Experiments on limitations of simulating Gaussian data with GANs
The package as well as the necessary requirements can be installed by running make or via
virtualenv -p /usr/local/bin/python3 venv
source venv/bin/activate
python setup.py install
The figure below is meant as a guide in order to keep track of distribution spaces and their respective dimensions, etc.
To generate some n-dimensional data, use the make-dataset.py script:
python make-dataset.py -n 1000 -s gauss -b 10 -d 1 2 10
where -n gives the samples per batch, -s specifies the parent distribution (options: gauss, trunc_gauss, cauchy, uniform),
-b is the number of batches to run and -d is a list to specify the dimensions of multi-dimensional datasets to generate (dim of x in figure).
This will create a directory datasets with the saved generated data named according to the dimensionality,
along with figures displaing the Euclidean norm distribution of the datasets:
datasets/
│ data_gauss_dim1.h5
│ data_gauss_dim2.h5
│ data_gauss_dim10.h5
│ hist_gauss_dim1.png
│ hist_gauss_dim2.png
│ hist_gauss_dim10.png
The histograms saved in the datasets directory show the distributions of the parent population's Euclidean norm. Below are shown shown some examples.
To train the generator on a specific n-dimensional dataset, use
python train.py -f datasets/data_gauss_dim10.h5 -d 100 -s 0.1 -n 100
where -f specifies the parent distribution dataset to model, -d defines the dimensions of the Gaussian latent space variable (dim of z in figure),
-s is the width of the Gaussian latent space for all elements, and -n is the number of epochs over which to train.
The option to use a Wasserstein + gradient penalty update rule is provided by the -w flag, with the Vanilla GAN being the default method.
This will save results from the training in the following directory structure:
runs/
│
└───gauss_dim10_100_0.01_van/
│ test_corr.png
│ training_details.csv
│ training_model_losses.png
│ training_pvalues.png
└────models/
│ generator.pth.tar
│ discriminator.pth.tar
└────samples/
│ comp_hist_epoch00000.png
│ ...
│ comp_hist_epoch00049.png
│ corr_epoch00000.png
│ ...
│ corr_epoch00040.png
│ ks_epoch00000.png
│ ...
│ ks_epoch00049.png
│ rhist_epoch00000.png
│ ...
│ rhist_epoch00049.png
Some example figures from training a GAN on a 100-dimensional Gaussian dataset with a 100-dimensional latent space vector having 0.01 sigma are shown below. These show results after having trained for 50 epochs.
True (black, x in figure) compared to generated (red, x' in figure) samples.
Correlation matrix of 1000 samples from generator. The distribution of the off-diagonal elements (cross-correlations) are shown in red in the left panel. The cross-correlations for a same-sized sample from the parent distribution is shown in black (representing the best we can do, statistically speaking).
Euclidean norm distribution (||x||, left) for parent and generated samples, and the KS-test results comparing a batch of samples for each vector component (right).
