For statistical inference on clustering, the mixture model-based framework is very popular. On the one hand, the model-based framework is convenient for producing probabilistic estimates of cluster assignments and uncertainty. On the other hand, the specification of a mixture model is fraught with the danger of misspecification that could lead to inconsistent clustering estimates. Graphical model-based clustering takes a different model specification strategy, in which the likelihood treats the data as arising dependently from a disjoint union of component graphs. To counter the large uncertainty of the graph, recent work on Bayesian spanning forest proposes using the integrated posterior of the node partition (marginalized over the latent edge distribution) to produce probabilistic estimates for clustering. Despite the strong empirical performance, it is not yet known whether the clustering estimator is consistent, especially when the data-generating mechanism is different from the specified graphical model. This article gives a positive answer in the asymptotic regime: when the data arise from an unknown mixture distribution, under mild conditions, the posterior concentrates on the ground-truth partition, producing correct clustering estimates including the number of clusters. This theoretical result is an encouraging development for the robust clustering literature, demonstrating the use of graphical models as a robust alternative to mixture models in model-based clustering.

翻译：在聚类统计推断中，基于混合模型的框架非常流行。一方面，该框架便于生成聚类分配的概率估计及不确定性度量；另一方面，混合模型的设定存在误设风险，可能导致不相合的聚类估计。基于图模型的聚类采用不同的模型设定策略：其似然函数将数据视为来自若干不相交分量图的依赖观测。为应对图结构的高度不确定性，近期关于贝叶斯生成森林的研究提出利用节点划分的积分后验（通过对隐边分布进行边缘化）来生成聚类的概率估计。尽管该方法在实证中表现优异，但其聚类估计量是否具有相合性尚未明确——尤其是在数据生成机制与设定的图模型不同时。本文在渐近框架下给出了肯定回答：当数据来自未知混合分布时，在温和条件下，后验概率集中于真实划分，从而产生正确的聚类估计（包括聚类数量）。该理论结果为鲁棒聚类研究提供了积极进展，证明了图模型可作为混合模型在基于模型的聚类中的鲁棒替代方案。