Dirichlet Fragmentation Processes
This work addresses the need for improved probabilistic models for tree-structured data in machine learning, offering a novel approach that is not incremental but builds on existing theory.
The authors tackled the problem of modeling tree-structured data by introducing the Dirichlet fragmentation process (DFP), a novel probability distribution over trees that combines Dirichlet processes and random fragmentation processes. Experiments demonstrated that the DFP mixture model outperformed state-of-the-art methods for hierarchical clustering and density modeling.
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese restaurant process (nCRP). Then we define a general class of probability distributions over trees: the Dirichlet fragmentation process (DFP) through a novel combination of the theory of Dirichlet processes and random fragmentation processes. This DFP presents a stick-breaking construction, and relates to the nCRP in the same way the Dirichlet process relates to the Chinese restaurant process. Furthermore, we develop a novel hierarchical mixture model with the DFP, and empirically compare the new model to similar models in machine learning. Experiments show the DFP mixture model to be convincingly better than existing state-of-the-art approaches for hierarchical clustering and density modelling.