use it directly as the
observation noise (must be of shape `(batch_shape) x q`). It is
assumed to be in the outcome-transformed space if an outcome
transform is used.
posterior_transform: An optional PosteriorTransform.
Returns:
A `GPyTorchPosterior` object, representing a batch of `b` joint
distributions over `q` points. Includes observation noise if
specified.
"""
self.eval() # make sure model is in eval mode
# input transforms are applied at `posterior` in `eval` mode, and at
# `model.forward()` at the training time
X = self.transform_inputs(X)
with gpt_posterior_settings():
# NOTE: BoTorch's GPyTorchModels also inherit from GPyTorch's ExactGP, thus
# self(X) calls GPyTorch's ExactGP's __call__, which computes the posterior,
# rather than e.g. SingleTaskGP's forward, which computes the prior.
mvn = self(X)
if observation_noise is not False:
if isinstance(observation_noise, torch.Tensor):
# TODO: Make sure observation noise is transformed correctly
self._validate_tensor_args(X=X, Y=observation_noise)
if observation_noise.size(-1) == 1:
observation_noise = observation_noise.squeeze(-1)
mvn = self.likelihood(mvn, X, noise=observation_noise)
else:
mvn = self.likelihood(mvn, X)
posterior = GPyTorchPosterior(distribution=mvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(posterior)
if posterior_transform is not None:
return posterior_transform(posterior)
return posterior
[docs]
def condition_on_observations(
self, X: Tensor, Y: Tensor, noise: Optional[Tensor] = None, **kwargs: Any
) -> Model:
r"""Condition the model on new observations.
Args:
X: A `batch_shape x n' x d`-dim Tensor, where `d` is the dimension of
the feature space, `n'` is the number of points per batch, and
`batch_shape` is the batch shape (must be compatible with the
batch shape of the model).
Y: A `batch_shape' x n x m`-dim Tensor, where `m` is the number of
model outputs, `n'` is the number of points per batch, and
`batch_shape'` is the batch shape of the observations.
`batch_shape'` must be broadcastable to `batch_shape` using
standard broadcasting semantics. If `Y` has fewer batch dimensions
than `X`, its is assumed that the missing batch dimensions are
the same for all `Y`.
noise: If not `None`, a tensor of the same shape as `Y` representing
the associated noise variance.
kwargs: Passed to `self.get_fantasy_model`.
Returns:
A `Model` object of the same type, representing the original model
conditioned on the new observations `(X, Y)` (and possibly noise
observations passed in via kwargs).
Example:
>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.sin(train_X[:, 0]) + torch.cos(train_X[:, 1])
>>> model = SingleTaskGP(train_X, train_Y)
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.sin(new_X[:, 0]) + torch.cos(new_X[:, 1])
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)
"""
Yvar = noise
if hasattr(self, "outcome_transform"):
# pass the transformed data to get_fantasy_model below
# (unless we've already trasnformed if BatchedMultiOutputGPyTorchModel)
if not isinstance(self, BatchedMultiOutputGPyTorchModel):
# `noise` is assumed to already be outcome-transformed.
Y, _ = self.outcome_transform(Y=Y, Yvar=Yvar)
# Validate using strict=False, since we cannot tell if Y has an explicit
# output dimension. Do not check shapes when fantasizing as they are
# not expected to match.
if fantasize_flag.off():
self._validate_tensor_args(X=X, Y=Y, Yvar=Yvar, strict=False)
if Y.size(-1) == 1:
Y = Y.squeeze(-1)
if Yvar is not None:
kwargs.update({"noise": Yvar.squeeze(-1)})
# get_fantasy_model will properly copy any existing outcome transforms
# (since it deepcopies the original model)
return self.get_fantasy_model(inputs=X, targets=Y, **kwargs)
# pyre-fixme[13]: uninitialized attributes _num_outputs, _input_batch_shape,
# _aug_batch_shape
[docs]
class BatchedMultiOutputGPyTorchModel(GPyTorchModel):
r"""Base class for batched multi-output GPyTorch models with independent outputs.
This model should be used when the same training data is used for all outputs.
