ozzie00 / kernel-gof

an interpretable linear-time kernel goodness-of-fit test

kgof

This repository contains a Python 2.7 implementation of the nonparametric linear-time goodness-of-fit test described in our paper

A Linear-Time Kernel Goodness-of-Fit Test
Wittawat Jitkrittum, Wenkai Xu, Zoltan Szabo, Kenji Fukumizu, Arthur Gretton
NIPS 2017
https://arxiv.org/abs/1705.07673

How to install?

The package can be installed with the pip command.

pip install git+https://github.com/wittawatj/kernel-gof.git

Once installed, you should be able to do import kgof without any error. pip will also resolve the following dependency automatically.

Dependency

The following Python packages were used during development. Ideally, the following packages with the specified version numbers or newer should be used. However, older versions may work as well. We did not specifically rely on newest features in these specified versions.

autograd == 1.1.7
matplotlib == 2.0.0
numpy == 1.11.3
scipy == 0.19.0

Demo

To get started, check demo_kgof.ipynb. This is a Jupyter notebook which will guide you through from the beginning. It can also be viewed on the web. 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

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 kgof/ex folder. Each file is runnable with a command line argument. For example in ex1_vary_n.py, we aim to check the test power of each testing algorithm as a function of the sample size n. The script ex1_vary_n.py takes a dataset name as its argument. See run_ex1.sh which is a standalone Bash script on how to execute ex1_power_vs_n.py.

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 ex1_vary_n.py, 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)

to

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. 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 kgof/config.py 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 ex1_vary_n.py see ipynb/ex1_results.ipynb to plot the results.

Some note

• When adding a new Kernel or new UnnormalizedDensity, use np.dot(X, Y) instead of X.dot(Y). autograd cannot differentiate the latter. Also, do not use x += .... Use x = x + .. instead.

• The sub-module kgof.intertst depends on the linear-time two-sample test of Jitkrittum et al., 2016 (NIPS 2016) implemented in the freqopttest Python package which can be found here.

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