class_docstr: Synthetic data generator for Mixture of Gaussians (MoG).
  
  Attributes:
    partition_generator: A partition generator with a `generate_batch` method
      for producing the cluster partitions, or `None`. `generate_batch(n,
      batch_size)` should return a list of `np.ndarray` representing a batch of
      partitions, where each array is a sampled partition configuration, and the
      k-th element in the array is the size of the k-th partition. If set to
      `None`, the `generate_by_partitions` method can be used to create MOG with
      an arbitrary partition configuration.
    x_dim: the number of dimensions.
    prior_sigma: the standard deviation for generating the centers of the
      mixture components.
    sigma_min: the minimum standard deviation for each mixture component.
    sigma_max: the maximum standard deviation for each mixture component.
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code: def __init__(
      self,
      partition_generator,
      x_dim: int,
      prior_sigma: float,
      sigma_min: float,
      sigma_max: float,
  ):
      self.partition_generator = partition_generator
      self.x_dim = x_dim
      self.prior_sigma = prior_sigma
      self.sigma_min = sigma_min
      self.sigma_max = sigma_max
  
imports: from typing import List, Tuple
  import numpy
label_desc: Use image node_id 1 to create a new MOGGenerator object  with example: obj = MOGGenerator(partition_generator, x_dim, prior_sigma, sigma_min, sigma_max)