Status: not able to replicate all of the results in the paper yet, see below.

This is a replication of the pre-print paper Variational Dropout and the Local Reparameterization Trick by Diederik Kingma, Tim Salimans and Max Welling.

The code is written using Theano and Lasagne, following Lasagne layer conventions so that it should be modular enough to use elsewhere. Instructions for how to replicate results are below.

Installation

The requirements listed in the requirements.txt are only what's required to install this package so you can use it as a module. They aren't sufficient to actually run all of the scripts and notebooks. In addition, you will need:

ipython[notebook]
holoviews
holo-nets
pandas
seaborn

There is a Dockerfile accompanying this repository, which can be pulled from Docker Hub. It's based on the IPython Scipyserver image. To run the image with a self-signed certificate you can do the following; first pull the image:

docker pull gngdb/variational-dropout

Then clone this repository so it can be mounted in this container and cd into it.

git clone https://github.com/gngdb/variational-dropout.git
cd variational-dropout

Then run the container with the following command (choosing a password):

docker run -d -p 443:8888 -e PASSWORD=<CHOOSE A PASSWORD> -v $PWD:/variational-dropout gngdb/variational-dropout

Now you can just navigate to https://localhost to use your notebook. Unfortunately, this has no support for CUDA or GPUs (although it is possible to do this inside a container) so any of the experiment scripts will take a very long time to run. They're not completely unworkable on a reasonable desktop though.

Finally, in order to run scripts or use most of the notebooks you must install the package in develop mode. Open a terminal on the Jupyter server (or otherwise get a shell inside the container):

python setup.py develop

Replicating Results

There are practically just two parts of the paper we'd like to be able to reproduce:

• Table 1 - showing empirical variance estimates of the method versus other methods.
• Figure 1 - showing performance in terms of percentage error on the test set for the following:
  • No dropout
  • Regular binary dropout
  • Gaussian dropout A (Srivastava et al)
  • Variational dropout A
  • Variational dropout A2
  • Gaussian dropout B (Wang et al)
  • Variational dropout B

Once this is done, we'd like to look at the adaptive gradients in a bit more detail (there doesn't appear to have been space in the paper to discuss them more) and see what kind of properties they have.

These are the current results on the test set, all we can really say is that it's better to have dropout than to not have it:

These graphs are produced in the notebook called "Opening Results" and the results are by running the scripts in the experiments directory.

Unfortunately, haven't been able to reproduce the results for the empirical variances of the gradients either. It's likely there is some issue with this implementation at the moment. These are the results comparing empirical variances at the moment:

stochastic gradient estimator	top	bottom
local reparameterization 10 epochs	6.7e+04	1.2e+03
local reparameterization 100 epochs	5.6e+04	6.8e+02
separate weight samples 10 epochs	1.7e+04	3e+02
separate weight samples 70 epochs	3.3e+03	5.7e+01
single weight sample 10 epochs	1.3e+04	2.2e+02
single weight sample 100 epochs	3.3e+03	5.5e+01
no dropout 10 epochs	7.8e+03	1.1e+02
no dropout 100 epochs	1.08e-02	2.71e-04

These are produces in the notebook "Comparing Empirical Variance".