We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a 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 based 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 data.
翻译:我们考虑了与可能非交换性群体分组数据的问题,其依赖性特征可以是定向环流图。为了允许非交换性群体之间共享集群,我们提议采用巴耶斯非参数性非参数性方法,称为图形Drichlet进程,即共同模拟依附群体随机计量方法,假设每个随机计量方法都作为Drichlet进程进行分配,其浓度参数和基于概率计量标准取决于其上级群体的浓度参数和概率。由此产生的联合随机程序尊重连接这些群体的定向环流图的Markov特性。我们使用新的超音速代表法以及断线代表法、餐馆型代表制和代表制作为一定混合物模型的一个限度。我们开发高效的后演算法,用模拟和真正的组合单细胞数据来说明我们的模型。