code: def fantasy_mean_cache(self):
      # first construct K_UU
      train_train_covar = self.train_prior_dist.lazy_covariance_matrix
      inducing_covar = train_train_covar.base_linear_op
  
      # now get L such that LL' \approx WD^{-1}W'
      interp_inner_prod_root = (
          self.interp_inner_prod.root_decomposition(
              method="cholesky"
          ).root
      )
      # M = KL
      inducing_compression_matrix = inducing_covar.matmul(
          interp_inner_prod_root
      )
  
      # Q = L'KL + 1
      current_qmatrix = (
          interp_inner_prod_root.transpose(-1, -2)
          .matmul(inducing_compression_matrix)
          .add_jitter(1.0)
      )
  
      # m = K_UU WD^{-1}(y - \mu)
      inducing_covar_response = inducing_covar.matmul(
          self.interp_response_cache
      )
  
      # L' m
      root_space_projection = interp_inner_prod_root.transpose(
          -1, -2
      ).matmul(inducing_covar_response)
      # Q^{-1} (L' m)
      qmat_solve = current_qmatrix.solve(root_space_projection)
  
      mean_cache = (
          inducing_covar_response
          - inducing_compression_matrix @ qmat_solve
      )
  
      # Prevent backprop through this variable
      if settings.detach_test_caches.on():
          return mean_cache.detach()
      else:
          return mean_cache
  
imports: import functools
  import string
  import warnings
  import torch
  from linear_operator import to_dense, to_linear_operator
  from linear_operator.operators import AddedDiagLinearOperator, BatchRepeatLinearOperator, ConstantMulLinearOperator, DenseLinearOperator, InterpolatedLinearOperator, LinearOperator, LowRankRootAddedDiagLinearOperator, MaskedLinearOperator, MatmulLinearOperator, RootLinearOperator, ZeroLinearOperator
  from linear_operator.utils.cholesky import psd_safe_cholesky
  from linear_operator.utils.interpolation import left_interp, left_t_interp
  from torch import Tensor
  from ..None import settings
  from ..distributions import MultitaskMultivariateNormal
  from ..lazy import LazyEvaluatedKernelTensor
  from ..utils.memoize import add_to_cache, cached, clear_cache_hook, pop_from_cache
label_desc: Use image node_id 9 for calling the InterpolatedPredictionStrategy obj's underlying member method code with example usage: obj.fantasy_mean_cache() and returns: mean_cache, mean_cache