Median-of-Means Kernel Density Estimator (MoM-KDE)

Code of the Median-of-Means Kernel Density Estimator (MoM-KDE) used in:

Robust Kernel Density Estimation with Median-of-Means principle.

Container

The reposity contains codes for MoM-KDE, RKDE [1], and SPKDE [2].

Requirements

This code runs on Python >= 3.5. Set up environment with:

pip install -r requirements.txt

Usage

Results rely on several runs over either real or synthetic data. For this purpose, there are three scripts to use.

1. compare_kde_methods.py

Runs MoM-KDE and other robust KDEs over real data.
Scores are saved as a CSV in outputs/scores/.
One can select the datasets to be tested and several other parameters (see 'Parameters' section in script).

2. compare_kde_methods_synth.py

Runs MoM-KDE and other robust KDEs over synthetic data.
Scores are saved as a CSV in outputs/scores/. One can select the synthetic schemes to be tested and several other parameters (see 'Parameters' section in script).

3. plot_results.py

Display results of selected dataset and metric (see 'Parameters' section in script)

For example, running successively compare_kde_methods.py and plot_results.py yields the following plots:

Likewise, running compare_kde_methods_synth.py and plot_results.py (changing the 'Parameters' section so that the synthetic dataset is selected and the Jensen divergence is displayed) yields:

References

[1] J. Kim and C. D. Scott. Robust kernel density estimation. Journal of Machine Learning Research, 13(Sep):2529–2565, 2012. [link]

[2] R. A. Vandermeulen and C. Scott. Robust kernel density estimation by scaling and projection in hilbert space. In Advances in Neural Information Processing Systems, pages 433–441, 2014. [link]