The Mondrian process
We describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over κd-tree data structures. Mondrian processes are multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generali...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1797101814812770304 |
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| author | Roy, D Teh, Y |
| author_facet | Roy, D Teh, Y |
| author_sort | Roy, D |
| collection | OXFORD |
| description | We describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over κd-tree data structures. Mondrian processes are multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generalizations of the stickbreaking process described by Sethuraman (1994), recovering the Dirichlet process in one dimension. After introducing the Aldous-Hoover representation for jointly and separately exchangeable arrays, we show how the process can be used as a nonparametric prior distribution in Bayesian models of relational data. |
| first_indexed | 2024-03-07T05:57:14Z |
| format | Journal article |
| id | oxford-uuid:eaf22218-e480-4806-a7ea-1d5b61c68100 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:57:14Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:eaf22218-e480-4806-a7ea-1d5b61c681002022-03-27T11:05:56ZThe Mondrian processJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:eaf22218-e480-4806-a7ea-1d5b61c68100EnglishSymplectic Elements at Oxford2009Roy, DTeh, YWe describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over κd-tree data structures. Mondrian processes are multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generalizations of the stickbreaking process described by Sethuraman (1994), recovering the Dirichlet process in one dimension. After introducing the Aldous-Hoover representation for jointly and separately exchangeable arrays, we show how the process can be used as a nonparametric prior distribution in Bayesian models of relational data. |
| spellingShingle | Roy, D Teh, Y The Mondrian process |
| title | The Mondrian process |
| title_full | The Mondrian process |
| title_fullStr | The Mondrian process |
| title_full_unstemmed | The Mondrian process |
| title_short | The Mondrian process |
| title_sort | mondrian process |
| work_keys_str_mv | AT royd themondrianprocess AT tehy themondrianprocess AT royd mondrianprocess AT tehy mondrianprocess |