Development of multi-modal, probabilistic prediction models has lead to a need for comprehensive evaluation metrics. While several metrics can characterize the accuracy of machine-learned models (e.g., negative log-likelihood, Jensen-Shannon divergence), these metrics typically operate on probability densities. Applying them to purely sample-based prediction models thus requires that the underlying density function is estimated. 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 density 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, promising a more robust evaluation of probabilistic machine learning models.

ROME (RObust Multi-modal density Estimator)是一种非参数密度估计方法，通过聚类将多模态样本分成多个单模态样本，并将得到的单独聚类的简单核密度估计结合在一起，以估计多模态、非正态和高相关性分布。与其他估计器相比，ROME不仅在密度估计中表现出色，而且更具鲁棒性，能够克服其他估计器的过拟合和过度平滑问题，从而为概率机器学习模型提供更可靠的评估。

稳健的多模态密度估计