**NB:** this is not current; I am doing too much research in the area to summarise it well, and it is large area.

I would summarize this as creating neural networks which infer whole probability densities rather than point predictions. Sometimes this term seems to be used to mean finding some manner of Bayesian justification for a nerual network.

AFAICT this usually boils down to doing variational inference, in which case the neural network is a big approximate probabilistic directed graphical model. Apparently you can also do simulation-based inference here, somehow using gradients? Must look into that. Also, Gaussian Processes can be made to fit into this framing.

To learn:

- how does this work outside of KL-divergence?
- marginal likelihood in model selection: how does it work with many optima?

## Backgrounders

Radford Neal’s thesis ((Neal 1996)] is a foundational asymptotically-Bayesian use of neural netwroks. Yarin Gal’s PhD Thesis (Gal 2016) summarizes some implicit approximate approaches (e.g. the Bayesian interpretation of dropout). Diederik P. Kingma’s thesis is the latest blockbuster in this tradition.

Alex Graves did a poster of his paper (Graves 2011) of a simplest prior uncertainty thing for recurrent nets - (diagonal Gaussian weight uncertainty) There is a 3rd party quick and dirty implementation.

One could refer to the 2019 NeurIPS Bayes deep learning workshop site which will have some more modern positioning.

One of the very popular method here is the variational autoencoder and affiliated reparameterization trick which I have recently sumarized for my own interest.

## Reparameterisation

## Autoencoders

See autoencoders.

## Practicalities

Tensorflow probability defines an ecosystem of probabilistic NN united by their terrible documentation (although they have many tutorials online). Blei Lab’s software tool, Edward (source) seems to be included in that tensorflow suite and it has good documentaiton.

There are is better documened but possibly less comprehensive probabilistc deep learning support for [pytorch]){filename}pytorch.md) in the pyro library.

Thomas Wiecki, Bayesian Deep Learning shows how to some variants with PyMC3.

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