code: def _get_induced_fantasy_model(
      model: Model,
      Xs: List[Tensor],
      samplers: List[Optional[MCSampler]],
  ) -> Model:
      r"""Recursive computation of the fantasy model induced by an input tree.
  
      Args:
          model: A Model of appropriate batch size. Specifically, it must be possible to
              evaluate the model's posterior at `Xs[0]`.
          Xs: A list `[X_j, ..., X_k]` of tensors, where `X_i` has shape
              `f_i x .... x f_1 x batch_shape x q_i x d`.
          samplers: A list of `k - j` samplers, such that the number of samples of sampler
              `i` is `f_i`. The last element of this list is considered the
              "inner sampler", which is used for evaluating the objective in case it is an
              MCAcquisitionObjective.
  
      Returns:
          A Model obtained by iteratively fantasizing over the input tree `Xs`.
      """
      if len(Xs) == 1:
          return model
      else:
          fantasy_model = model.fantasize(
              X=Xs[0],
              sampler=samplers[0],
          )
  
          return _get_induced_fantasy_model(
              model=fantasy_model, Xs=Xs[1:], samplers=samplers[1:]
          )
  
imports: from __future__ import annotations
  import math
  import warnings
  from typing import Any, Callable, Dict, List, Optional, Tuple, Type
  import numpy
  import torch
  from botorch.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.analytic import AnalyticAcquisitionFunction, PosteriorMean
  from botorch.acquisition.monte_carlo import MCAcquisitionFunction
  from botorch.acquisition.objective import MCAcquisitionObjective, PosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.model import Model
  from botorch.optim.initializers import initialize_q_batch
  from botorch.sampling.base import MCSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.transforms import match_batch_shape, t_batch_mode_transform, unnormalize
  from torch import Size, Tensor
  from torch.distributions import Beta
  from torch.nn import ModuleList
label_desc: Use image node_id 5 for calling a global function with example usage: _get_induced_fantasy_model(model, Xs, samplers) and returns: model, _get_induced_fantasy_model