# Source code for botorch.models.gpytorch

```
#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its 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, Iterator, List, Optional, Tuple, Union
import torch
from botorch.exceptions.errors import BotorchTensorDimensionError
from botorch.exceptions.warnings import BotorchTensorDimensionWarning
from botorch.models.model import Model
from botorch.models.utils import (
_make_X_full,
add_output_dim,
gpt_posterior_settings,
mod_batch_shape,
multioutput_to_batch_mode_transform,
)
from botorch.posteriors.gpytorch import GPyTorchPosterior
from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
from gpytorch.lazy import lazify
from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood
from torch import Tensor
[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`.
"""
@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.
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 strict:
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: {Y.dim()} (got {X.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()}."
)
raise BotorchTensorDimensionError(message)
else:
warnings.warn(
"Non-strict enforcement of botorch tensor conventions. Ensure that "
f"target tensors Y{' and Yvar have' if Yvar is not None else ' has an'}"
f" explicit output dimension{'s' if Yvar is not None else ''}.",
BotorchTensorDimensionWarning,
)
# 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})."
)
@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
[docs] def posterior(
self, X: Tensor, observation_noise: Union[bool, Tensor] = False, **kwargs: Any
) -> GPyTorchPosterior:
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`).
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():
mvn = self(X)
if observation_noise is not False:
if torch.is_tensor(observation_noise):
# 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(mvn=mvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(posterior)
return posterior
[docs] def condition_on_observations(self, X: Tensor, Y: Tensor, **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`.
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 = kwargs.get("noise", None)
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):
Y, Yvar = self.outcome_transform(Y, Yvar)
# validate using strict=False, since we cannot tell if Y has an explicit
# output dimension
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)
[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)
[docs] def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
**kwargs: Any,
) -> GPyTorchPosterior:
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`).
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
)
mvn = self(X)
if observation_noise is not False:
if torch.is_tensor(observation_noise):
# TODO: Validate noise shape
# make observation_noise `batch_shape x q x n`
obs_noise = observation_noise.transpose(-1, -2)
mvn = self.likelihood(mvn, X, noise=obs_noise)
elif isinstance(self.likelihood, FixedNoiseGaussianLikelihood):
# Use the mean of the previous noise values (TODO: be smarter here).
noise = self.likelihood.noise.mean().expand(X.shape[:-1])
mvn = self.likelihood(mvn, X, noise=noise)
else:
mvn = self.likelihood(mvn, X)
if self._num_outputs > 1:
mean_x = mvn.mean
covar_x = mvn.covariance_matrix
output_indices = output_indices or range(self._num_outputs)
mvns = [
MultivariateNormal(
mean_x.select(dim=output_dim_idx, index=t),
lazify(covar_x.select(dim=output_dim_idx, index=t)),
)
for t in output_indices
]
mvn = MultitaskMultivariateNormal.from_independent_mvns(mvns=mvns)
posterior = GPyTorchPosterior(mvn=mvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(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
Y, noise = self.outcome_transform(Y, noise)
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)
]
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)
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
return new_model
[docs]class ModelListGPyTorchModel(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.
"""
@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`.
"""
# TODO: Either check that batch shapes match across models, or broadcast them
batch_shape = self.models[0].batch_shape
if all(batch_shape == m.batch_shape for m in self.models[1:]):
return batch_shape
raise NotImplementedError(
"ModelListGPyTorchModel.batch_shape is only supported if all "
"constituent models have the same batch_shape."
)
[docs] def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
**kwargs: Any,
) -> GPyTorchPosterior:
r"""Computes the posterior over model outputs at the provided points.
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).
Returns:
A `GPyTorchPosterior` 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.
