tensorflow_probability/python/distributions/pareto.py
def _kl_pareto_pareto(a, b, name=None):
  """Calculate the batched KL divergence KL(a || b) with a and b Pareto.

  Args:
    a: instance of a Pareto distribution object.
    b: instance of a Pareto distribution object.
    name: (optional) Name to use for created operations.
      default is "kl_pareto_pareto".

  Returns:
    Batchwise KL(a || b)
  """
  with tf.name_scope(name or "kl_pareto_pareto"):
    # Consistent with
    # http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf, page 55
    # Terminology is different from source to source for Pareto distributions.
    # The 'concentration' parameter corresponds to 'a' in that source, and the
    # 'scale' parameter corresponds to 'm'.
    final_batch_shape = distribution_util.get_broadcast_shape(
        a.concentration, b.concentration, a.scale, b.scale)
    common_type = dtype_util.common_dtype(
        [a.concentration, b.concentration, a.scale, b.scale], tf.float32)
    return tf.where(
        a.scale >= b.scale,
        b.concentration * (tf.math.log(a.scale) - tf.math.log(b.scale)) +
        tf.math.log(a.concentration) - tf.math.log(b.concentration) +
        b.concentration / a.concentration - 1.0,
        tf.broadcast_to(tf.cast(np.inf, common_type), final_batch_shape))
def _kl_pareto_pareto(a, b, name=None):
  """Calculate the batched KL divergence KL(a || b) with a and b Pareto.

  Args:
    a: instance of a Pareto distribution object.
    b: instance of a Pareto distribution object.
    name: (optional) Name to use for created operations.
      default is "kl_pareto_pareto".

  Returns:
    Batchwise KL(a || b)
  """
  with tf.name_scope(name or "kl_pareto_pareto"):
    # Consistent with
    # http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf, page 55
    # Terminology is different from source to source for Pareto distributions.
    # The 'concentration' parameter corresponds to 'a' in that source, and the
    # 'scale' parameter corresponds to 'm'.
    final_batch_shape = distribution_util.get_broadcast_shape(
        a.concentration, b.concentration, a.scale, b.scale)
    common_type = dtype_util.common_dtype(
        [a.concentration, b.concentration, a.scale, b.scale], tf.float32)
    return tf.where(
        a.scale >= b.scale,
        b.concentration * (tf.math.log(a.scale) - tf.math.log(b.scale)) +
        tf.math.log(a.concentration) - tf.math.log(b.concentration) +
        b.concentration / a.concentration - 1.0,
        tf.broadcast_to(tf.cast(np.inf, common_type), final_batch_shape))
Calculate the batched KL divergence KL(a || b) with a and b Pareto.

  Args:
    a: instance of a Pareto distribution object.
    b: instance of a Pareto distribution object.
    name: (optional) Name to use for created operations.
      default is "kl_pareto_pareto".

  Returns:
    Batchwise KL(a || b)