Losses
------

Most lost functions behave similarly to `PyTorch loss functions <https://pytorch.org/docs/stable/nn.html#loss-functions>`_.
The take in an input tensor :math:`x` and a target :math:`y` and return a tensor representing the distance between the two.

In contrast, the divergence functions presented here are not like the Torch loss functions.
Divergences compute a distance between the prior and posterior distributions of a Bayesian neural network.
They take a single :py:class:`torch.nn.Module` as an input to compute a distance between the prior and posterior distribution.

Loss Baseclass
^^^^^^^^^^^^^^

The :py:class:`Loss` is an abstract baseclass and a subclass of :py:class:`torch.nn.Module`.
This is an abstract baseclass and the parent class to all loss functions.
Like all abstract baseclasses, this cannot be instantiated but can be subclassed to write custom losses.

The documentation in the :class:`Loss` may be inherited from PyTorch docstrings.

Methods
~~~~~~~
.. autoclass:: UQpy.scientific_machine_learning.baseclass.Loss
    :members: forward

----

List of Losses
^^^^^^^^^^^^^^

:math:`L_p` Loss
~~~~~~~~~~~~~~~~~~~~

.. autoclass:: UQpy.scientific_machine_learning.losses.LpLoss
    :members: forward

------

Gaussian Kullback-Leibler
~~~~~~~~~~~~~~~~~~~~~~~~~

This is an implementation of Kullback and Liebler's work in a closed form :cite:`kullback1951kldivergence`.

.. autoclass:: UQpy.scientific_machine_learning.losses.GaussianKullbackLeiblerDivergence
    :members: forward

------

Monte Carlo Kullback-Leibler
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This is based on Kullback and Liebler's work :cite:`kullback1951kldivergence`.

.. autoclass:: UQpy.scientific_machine_learning.losses.MCKullbackLeiblerDivergence
    :members: forward


------

Generalized Jensen-Shannon
~~~~~~~~~~~~~~~~~~~~~~~~~~

This implements a Jensen-Shannon formula :cite:`thiagarajan2022jensen`.

.. autoclass:: UQpy.scientific_machine_learning.losses.GeneralizedJensenShannonDivergence
    :members: forward

------

Geometric Jensen-Shannon
~~~~~~~~~~~~~~~~~~~~~~~~

This implements a Jensen-Shannon formula :cite:`thiagarajan2022jensen` :cite:`deasy2020jsdivergence`.

.. autoclass:: UQpy.scientific_machine_learning.losses.GeometricJensenShannonDivergence
    :members: forward