code: def batched_multi_output_to_single_output(
      batch_mo_model: BatchedMultiOutputGPyTorchModel,
  ) -> BatchedMultiOutputGPyTorchModel:
      """Convert a model from batched multi-output to a batched single-output.
  
      Note: the underlying GPyTorch GP does not change. The GPyTorch GP's batch_shape
      (referred to as `_aug_batch_shape`) is still `_input_batch_shape x num_outputs`.
      The only things that change are the attributes of the
      BatchedMultiOutputGPyTorchModel that are responsible the internal accounting of
      the number of outputs: namely, num_outputs, _input_batch_shape, and
      _aug_batch_shape.
      Initially for the batched MO models these are: `num_outputs = m`,
      `_input_batch_shape = train_X.batch_shape`, and
      `_aug_batch_shape = train_X.batch_shape + torch.Size([num_outputs])`.
      In the new SO model, these are: `num_outputs = 1`,
      `_input_batch_shape = train_X.batch_shape + torch.Size([num_outputs])`,
      and `_aug_batch_shape = train_X.batch_shape + torch.Size([num_outputs])`.
  
      This is a (hopefully) temporary measure until multi-output MVNs with
      independent outputs have better support in GPyTorch (see
      https://github.com/cornellius-gp/gpytorch/pull/1083).
  
      Args:
          batched_mo_model: The BatchedMultiOutputGPyTorchModel
  
      Returns:
          The model converted into a batch single-output model.
  
      Example:
          >>> train_X = torch.rand(5, 2)
          >>> train_Y = torch.rand(5, 2)
          >>> batch_mo_gp = SingleTaskGP(train_X, train_Y)
          >>> batch_so_gp = batched_multioutput_to_single_output(batch_gp)
      """
      was_training = batch_mo_model.training
      batch_mo_model.train()
      # TODO: Add support for HeteroskedasticSingleTaskGP.
      if isinstance(batch_mo_model, HeteroskedasticSingleTaskGP):
          raise NotImplementedError(
              "Conversion of HeteroskedasticSingleTaskGP currently not supported."
          )
      elif not isinstance(
          batch_mo_model, BatchedMultiOutputGPyTorchModel
      ):
          raise UnsupportedError(
              "Only BatchedMultiOutputGPyTorchModels are supported."
          )
      # TODO: Add support for custom likelihoods.
      elif getattr(batch_mo_model, "_is_custom_likelihood", False):
          raise NotImplementedError(
              "Conversion of models with custom likelihoods is currently unsupported."
          )
      input_transform = getattr(batch_mo_model, "input_transform", None)
      batch_sd = batch_mo_model.state_dict()
  
      # TODO: add support for outcome transforms.
      if hasattr(batch_mo_model, "outcome_transform"):
          raise NotImplementedError(
              "Converting batched multi-output models with outcome transforms "
              "is not currently supported."
          )
  
      kwargs = {
          "train_X": batch_mo_model.train_inputs[0].clone(),
          "train_Y": batch_mo_model.train_targets.clone().unsqueeze(-1),
      }
      if isinstance(
          batch_mo_model.likelihood, FixedNoiseGaussianLikelihood
      ):
          noise_covar = batch_mo_model.likelihood.noise_covar
          kwargs["train_Yvar"] = noise_covar.noise.clone().unsqueeze(-1)
      if isinstance(batch_mo_model, SingleTaskMultiFidelityGP):
          kwargs.update(batch_mo_model._init_args)
      single_outcome_model = batch_mo_model.__class__(
          input_transform=input_transform, **kwargs
      )
      single_outcome_model.load_state_dict(batch_sd)
      return single_outcome_model.train(mode=was_training)
  
imports: from __future__ import annotations
  from copy import deepcopy
  from typing import Dict, Optional, Set, Tuple
  import torch
  from botorch.exceptions import UnsupportedError
  from botorch.models.gp_regression import HeteroskedasticSingleTaskGP
  from botorch.models.gp_regression_fidelity import SingleTaskMultiFidelityGP
  from botorch.models.gp_regression_mixed import MixedSingleTaskGP
  from botorch.models.gpytorch import BatchedMultiOutputGPyTorchModel
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.transforms.input import InputTransform
  from botorch.models.transforms.outcome import OutcomeTransform
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood
  from torch import Tensor
  from torch.nn import Module
label_desc: Use image node_id 8 for calling a global function with example usage: batched_multi_output_to_single_output(batch_mo_model) and returns: single_outcome_model