Linear-time interpretable nonparametric two-sample test
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Interpretable Test

Build Status

17 April 2018: We updated the code base to provide support for both Python 3 and Python 2.7. Please contact Wittawat Jitkrittum if you found a bug.

The goal of this project is to learn a set of features to distinguish two given distributions P and Q, as observed through two samples. This task is formulated as a two-sample test problem. The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally (when the null hypothesis i.e., P=Q is rejected).

This repository contains a Python implementation of the Mean Embeddings (ME) test, and Smooth Characteristic Function (SCF) test in which features are automatically optimized as described in our paper

Interpretable Distribution Features with Maximum Testing Power
Wittawat Jitkrittum, Zoltán Szabó, Kacper Chwialkowski, Arthur Gretton
NIPS, 2016

How to install?

The package can be installed with the pip command.

pip install git+

Once installed, you should be able to do import freqopttest without any error.

Demo scripts

To get started, check demo_interpretable_test.ipynb which will guide you through from the beginning. There are many Jupyter notebooks in ipynb folder. Be sure to check them if you want to explore more.

Reproduce experimental results

Each experiment is defined in its own Python file with a name starting with exXX where XX is a number. All the experiment files are in freqopttest/ex folder. 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 two-sample tests). For example, for, a job is created for each combination of (dataset, 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. See independent-jobs's repository page. For real-data experiments, all the preprocessed data are included in freqopttest/data/ as Pickle files. An experiment script will create a lot of results saved as Pickle files in freqopttest/result/exXX/ where XX is the experiment number. To plot these results, see the experiment's corresponding Jupyter notebook in the ipynb/ folder. For example, for see ipynb/ex1_results.ipynb to plot the results.

Preprocessed NIPS text collection

We will add a link to the proprocessed collection of NIPS papers from 1988 to 2015 that we used in the paper soon. All the scripts used will also be added. Stay tuned.


MIT license.

If you have questions or comments about anything regarding this work, please do not hesitate to contact Wittawat Jitkrittum.