Reproduce “Median of Forests for Robust Density Estimation” on OpenResearch

About this paper

Hongwei Wen, Annika Betken, Tao Huang

Researchers developed Medians of Forests for Robust Density Estimation (MFRDE), a method combining random forest density estimation with the Median-of-Means principle to robustly estimate density even with significant outlier contamination. This approach achieves convergence rates nearly identical to those on uncontaminated data and outperforms existing robust kernel-based methods in both simulations and real-world anomaly detection tasks.

Key insights

• Random forest density estimators are inherently robust to non-local outliers but vulnerable to local outliers, a limitation addressed by the MoM principle.
• The Median-of-Means principle effectively provides comprehensive robustness by ensuring that at least half of the subsamples used for density estimation are free of local outliers at any given point.
• A novel "outlier proportion exponent" (β) was introduced to quantify outlier concentration, enabling a more general characterization of outlier distributions and their impact on convergence rates.

Summary by alphaXiv.