Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data

Area of Science:

• Statistics
• Computational Biology
• Machine Learning

Background:

• Clustering grouped data with non-exchangeable groups presents analytical challenges.
• Existing methods often struggle to model complex dependencies between groups.

Purpose of the Study:

• To propose a novel Bayesian nonparametric method for clustering grouped data with dependencies.
• To enable sharing of clusters among non-exchangeable groups using a directed acyclic graph structure.

Main Methods:

• Introduced the graphical Dirichlet process, a Bayesian nonparametric model.
• Leveraged a directed acyclic graph to characterize dependencies between group-specific random measures.
• Developed an efficient posterior inference algorithm for model estimation.

Main Results:

• The graphical Dirichlet process jointly models dependent group-specific random measures.
• The model respects the Markov property of the directed acyclic graph.
• Demonstrated model utility through simulations and analysis of single-cell data.

Conclusions:

• The graphical Dirichlet process offers a flexible framework for clustering complex grouped data.
• The method effectively handles non-exchangeable groups and their dependencies.
• Applicable to various fields, including bioinformatics and single-cell data analysis.