Outputs are modeled independently by using a different batch for each output.
"""
_num_outputs: int
_input_batch_shape: torch.Size
_aug_batch_shape: torch.Size
[docs]
@staticmethod
def get_batch_dimensions(
train_X: Tensor, train_Y: Tensor
) -> Tuple[torch.Size, torch.Size]:
r"""Get the raw batch shape and output-augmented batch shape of the inputs.
Args:
train_X: A `n x d` or `batch_shape x n x d` (batch mode) tensor of training
features.
train_Y: A `n x m` or `batch_shape x n x m` (batch mode) tensor of
training observations.
Returns:
2-element tuple containing
- The `input_batch_shape`
- The output-augmented batch shape: `input_batch_shape x (m)`
"""
input_batch_shape = train_X.shape[:-2]
aug_batch_shape = input_batch_shape
num_outputs = train_Y.shape[-1]
if num_outputs > 1:
aug_batch_shape += torch.Size([num_outputs])
return input_batch_shape, aug_batch_shape
def _set_dimensions(self, train_X: Tensor, train_Y: Tensor) -> None:
r"""Store the number of outputs and the batch shape.
Args:
train_X: A `n x d` or `batch_shape x n x d` (batch mode) tensor of training
features.
train_Y: A `n x m` or `batch_shape x n x m` (batch mode) tensor of
training observations.
"""
self._num_outputs = train_Y.shape[-1]
self._input_batch_shape, self._aug_batch_shape = self.get_batch_dimensions(
train_X=train_X, train_Y=train_Y
)
@property
def batch_shape(self) -> torch.Size:
r"""The batch shape of the model.
This is a batch shape from an I/O perspective, independent of the internal
representation of the model (as e.g. in BatchedMultiOutputGPyTorchModel).
For a model with `m` outputs, a `test_batch_shape x q x d`-shaped input `X`
to the `posterior` method returns a Posterior object over an output of
shape `broadcast(test_batch_shape, model.batch_shape) x q x m`.
"""
return self._input_batch_shape
def _transform_tensor_args(
self, X: Tensor, Y: Tensor, Yvar: Optional[Tensor] = None
) -> Tuple[Tensor, Tensor, Optional[Tensor]]:
r"""Transforms tensor arguments: for single output models, the output
dimension is squeezed and for multi-output models, the output dimension is
transformed into the left-most batch dimension.
Args:
X: A `n x d` or `batch_shape x n x d` (batch mode) tensor of training
features.
Y: A `n x m` or `batch_shape x n x m` (batch mode) tensor of
training observations.
Yvar: A `n x m` or `batch_shape x n x m` (batch mode) tensor of
observed measurement noise. Note: this will be None when using a model
that infers the noise level (e.g. a `SingleTaskGP`).
Returns:
3-element tuple containing
- A `input_batch_shape x (m) x n x d` tensor of training features.
- A `target_batch_shape x (m) x n` tensor of training observations.
- A `target_batch_shape x (m) x n` tensor observed measurement noise
(or None).
"""
if self._num_outputs > 1:
return multioutput_to_batch_mode_transform(
train_X=X, train_Y=Y, train_Yvar=Yvar, num_outputs=self._num_outputs
)
return X, Y.squeeze(-1), None if Yvar is None else Yvar.squeeze(-1)
def _apply_noise(
self,
X: Tensor,
mvn: MultivariateNormal,
observation_noise: Union[bool, Tensor] = False,
) -> MultivariateNormal:
"""Adds the observation noise to the posterior.
Args:
X: A tensor of shape `batch_shape x q x d`.
mvn: A `MultivariateNormal` object representing the posterior over the true
latent function.
num_outputs: The number of outputs of the model.
observation_noise: If True, add the observation noise from the
likelihood to the posterior. If a Tensor, use it directly as the
observation noise (must be of shape `(batch_shape) x q x m`).
Returns:
The posterior predictive.
