class_docstr: Implements REMBO (Bayesian optimization in a linear subspace).
  
  The (D x d) projection matrix A must be provided, and must be that used for
  the initialization. In the original REMBO paper A ~ N(0, 1). Box bounds
  in the low-d space must also be provided, which in the REMBO paper should
  be [(-sqrt(d), sqrt(d)]^d.
  
  Function evaluations happen in the high-D space, and so the arms on the
  experiment will also be tracked in the high-D space. This class maintains
  a list of points in the low-d spac that have been launched, so we can match
  arms in high-D space back to their low-d point on update.
  
  Args:
      A: (D x d) projection matrix.
      initial_X_d: Points in low-d space for initial data.
      bounds_d: Box bounds in the low-d space.
      kwargs: kwargs for BotorchModel init
code: def predict(self, X: Tensor) -> Tuple[Tensor, Tensor]:
      # Suports preditions in both low-d and high-D space, depending on shape
      # of X. For high-D, predictions are restricted to within the linear
      # embedding, so can project down with pseudoinverse.
      if X.shape[1] == self.A.shape[1]:
          # X is in low-d space
          X_d = X
      else:
          # Project down to low-d space
          X_d = X @ torch.t(self._pinvA)
          # Project X_d back up to verify X was within linear embedding
          if not torch.allclose(X, X_d @ torch.t(self.A)):
              raise NotImplementedError(
                  "Predictions outside the linear embedding not supported."
              )
      return super().predict(X=self.to_01(X_d))
  
imports: import dataclasses
  from typing import Any, List, Optional, Tuple
  from warnings import warn
  import torch
  from ax.core.search_space import SearchSpaceDigest
  from ax.core.types import TCandidateMetadata
  from ax.models.torch.botorch import BotorchModel
  from ax.models.torch_base import TorchGenResults, TorchModel, TorchOptConfig
  from ax.utils.common.docutils import copy_doc
  from botorch.utils.datasets import SupervisedDataset
  from torch import Tensor
label_desc: Use image node_id 7 for calling the REMBO obj's underlying member method code with example usage: obj.predict(X) and returns: super