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This repository contains a Python 3.6 implementation of the nonparametric linear-time relative goodness-of-fit tests (i.e., Rel-UME and Rel-FSSD) described in our paper

Informative Features for Model Comparison
Wittawat Jitkrittum, Heishiro Kanagawa, Patsorn Sangkloy, James Hays, Bernhard Schölkopf, Arthur Gretton
NIPS 2018

How to install?

If you plan to reproduce experimental results, you will probably want to modify our code. It is best to install by:

  1. Clone the repository by git clone

  2. cd to the folder that you get, and install our package by

    pip install -e .

Alternatively, if you only want to use the developed package, you can do the following without cloning the repository.

pip install git+

Either way, once installed, you should be able to do import kmod without any error.


autograd, matplotlib, numpy, scipy, Pytorch 0.4.1 and the following two packages.

In Python, make sure you can import freqopttest and import kgof without any error.


To get started, check demo_kmod.ipynb. This is a Jupyter notebook which will guide you through from the beginning. There are many Jupyter notebooks in ipynb folder demonstrating other implemented tests. Be sure to check them if you would like to explore.

Reproduce experimental results

Experiments on test powers

All experiments which involve test powers can be found in kmod/ex/, kmod/ex/, and kmod/ex/ Each file is runnable with a command line argument. For example in, we aim to check the test power of each testing algorithm as a function of the sample size n. The script takes a dataset name as its argument. See which is a standalone Bash script on how to execute

We used independent-jobs package to parallelize our experiments over a Slurm cluster (the package is not needed if you just need to use our developed tests). For example, for, a job is created for each combination of

(dataset, test algorithm, n, trial)

If you do not use Slurm, you can change the line

engine = SlurmComputationEngine(batch_parameters)


engine = SerialComputationEngine()

which will instruct the computation engine to just use a normal for-loop on a single machine (will take a lot of time). Other computation engines that you use might be supported. Running simulation will create a lot of result files (one for each tuple above) saved as Pickle. Also, the independent-jobs package requires a scratch folder to save temporary files for communication among computing nodes. Path to the folder containing the saved results can be specified in kmod/ by changing the value of expr_results_path:

# Full path to the directory to store experimental results.
'expr_results_path': '/full/path/to/where/you/want/to/save/results/',

The scratch folder needed by the independent-jobs package can be specified in the same file by changing the value of scratch_path

# Full path to the directory to store temporary files when running experiments
'scratch_path': '/full/path/to/a/temporary/folder/',

To plot the results, see the experiment's corresponding Jupyter notebook in the ipynb/ folder. For example, for see ipynb/ex1_results.ipynb to plot the results.

Experiments on images

  • Preprocessing scripts for celeba and cifar10 data can be found under preprocessing/. See the readme files in the sub-folders under proprocessing/.

  • The CNN feature extractor (used to define the kernel) in our Mnist experiment is trained with kmod/mnist/

  • Many GAN variants we used (i.e., in experiment 5 in the main text and in the appendix) were trained using the code from

  • Trained GAN models (Pytorch 0.4.1) used in this work can be found at The readme files in the sub-folders under preprocessing/ will tell you how to download the model files, for the purpose of reproducing the results.

Coding guideline

  • Use autograd.numpy instead of numpy. Part of the code relies on autograd to do automatic differentiation. Also use, Y) instead of autograd cannot differentiate the latter. Also, do not use x += .... Use x = x + .. instead.

If you have questions or comments about anything related to this work, please do not hesitate to contact Wittawat Jitkrittum and Heishiro Kanagawa