用于聚类非可交换分组数据的图 Dirichlet 过程
Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data
AI总结：
针对非可交换分组数据的聚类问题，提出 graphical Dirichlet process 这一 Bayesian nonparametric 方法，利用 directed acyclic graph 联合建模组间依赖的随机测度并实现聚类共享。
摘要：
我们考虑对具有潜在非可交换组的分组数据进行聚类的问题，这些组的依赖关系可通过已知的 directed acyclic graph 来刻画。为允许在非可交换组间共享聚类，我们提出了一种 Bayesian nonparametric 方法，称为 graphical Dirichlet process。该方法通过假设每个随机测度服从 Dirichlet process，且其 concentration parameter 和 base probability measure 依赖于其父组的对应参数，从而对依赖的组特定随机测度进行联合建模。由此产生的联合随机过程遵循连接各组的 directed acyclic graph 的 Markov property。我们使用一种新颖的 hypergraph representation 以及 stick-breaking representation、restaurant-type representation 和作为 finite mixture model 极限的表示来刻画 graphical Dirichlet process。我们开发了一种高效的 posterior inference 算法，并通过模拟实验和真实的分组 single-cell dataset 阐明了我们的模型。
英文摘要：
We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we propose a Bayesian nonparametric approach, termed graphical Dirichlet process, that jointly models the dependent group-specific random measures by assuming each random measure to be distributed as a Dirichlet process whose concentration parameter and base probability measure depend on those of its parent groups. The resulting joint stochastic process respects the Markov property of the directed acyclic graph that links the groups. We characterize the graphical Dirichlet process using a novel hypergraph representation as well as the stick-breaking representation, the restaurant-type representation, and the representation as a limit of a finite mixture model. We develop an efficient posterior inference algorithm and illustrate our model with simulations and a real grouped single-cell dataset.
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