"""
if observation_noise is False:
return mvn
# noise_shape is `broadcast(test_batch_shape, model.batch_shape) x m x q`
noise_shape = mvn.batch_shape + mvn.event_shape
if torch.is_tensor(observation_noise):
# TODO: Validate noise shape
# make observation_noise's shape match noise_shape
if self.num_outputs > 1:
obs_noise = observation_noise.transpose(-1, -2)
else:
obs_noise = observation_noise.squeeze(-1)
mvn = self.likelihood(
mvn,
X,
noise=obs_noise.expand(noise_shape),
)
elif isinstance(self.likelihood, FixedNoiseGaussianLikelihood):
# Use the mean of the previous noise values (TODO: be smarter here).
observation_noise = self.likelihood.noise.mean(dim=-1, keepdim=True)
mvn = self.likelihood(
mvn,
X,
noise=observation_noise.expand(noise_shape),
)
else:
mvn = self.likelihood(mvn, X)
return mvn
[docs]
def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
posterior_transform: Optional[PosteriorTransform] = None,
) -> Union[GPyTorchPosterior, TransformedPosterior]:
r"""Computes the posterior over model outputs at the provided points.
Args:
X: A `(batch_shape) x q x d`-dim Tensor, where `d` is the dimension
of the feature space and `q` is the number of points considered
jointly.
output_indices: A list of indices, corresponding to the outputs over
which to compute the posterior (if the model is multi-output).
Can be used to speed up computation if only a subset of the
model's outputs are required for optimization. If omitted,
computes the posterior over all model outputs.
observation_noise: If True, add the observation noise from the
likelihood to the posterior. If a Tensor, use it directly as the
observation noise (must be of shape `(batch_shape) x q x m`).
posterior_transform: An optional PosteriorTransform.
Returns:
A `GPyTorchPosterior` object, representing `batch_shape` joint
distributions over `q` points and the outputs selected by
`output_indices` each. Includes observation noise if specified.
"""
self.eval() # make sure model is in eval mode
# input transforms are applied at `posterior` in `eval` mode, and at
# `model.forward()` at the training time
X = self.transform_inputs(X)
with gpt_posterior_settings():
# insert a dimension for the output dimension
if self._num_outputs > 1:
X, output_dim_idx = add_output_dim(
X=X, original_batch_shape=self._input_batch_shape
)
# NOTE: BoTorch's GPyTorchModels also inherit from GPyTorch's ExactGP, thus
# self(X) calls GPyTorch's ExactGP's __call__, which computes the posterior,
# rather than e.g. SingleTaskGP's forward, which computes the prior.
mvn = self(X)
mvn = self._apply_noise(X=X, mvn=mvn, observation_noise=observation_noise)
if self._num_outputs > 1:
mean_x = mvn.mean
covar_x = mvn.lazy_covariance_matrix
output_indices = output_indices or range(self._num_outputs)
mvns = [
MultivariateNormal(
mean_x.select(dim=output_dim_idx, index=t),
covar_x[(slice(None),) * output_dim_idx + (t,)],
)
for t in output_indices
]
mvn = MultitaskMultivariateNormal.from_independent_mvns(mvns=mvns)
posterior = GPyTorchPosterior(distribution=mvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(posterior)
if posterior_transform is not None:
return posterior_transform(posterior)
return posterior
[docs]
def condition_on_observations(
self, X: Tensor, Y: Tensor, **kwargs: Any
) -> BatchedMultiOutputGPyTorchModel:
r"""Condition the model on new observations.
Args:
X: A `batch_shape x n' x d`-dim Tensor, where `d` is the dimension of
the feature space, `m` is the number of points per batch, and
`batch_shape` is the batch shape (must be compatible with the
batch shape of the model).
Y: A `batch_shape' x n' x m`-dim Tensor, where `m` is the number of
model outputs, `n'` is the number of points per batch, and
`batch_shape'` is the batch shape of the observations.
`batch_shape'` must be broadcastable to `batch_shape` using
standard broadcasting semantics. If `Y` has fewer batch dimensions
than `X`, its is assumed that the missing batch dimensions are
the same for all `Y`.