"""
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
transformed_X = self.transform_inputs(X)
mvn_gen: Iterator
with gpt_posterior_settings():
# only compute what's necessary
if output_indices is not None:
mvns = [self.forward_i(i, transformed_X[i]) for i in output_indices]
if observation_noise is not False:
if torch.is_tensor(observation_noise):
lh_kwargs = [
{"noise": observation_noise[..., i]}
for i, lh in enumerate(self.likelihood.likelihoods)
]
else:
lh_kwargs = [
{"noise": lh.noise.mean().expand(t_X.shape[:-1])}
if isinstance(lh, FixedNoiseGaussianLikelihood)
else {}
for t_X, lh in zip(
transformed_X, self.likelihood.likelihoods
)
]
mvns = [
self.likelihood_i(i, mvn, transformed_X[i], **lkws)
for i, mvn, lkws in zip(output_indices, mvns, lh_kwargs)
]
mvn_gen = zip(output_indices, mvns)
else:
mvns = self(*transformed_X)
if observation_noise is not False:
mvnX = [(mvn, transformed_X[i]) for i, mvn in enumerate(mvns)]
if torch.is_tensor(observation_noise):
mvns = self.likelihood(*mvnX, noise=observation_noise)
else:
mvns = self.likelihood(*mvnX)
mvn_gen = enumerate(mvns)
# apply output transforms of individual models if present
mvns = []
for i, mvn in mvn_gen:
try:
oct = self.models[i].outcome_transform
tf_mvn = oct.untransform_posterior(GPyTorchPosterior(mvn)).mvn
except AttributeError:
tf_mvn = mvn
mvns.append(tf_mvn)
# return result as a GPyTorchPosteriors
if len(mvns) == 1:
return GPyTorchPosterior(mvn=mvns[0])
return GPyTorchPosterior(
mvn=MultitaskMultivariateNormal.from_independent_mvns(mvns=mvns)
)
[docs] def condition_on_observations(
self, X: Tensor, Y: Tensor, **kwargs: Any
) -> ModelListGPyTorchModel:
class_name = self.__class__.__name__
raise NotImplementedError(
f"`condition_on_observations` not implemented in {class_name}"
)
[docs] def transform_inputs(self, X: Tensor) -> List[Tensor]:
r"""Individually transform the inputs for each model.
Args:
X: A tensor of inputs
Returns:
A list of tensors of transformed inputs
"""
transformed_X_list = []
for model in self.models:
try:
transformed_X_list.append(model.input_transform(X))
except AttributeError:
transformed_X_list.append(X)
return transformed_X_list
[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`.
"""
[docs] def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: Union[bool, Tensor] = False,
**kwargs: Any,
) -> GPyTorchPosterior:
r"""Computes the posterior over model outputs at the provided points.
Args:
X: A `q x d` or `batch_shape x q x d` (batch mode) tensor, where `d` is the
dimension of the feature space (not including task indices) 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 observation noise from the respective
likelihoods. If a Tensor, specifies the observation noise levels
to add.
Returns:
A `GPyTorchPosterior` object, representing `batch_shape` joint
distributions over `q` points and the outputs selected by
`output_indices`. Includes measurement noise if
`observation_noise` is specified.
"""
if output_indices is None:
output_indices = self._output_tasks
num_outputs = len(output_indices)
if any(i not in self._output_tasks for i in output_indices):
raise ValueError("Too many output indices")
cls_name = self.__class__.__name__
# construct evaluation X
X_full = _make_X_full(X=X, output_indices=output_indices, tf=self._task_feature)
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)
if observation_noise is not False:
raise NotImplementedError(
f"Specifying observation noise is not yet supported by {cls_name}"
)
# If single-output, return the posterior of a single-output model
if num_outputs == 1:
return GPyTorchPosterior(mvn=mvn)
# Otherwise, make a MultitaskMultivariateNormal out of this
mtmvn = MultitaskMultivariateNormal(
mean=mvn.mean.view(*X.shape[:-2], num_outputs, -1).transpose(-1, -2),
covariance_matrix=mvn.lazy_covariance_matrix,
interleaved=False,
)
posterior = GPyTorchPosterior(mvn=mtmvn)
if hasattr(self, "outcome_transform"):
posterior = self.outcome_transform.untransform_posterior(posterior)
return posterior
```