code: def mean_cache(self):
      train_train_covar = self.train_prior_dist.lazy_covariance_matrix
      train_interp_indices = train_train_covar.left_interp_indices
      train_interp_values = train_train_covar.left_interp_values
  
      mvn = self.likelihood(self.train_prior_dist, self.train_inputs)
      train_mean, train_train_covar_with_noise = (
          mvn.mean,
          mvn.lazy_covariance_matrix,
      )
  
      mean_diff = (self.train_labels - train_mean).unsqueeze(-1)
      train_train_covar_inv_labels = train_train_covar_with_noise.solve(
          mean_diff
      )
  
      # New root factor
      base_size = train_train_covar.base_linear_op.size(-1)
      mean_cache = train_train_covar.base_linear_op.matmul(
          left_t_interp(
              train_interp_indices,
              train_interp_values,
              train_train_covar_inv_labels,
              base_size,
          )
      )
  
      # 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 8 for calling the InterpolatedPredictionStrategy obj's underlying member method code with example usage: obj.mean_cache() and returns: mean_cache, mean_cache