**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.

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 popular methods here is the variational autoencoder and affiliated reparameterization trick. Lielihood free methods seem to be in the air too.

## Reparameterisation

## Autoencoders

See autoencoders.

## Practicalities

Generally the toolsets for “neural” probabilistic programming and vanilla probabilistic programming are converging. See the tool listing under probabilistic programming.

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