  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.
