class_docstr: A multivariate normal :obj:`~gpytorch.variational._VariationalDistribution`,
  parameterized by **natural** parameters.
  
  .. note::
     The :obj:`~gpytorch.variational.NaturalVariationalDistribution` can only
     be used with :obj:`gpytorch.optim.NGD`, or other optimizers
     that follow exactly the gradient direction. Failure to do so will cause
     the natural matrix :math:`\mathbf \Theta_\text{mat}` to stop being
     positive definite, and a :obj:`~RuntimeError` will be raised.
  
  .. seealso::
      The `natural gradient descent tutorial
      <examples/04_Variational_and_Approximate_GPs/Natural_Gradient_Descent.ipynb>`_
      for use instructions.
  
      The :obj:`~gpytorch.variational.TrilNaturalVariationalDistribution` for
      a more numerically stable parameterization, at the cost of needing more
      iterations to make variational regression converge.
  
  :param int num_inducing_points: Size of the variational distribution. This implies that the variational mean
      should be this size, and the variational covariance matrix should have this many rows and columns.
  :param batch_shape: Specifies an optional batch size
      for the variational parameters. This is useful for example when doing additive variational inference.
  :type batch_shape: :obj:`torch.Size`, optional
  :param float mean_init_std: (Default: 1e-3) Standard deviation of gaussian noise to add to the mean initialization.
code: def initialize_variational_distribution(self, prior_dist):
      prior_prec = prior_dist.covariance_matrix.inverse()
      prior_mean = prior_dist.mean
      noise = torch.randn_like(prior_mean).mul_(self.mean_init_std)
  
      self.natural_vec.data.copy_(
          (prior_prec @ prior_mean.unsqueeze(-1))
          .squeeze(-1)
          .add_(noise)
      )
      self.natural_mat.data.copy_(prior_prec.mul(-0.5))
  
imports: import abc
  import torch
  from linear_operator.operators import CholLinearOperator, TriangularLinearOperator
  from linear_operator.utils.cholesky import psd_safe_cholesky
  from ..distributions import MultivariateNormal
  from ._variational_distribution import _VariationalDistribution
label_desc: Use image node_id 3 for calling the NaturalVariationalDistribution obj's underlying member method code with example usage: obj.initialize_variational_distribution(prior_dist) without return types