Returns:
A `BatchedMultiOutputGPyTorchModel` object of the same type with
`n + n'` training examples, representing the original model
conditioned on the new observations `(X, Y)` (and possibly noise
observations passed in via kwargs).
Example:
>>> train_X = torch.rand(20, 2)
>>> train_Y = torch.cat(
>>> [torch.sin(train_X[:, 0]), torch.cos(train_X[:, 1])], -1
>>> )
>>> model = SingleTaskGP(train_X, train_Y)
>>> new_X = torch.rand(5, 2)
>>> new_Y = torch.cat([torch.sin(new_X[:, 0]), torch.cos(new_X[:, 1])], -1)
>>> model = model.condition_on_observations(X=new_X, Y=new_Y)
"""
noise = kwargs.get("noise")
if hasattr(self, "outcome_transform"):
# We need to apply transforms before shifting batch indices around.
# `noise` is assumed to already be outcome-transformed.
Y, _ = self.outcome_transform(Y)
# Do not check shapes when fantasizing as they are not expected to match.
if fantasize_flag.off():
self._validate_tensor_args(X=X, Y=Y, Yvar=noise, strict=False)
inputs = X
if self._num_outputs > 1:
inputs, targets, noise = multioutput_to_batch_mode_transform(
train_X=X, train_Y=Y, num_outputs=self._num_outputs, train_Yvar=noise
)
# `multioutput_to_batch_mode_transform` removes the output dimension,
# which is necessary for `condition_on_observations`
targets = targets.unsqueeze(-1)
if noise is not None:
noise = noise.unsqueeze(-1)
else:
inputs = X
targets = Y
if noise is not None:
kwargs.update({"noise": noise})
fantasy_model = super().condition_on_observations(X=inputs, Y=targets, **kwargs)
fantasy_model._input_batch_shape = fantasy_model.train_targets.shape[
: (-1 if self._num_outputs == 1 else -2)
]
if not self._is_fully_bayesian:
fantasy_model._aug_batch_shape = fantasy_model.train_targets.shape[:-1]
return fantasy_model
[docs]
def subset_output(self, idcs: List[int]) -> BatchedMultiOutputGPyTorchModel:
r"""Subset the model along the output dimension.
Args:
idcs: The output indices to subset the model to.
Returns:
The current model, subset to the specified output indices.
"""
try:
subset_batch_dict = self._subset_batch_dict
except AttributeError:
raise NotImplementedError(
"subset_output requires the model to define a `_subset_dict` attribute"
)
m = len(idcs)
new_model = deepcopy(self)
subset_everything = self.num_outputs == m and idcs == list(range(m))
if subset_everything:
return new_model
tidxr = torch.tensor(idcs, device=new_model.train_targets.device)
idxr = tidxr if m > 1 else idcs[0]
new_tail_bs = torch.Size([m]) if m > 1 else torch.Size()
new_model._num_outputs = m
new_model._aug_batch_shape = new_model._aug_batch_shape[:-1] + new_tail_bs
new_model.train_inputs = tuple(
ti[..., idxr, :, :] for ti in new_model.train_inputs
)
new_model.train_targets = new_model.train_targets[..., idxr, :]
# adjust batch shapes of parameters/buffers if necessary
for full_name, p in itertools.chain(
new_model.named_parameters(), new_model.named_buffers()
):
if full_name in subset_batch_dict:
idx = subset_batch_dict[full_name]
new_data = p.index_select(dim=idx, index=tidxr)
if m == 1:
new_data = new_data.squeeze(idx)
p.data = new_data
mod_name = full_name.split(".")[:-1]
mod_batch_shape(new_model, mod_name, m if m > 1 else 0)
# subset outcome transform if present
try:
subset_octf = new_model.outcome_transform.subset_output(idcs=idcs)
new_model.outcome_transform = subset_octf
except AttributeError:
pass
# Subset fixed noise likelihood if present.
if isinstance(self.likelihood, FixedNoiseGaussianLikelihood):
full_noise = new_model.likelihood.noise_covar.noise
new_noise = full_noise[..., idcs if len(idcs) > 1 else idcs[0], :]
new_model.likelihood.noise_covar.noise = new_noise
return new_model
[docs]
class ModelListGPyTorchModel(ModelList, GPyTorchModel, ABC):
r"""Abstract base class for models based on multi-output GPyTorch models.
