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24 April 2024 |
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Article overview
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Dirichlet Fragmentation Processes | | Hong Ge
; Yarin Gal
; Zoubin Ghahramani
; | | Date: |
16 Sep 2015 | | Abstract: | 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. | | Source: | arXiv, 1509.4781 | | Services: | Forum | Review | PDF | Favorites | |
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