标题： 低维后验密度和高参数化贝叶斯模型的聚类摘要 显示英文标题

标题： Lower-dimensional posterior density and cluster summaries for overparameterized Bayesian models

摘要： 贝叶斯模型在密度和聚类估计中的实用性已在多个文献中得到确立。 然而，在使用更简单、更易解释的模型与更灵活、复杂的模型之间仍存在已知的矛盾。 在本文中，我们提出了一种新方法，通过将一个灵活的过参数化模型的拟合投影到一个低维的参数化替代模型上，从而整合这两种方法，该替代模型作为总结。 这一过程提高了可解释性，同时保留了原始模型的大部分拟合效果。 我们的方法包括三个主要步骤。 首先，我们使用非参数或过参数化模型来拟合数据。 其次，我们使用决策理论方法，将原始模型的后验预测分布投影到一系列不同维度的参数化总结点估计上。 最后，给定在第二步中获得的最佳近似原始模型的参数化总结估计，我们通过将原始后验分布投影来为这个总结构建不确定性量化。 我们展示了该方法在生成非参数和过参数化模型的总结方面的有效性，能够在合成和真实数据集上为密度和聚类总结提供点估计和不确定性量化。 显示英文摘要

摘要： The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex ones. In this paper, we propose a novel method that integrates these two approaches by projecting the fit of a flexible, overparameterized model onto a lower-dimensional parametric surrogate, which serves as a summary. This process increases interpretability while preserving most of the fit of the original model. Our approach involves three main steps. First, we fit the data using nonparametric or overparameterized models. Second, we project the posterior predictive distribution of the original model onto a sequence of parametric summary point estimates with varying dimensions using a decision-theoretic approach. Finally, given the parametric summary estimate, obtained in the second step, that best approximates the original model, we construct uncertainty quantification for this summary by projecting the original posterior distribution. We demonstrate the effectiveness of our method for generating summaries for both nonparametric and overparameterized models, delivering both point estimates and uncertainty quantification for density and cluster summaries across synthetic and real datasets.