This is meant to be used with a gpytorch ModelList wrapper for independent
evaluation of submodels. Those submodels can themselves be multi-output
models, in which case the task covariances will be ignored.
"""
@property
def batch_shape(self) -> torch.Size:
r"""The batch shape of the model.
This is a batch shape from an I/O perspective, independent of the internal
representation of the model (as e.g. in BatchedMultiOutputGPyTorchModel).
For a model with `m` outputs, a `test_batch_shape x q x d`-shaped input `X`
to the `posterior` method returns a Posterior object over an output of
shape `broadcast(test_batch_shape, model.batch_shape) x q x m`.
"""
batch_shapes = {m.batch_shape for m in self.models}
if len(batch_shapes) > 1:
msg = (
f"Component models of {self.__class__.__name__} have different "
"batch shapes"
)
try:
broadcast_shape = torch.broadcast_shapes(*batch_shapes)
warnings.warn(msg + ". Broadcasting batch shapes.", stacklevel=2)
return broadcast_shape
except RuntimeError:
raise NotImplementedError(msg + " that are not broadcastble.")
return next(iter(batch_shapes))
# pyre-fixme[15]: Inconsistent override in return types
[docs]
def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
posterior_transform: Optional[PosteriorTransform] = None,
) -> Union[GPyTorchPosterior, PosteriorList]:
r"""Computes the posterior over model outputs at the provided points.
If any model returns a MultitaskMultivariateNormal posterior, then that
will be split into individual MVNs per task, with inter-task covariance
ignored.
Args:
X: A `b x q x d`-dim Tensor, where `d` is the dimension of the
feature space, `q` is the number of points considered jointly,
and `b` is the batch dimension.
output_indices: A list of indices, corresponding to the outputs over
which to compute the posterior (if the model is multi-output).
Can be used to speed up computation if only a subset of the
model's outputs are required for optimization. If omitted,
computes the posterior over all model outputs.
observation_noise: If True, add the observation noise from the
respective likelihoods to the posterior. If a Tensor of shape
`(batch_shape) x q x m`, use it directly as the observation
noise (with `observation_noise[...,i]` added to the posterior
of the `i`-th model).
posterior_transform: An optional PosteriorTransform.
Returns:
- If no `posterior_transform` is provided and the component models have no
`outcome_transform`, or if the component models only use linear outcome
transforms like `Standardize` (i.e. not `Log`), returns a
`GPyTorchPosterior` or `GaussianMixturePosterior` object,
representing `batch_shape` joint distributions over `q` points
and the outputs selected by `output_indices` each. Includes
measurement noise if `observation_noise` is specified.
- If no `posterior_transform` is provided and component models have
nonlinear transforms like `Log`, returns a `PosteriorList` with
sub-posteriors of type `TransformedPosterior`
- If `posterior_transform` is provided, that posterior transform will be
applied and will determine the return type. This could potentially be
any subclass of `Posterior`, but common choices give a
`GPyTorchPosterior`.
"""
# Nonlinear transforms untransform to a `TransformedPosterior`,
# which can't be made into a `GPyTorchPosterior`
returns_untransformed = any(
hasattr(mod, "outcome_transform") and (not mod.outcome_transform._is_linear)
for mod in self.models
)
# NOTE: We're not passing in the posterior transform here. We'll apply it later.
posterior = ModelList.posterior(
self,
X=X,
output_indices=output_indices,
observation_noise=observation_noise,
)
if not returns_untransformed:
mvns = [p.distribution for p in posterior.posteriors]
if any(isinstance(m, MultitaskMultivariateNormal) for m in mvns):
mvn_list = []
for mvn in mvns:
if len(mvn.event_shape) == 2:
