Explained variance, also known as R^2.

def padded_variance_explained(predictions,
                              labels,
                              weights_fn=common_layers.weights_all):
  """Explained variance, also known as R^2."""
  predictions, labels = common_layers.pad_with_zeros(predictions, labels)
  targets = labels
  weights = weights_fn(targets)

  y_bar = tf.reduce_mean(weights * targets)
  tot_ss = tf.reduce_sum(weights * tf.pow(targets - y_bar, 2))
  res_ss = tf.reduce_sum(weights * tf.pow(targets - predictions, 2))
  r2 = 1. - res_ss / tot_ss
  return r2, tf.reduce_sum(weights)