human
Solve the following python programming problem given the following code:
# @title CFModel helper class (run this cell)
class CFModel(object):
  """Simple class that represents a collaborative filtering model"""
  def __init__(self, embedding_vars, loss, metrics=None):
    """Initializes a CFModel.
    Args:
      embedding_vars: A dictionary of tf.Variables.
      loss: A float Tensor. The loss to optimize.
      metrics: optional list of dictionaries of Tensors. The metrics in each
        dictionary will be plotted in a separate figure during training.
    """
    self._embedding_vars = embedding_vars
    self._loss = loss
    self._metrics = metrics
    self._embeddings = {k: None for k in embedding_vars}
    self._session = None

  @property
  def embeddings(self):
    """The embeddings dictionary."""
    return self._embeddings

  def train(self, num_iterations=100, learning_rate=1.0, plot_results=True,
            optimizer=tf.train.GradientDescentOptimizer):
    """Trains the model.
    Args:
      iterations: number of iterations to run.
      learning_rate: optimizer learning rate.
      plot_results: whether to plot the results at the end of training.
      optimizer: the optimizer to use. Default to GradientDescentOptimizer.
    Returns:
      The metrics dictionary evaluated at the last iteration.
    """
    with self._loss.graph.as_default():
      opt = optimizer(learning_rate)
      train_op = opt.minimize(self._loss)
      local_init_op = tf.group(
          tf.variables_initializer(opt.variables()),
          tf.local_variables_initializer())
      if self._session is None:
        self._session = tf.Session()
        with self._session.as_default():
          self._session.run(tf.global_variables_initializer())
          self._session.run(tf.tables_initializer())
          tf.train.start_queue_runners()

    with self._session.as_default():
      local_init_op.run()
      iterations = []
      metrics = self._metrics or ({},)
      metrics_vals = [collections.defaultdict(list) for _ in self._metrics]

      # Train and append results.
      for i in...
Given the above code, generate some markdown instructions for it.
assistant
#Here is the Python program you requested.

III. Training a Matrix Factorization model
CFModel (Collaborative Filtering Model) helper class
This is a simple class to train a matrix factorization model using stochastic gradient descent.
The class constructor takes
- the user embeddings U (a tf.Variable).
- the movie embeddings V, (a tf.Variable).
- a loss to optimize (a tf.Tensor).
- an optional list of metrics dictionaries, each mapping a string (the name of the metric) to a tensor. These are evaluated and plotted during training (e.g. training error and test error).
After training, one can access the trained embeddings using the model.embeddings dictionary.
Example usage:
U_var = ...
V_var = ...
loss = ...
model = CFModel(U_var, V_var, loss)
model.train(iterations=100, learning_rate=1.0)
user_embeddings = model.embeddings['user_id']
movie_embeddings = model.embeddings['movie_id']