# We separate MTMVNs into independent-across-task MVNs for
# the convenience of using BlockDiagLinearOperator below.
# (b x q x m x m) -> list of m (b x q x 1 x 1)
mvn_list.extend(separate_mtmvn(mvn))
else:
mvn_list.append(mvn)
mean = torch.stack([mvn.mean for mvn in mvn_list], dim=-1)
covars = CatLinearOperator(
*[mvn.lazy_covariance_matrix.unsqueeze(-3) for mvn in mvn_list],
dim=-3,
) # List of m (b x q x 1 x 1) -> (b x q x m x 1 x 1)
mvn = MultitaskMultivariateNormal(
mean=mean,
covariance_matrix=BlockDiagLinearOperator(covars, block_dim=-3).to(
X
), # (b x q x m x 1 x 1) -> (b x q x m x m)
interleaved=False,
)
else:
mvn = (
mvns[0]
if len(mvns) == 1
else MultitaskMultivariateNormal.from_independent_mvns(mvns=mvns)
)
# Return the result as a GPyTorchPosterior/GaussianMixturePosterior.
if any(is_ensemble(m) for m in self.models):
# Mixing fully Bayesian and other GP models is currently
# not supported.
posterior = GaussianMixturePosterior(distribution=mvn)
else:
posterior = GPyTorchPosterior(distribution=mvn)
if posterior_transform is not None:
return posterior_transform(posterior)
return posterior
[docs]
def condition_on_observations(self, X: Tensor, Y: Tensor, **kwargs: Any) -> Model:
raise NotImplementedError()
[docs]
class MultiTaskGPyTorchModel(GPyTorchModel, ABC):
r"""Abstract base class for multi-task models based on GPyTorch models.
This class provides the `posterior` method to models that implement a
"long-format" multi-task GP in the style of `MultiTaskGP`.
"""
def _map_tasks(self, task_values: Tensor) -> Tensor:
"""Map raw task values to the task indices used by the model.
Args:
task_values: A tensor of task values.
Returns:
A tensor of task indices with the same shape as the input
tensor.
"""
if self._task_mapper is None:
if not (
torch.all(0 <= task_values) and torch.all(task_values < self.num_tasks)
):
raise ValueError(
"Expected all task features in `X` to be between 0 and "
f"self.num_tasks - 1. Got {task_values}."
)
else:
task_values = task_values.long()
unexpected_task_values = set(task_values.unique().tolist()).difference(
self._expected_task_values
)
if len(unexpected_task_values) > 0:
raise ValueError(
"Received invalid raw task values. Expected raw value to be in"
f" {self._expected_task_values}, but got unexpected task values:"
f" {unexpected_task_values}."
)
task_values = self._task_mapper[task_values]
return task_values
def _apply_noise(
self,
X: Tensor,
mvn: MultivariateNormal,
num_outputs: int,
observation_noise: Union[bool, Tensor],
) -> MultivariateNormal:
"""Adds the observation noise to the posterior.
If the likelihood is a `FixedNoiseGaussianLikelihood`, then
the average noise per task is computed, and a diagonal noise
matrix is added to the posterior covariance matrix, where
the noise per input is the average noise for its respective
task. If the likelihood is a Gaussian likelihood, then
currently there is a shared inferred noise level for all
tasks.
TODO: implement support for task-specific inferred noise levels.
Args:
X: A tensor of shape `batch_shape x q x d + 1`,
where `d` is the dimension of the feature space and the `+ 1`
dimension is the task feature / index.
mvn: A `MultivariateNormal` object representing the posterior over the true
latent function.
num_outputs: The number of outputs of the model.
observation_noise: If True, add observation noise from the respective
likelihood. Tensor input is currently not supported.
Returns:
The posterior predictive.
"""
if torch.is_tensor(observation_noise):
raise NotImplementedError(
"Passing a tensor of observations is not supported by MultiTaskGP."
