written by Eric J. Ma on 2017-07-22 | tags: bayesian deep learning data science

During this week, while us Insight Fellows begin going out to interview with other companies, my "side hustle" has been working on my Bayesian Analysis Recipes repository.

Two particularly interesting problems I've wanted to write my own implementation for are multinomial classification and Bayesian deep learning. I finally got both of them done today, after about 2-3 days of hacking on them.

Multinomial classification (notebook here) is the problem where we try to classify an item as being one of multiple classes. This is the natural extension to binary classification (done by logistic regression). To do this, I took the forest cover dataset and used PyMC3 to implement multinomial logistic regression. Seeing how to do it with PyMC3 was the most important aspect of this; actual accuracy wasn't much of a concern for me.

However, having seen the classification report (at the bottom of the notebook), and having read that the dataset was originally classified using neural networks, I immediately had the thought of doing a Bayesian neural network for multi-class classification, having seen it implemented for binary classification on the PyMC3 website.

Bayesian neural networks are not hard to intuit - basically, we place priors on the weights, rather than learning point estimates. In doing so, we are able to propagate uncertainty forward to predictions. Speaking as a non-expert in the field, I think the tricky part is the sampling algorithms needed.

One thing nice about the field of Bayesian deep learning is the use of variational inference to approximate the true distribution of predictions with a mathematically more tractable one (e.g. a Gaussian). In doing so, we gain a fast way towards approximately learning the uncertainty in predictions - essentially we trade a little bit of accuracy for a lot of speed. For complex models like neural nets, this can be very valuable, as the number of parameters to learn grows very, very quickly with model complexity, so anything fast can make iteration easier.

Starting with the code from Thomas Wiecki's website, I hacked together a few utility functions and boiled down the example to its essentials. Feed-forward neural nets aren't difficult to write - just a bunch of matrix ops and we're done. The notebook is available as well. One nice little feature is that by going with a deep neural network, we have additional predictive accuracy!

Moving forward, I'd like to improve on that notebook a bit more, by somehow implementing/developing a visualization for multiclass classification **uncertainty** which is the thing we gain from going Bayesian. Hopefully I'll be able to get to that next week - it's shaping up to look quite hectic!

As a side note, I found a bug with the multinomial distribution implementation in PyMC3, and am working with one of the core developers to get it fixed in PyMC3's master branch. (Thanks a ton, Junpeng, if you ever get to read this! ) In the meantime, I simply took his patch, modified mine a little bit, and used the patched up PyMC3 for my own purposes.

This is why I think open source is amazing - I can literally patch the source code to get it to do what I need correctly! Wherever I work next has to be supportive of things like this, and have to allow re-release of generally/broadly useful code that I touch - it is the right thing to do!

```
@article{
ericmjl-2017-bayesian-networks,
author = {Eric J. Ma},
title = {Bayesian Neural Networks},
year = {2017},
month = {07},
day = {22},
howpublished = {\url{https://ericmjl.github.io}},
journal = {Eric J. Ma's Blog},
url = {https://ericmjl.github.io/blog/2017/7/22/bayesian-neural-networks},
}
```

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