docstr: Compute hypervolume over X_baseline under each posterior sample.
  
  Returns:
      A `sample_shape`-dim tensor of hypervolumes.
docstr_tok: ["Compute","hypervolume","over","X_baseline","under","each","posterior","sample",".","Returns",":","A","`","sample_shape","`","-dim","tensor","of","hypervolumes","."]
code: def _hypervolumes(self) -> Tensor:
      r"""Compute hypervolume over X_baseline under each posterior sample.
  
      Returns:
          A `sample_shape`-dim tensor of hypervolumes.
      """
      return (
          self.partitioning.compute_hypervolume()
          .to(
              self.ref_point
          )  # for m > 2, the partitioning is on the CPU
          .view(self._batch_sample_shape)
      )
  
imports: from __future__ import annotations
  import warnings
  from copy import deepcopy
  from itertools import combinations
  from typing import Callable, List, Optional, Union
  import torch
  from botorch.acquisition.cached_cholesky import CachedCholeskyMCSamplerMixin
  from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective
  from botorch.acquisition.multi_objective.utils import prune_inferior_points_multi_objective
  from botorch.exceptions.errors import BotorchError, BotorchTensorDimensionError, UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.model import Model
  from botorch.sampling.base import MCSampler
  from botorch.utils.multi_objective.box_decompositions.box_decomposition_list import BoxDecompositionList
  from botorch.utils.multi_objective.box_decompositions.dominated import DominatedPartitioning
  from botorch.utils.multi_objective.box_decompositions.non_dominated import FastNondominatedPartitioning, NondominatedPartitioning
  from botorch.utils.multi_objective.box_decompositions.utils import _pad_batch_pareto_frontier
  from botorch.utils.objective import compute_feasibility_indicator
  from botorch.utils.torch import BufferDict
  from torch import Tensor
label_desc: Use image node_id 6 for calling the NoisyExpectedHypervolumeMixin obj's underlying member method code with example usage: obj._hypervolumes() and returns: self