Probabilistic neural nets

Inferring distributions in neural nets

January 11, 2017 — April 7, 2022

Bayes
convolution
density
likelihood free
machine learning
neural nets
nonparametric
sparser than thou
uncertainty

Inferring densities and distributions in a massively parameterized deep learning setting.

This is not intrinsically a Bayesian thing to do, but in practice, much of the demand to do probabilistic nets comes from the demand for Bayesian posterior inference for neural nets. Bayesian inference is, however, not the only way to do uncertainty quantification.

Neural networks are very far from simple exponential families where conjugate distributions might help, so they typically rely upon approximations or luck to approximate our true target of interest.

Closely related: Generative models where we train a process to generate a (possibly stochastic) phenomenon of interest.

1 Backgrounders

Jospin et al. (2022) is a modern high-speed intro and summary of many approaches.

There was a tutorial in 2020 by Dustin Tran, Jasper Snoek, and Balaji Lakshminarayanan: Practical Uncertainty Estimation & Out-of-Distribution Robustness in Deep Learning.

2 Mixture density networks

Figure 1

Nothing to say for now, but here are some recommendations I received about this classic (C. Bishop 1994) method.

3 Ensemble methods

Figure 2

Deep learning has its own variants model averaging and bagging: Neural ensembles. Yarin Gal’s PhD Thesis (Gal 2016) summarizes some implicit approximate approaches (e.g. the Bayesian interpretation of dropout) although dropout as he frames it has become highly controversial these days as a means of inference.

4 Practicalities

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

5 Incoming

6 References

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