Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data
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.
Code (0)
등록된 구현이 없습니다.
Tasks
ClusteringMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Generalized Species Sampling Priors with Latent Beta reinforcements
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probab…
ClusteringScalable and Flexible Clustering of Grouped Data via Parallel and Distributed Sampling in Versatile Hierarchical Dirichlet Processes
Adaptive clustering of grouped data is often done via the Hierarchical Dirichlet Process Mixture Model (HDPMM). That approach, however, is limited in its flexibility and usually does not scale well. As a remedy, we pro…
ClusteringFlexible Models for Microclustering with Application to Entity Resolution
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pit…
ClusteringEntity ResolutionMicroclustering: When the Cluster Sizes Grow Sublinearly with the Size of the Data Set
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pit…
ClusteringEntity ResolutionThe supervised hierarchical Dirichlet process
We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. W…
regression