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.

翻译：概率密度函数的估计是科学与工程领域的基本问题。然而，诸如核密度估计（KDE）等常见方法已被证明缺乏鲁棒性，而更复杂的方法尚未在多模态估计问题中得到评估。本文提出ROME（鲁棒多模态估计器），这是一种非参数密度估计方法，专门解决多模态、非正态及高度相关分布估计的挑战。该方法通过聚类将多模态样本集分割为多个单模态子集，再将各子集简单KDE估计结果整合为单一多模态估计。我们将所提方法与当前最先进的密度估计方法及ROME的消融实验进行对比，结果显示该方法不仅优于现有方法，而且对各类分布具有更强的鲁棒性。实验结果表明，ROME能够克服其他估计器存在的过拟合与过度平滑问题。