)
elif observation_noise is False:
return mvn
elif isinstance(self.likelihood, FixedNoiseGaussianLikelihood):
# get task features for test points
test_task_features = X[..., self._task_feature]
test_task_features = self._map_tasks(test_task_features).long()
unique_test_task_features = test_task_features.unique()
# get task features for training points
train_task_features = self.train_inputs[0][..., self._task_feature]
train_task_features = self._map_tasks(train_task_features).long()
noise_by_task = torch.zeros(self.num_tasks, dtype=X.dtype, device=X.device)
for task_feature in unique_test_task_features:
mask = train_task_features == task_feature
noise_by_task[task_feature] = self.likelihood.noise[mask].mean(
dim=-1, keepdim=True
)
# noise_shape is `broadcast(test_batch_shape, model.batch_shape) x q`
noise_shape = X.shape[:-1]
observation_noise = noise_by_task[test_task_features].expand(noise_shape)
return self.likelihood(
mvn,
X,
noise=observation_noise,
)
return self.likelihood(mvn, X)
[docs]
def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
posterior_transform: Optional[PosteriorTransform] = None,
) -> Union[GPyTorchPosterior, TransformedPosterior]:
r"""Computes the posterior over model outputs at the provided points.
Args:
X: A tensor of shape `batch_shape x q x d` or `batch_shape x q x (d + 1)`,
where `d` is the dimension of the feature space (not including task
indices) and `q` is the number of points considered jointly. The `+ 1`
dimension is the optional task feature / index. If given, the model
produces the outputs for the given task indices. If omitted, the
model produces outputs for tasks in in `self._output_tasks` (specified
as `output_tasks` while constructing the model), which can overwritten
using `output_indices`.
output_indices: A list of task values over which to compute the posterior.
Only used if `X` does not include the task feature. If omitted,
defaults to `self._output_tasks`.
observation_noise: If True, add observation noise from the respective
likelihoods. If a Tensor, specifies the observation noise levels
to add.
posterior_transform: An optional PosteriorTransform.
Returns:
A `GPyTorchPosterior` object, representing `batch_shape` joint
distributions over `q` points. If the task features are included in `X`,
the posterior will be single output. Otherwise, the posterior will be
single or multi output corresponding to the tasks included in
either the `output_indices` or `self._output_tasks`.
"""
includes_task_feature = X.shape[-1] == self.num_non_task_features + 1
if includes_task_feature:
if output_indices is not None:
raise ValueError(
"`output_indices` must be None when `X` includes task features."
)
task_features = X[..., self._task_feature].unique()
num_outputs = 1
X_full = X
else:
# Add the task features to construct the full X for evaluation.
task_features = torch.tensor(
self._output_tasks if output_indices is None else output_indices,
dtype=torch.long,
device=X.device,
)
num_outputs = len(task_features)
X_full = _make_X_full(
X=X, output_indices=task_features.tolist(), tf=self._task_feature
)
# Make sure all task feature values are valid.
task_features = self._map_tasks(task_values=task_features)
self.eval() # make sure model is in eval mode
# input transforms are applied at `posterior` in `eval` mode, and at
# `model.forward()` at the training time
X_full = self.transform_inputs(X_full)
with gpt_posterior_settings():
mvn = self(X_full)
mvn = self._apply_noise(
X=X_full,
mvn=mvn,
num_outputs=num_outputs,
observation_noise=observation_noise,
)
# If single-output, return the posterior of a single-output model
if num_outputs == 1:
posterior = GPyTorchPosterior(distribution=mvn)
else:
# Otherwise, make a MultitaskMultivariateNormal out of this
mtmvn = MultitaskMultivariateNormal(
mean=mvn.mean.view(*mvn.mean.shape[:-1], num_outputs, -1).transpose(
-1, -2
),
covariance_matrix=mvn.lazy_covariance_matrix,
interleaved=False,
)
posterior = GPyTorchPosterior(distribution=mtmvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(posterior)
if posterior_transform is not None:
return posterior_transform(posterior)
return posterior
[docs]
def subset_output(self, idcs: List[int]) -> MultiTaskGPyTorchModel:
r"""Returns a new model that only outputs a subset of the outputs.
Args:
idcs: A list of output indices, corresponding to the outputs to keep.
Returns:
A new model that only outputs the requested outputs.
"""
raise UnsupportedError(
"Subsetting outputs is not supported by `MultiTaskGPyTorchModel`."
)
