ROME: Robust Multi-Modal Density Estimator

TL;DR

ROMÉ is a new non-parametric density estimator that effectively handles multi-modal, non-normal, and correlated distributions by combining clustering with KDE, outperforming existing methods in robustness and accuracy.

Contribution

Introduces ROME, a robust multi-modal density estimation method that segments data via clustering and combines KDEs, addressing limitations of traditional approaches.

Findings

Outperforms state-of-the-art density estimation methods.

More robust to distributional variations and overfitting.

Effectively estimates complex multi-modal distributions.

Abstract

The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have not been evaluated in multi-modal estimation problems. In this paper, we present ROME (RObust Multi-modal Estimator), a non-parametric approach for density estimation which addresses the challenge of estimating multi-modal, non-normal, and highly correlated distributions. ROME utilizes clustering to segment a multi-modal set of samples into multiple uni-modal ones and then combines simple KDE estimates obtained for individual clusters in a single multi-modal estimate. We compared our approach to state-of-the-art methods for density estimation as well as ablations of ROME, showing that it not only outperforms established methods but is also more robust to a variety of distributions. Our results demonstrate that ROME can overcome the issues of over-fitting and over-smoothing exhibited by other estimators.