Beta Diffusion Trees. Heaukulani, C., Knowles, D. A., & Ghahramani, Z. In *Proceedings of The 31st International Conference on Machine Learning*, pages 1809–1817, 2014. Paper abstract bibtex We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.

@inproceedings{Heaukulani2014beta,
Abstract = {We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.},
Archiveprefix = {arXiv},
Arxivid = {1408.3378},
Author = {Heaukulani, Creighton and Knowles, David A. and Ghahramani, Zoubin},
Booktitle = {Proceedings of The 31st International Conference on Machine Learning},
Eprint = {1408.3378},
Isbn = {9781634393973},
Keywords = {Machine Learning/Statistics},
Number = {2011},
Pages = {1809--1817},
Title = {{Beta Diffusion Trees}},
Url = {http://proceedings.mlr.press/v32/heaukulani14.pdf},
Year = {2014}}

Downloads: 0

{"_id":"fAzjdCNMLsexSjoDT","bibbaseid":"heaukulani-knowles-ghahramani-betadiffusiontrees-2014","downloads":0,"creationDate":"2017-05-18T02:00:25.662Z","title":"Beta Diffusion Trees","author_short":["Heaukulani, C.","Knowles, D. A.","Ghahramani, Z."],"year":2014,"bibtype":"inproceedings","biburl":"http://cs.stanford.edu/people/davidknowles/reordered.bib","bibdata":{"bibtype":"inproceedings","type":"inproceedings","abstract":"We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.","archiveprefix":"arXiv","arxivid":"1408.3378","author":[{"propositions":[],"lastnames":["Heaukulani"],"firstnames":["Creighton"],"suffixes":[]},{"propositions":[],"lastnames":["Knowles"],"firstnames":["David","A."],"suffixes":[]},{"propositions":[],"lastnames":["Ghahramani"],"firstnames":["Zoubin"],"suffixes":[]}],"booktitle":"Proceedings of The 31st International Conference on Machine Learning","eprint":"1408.3378","isbn":"9781634393973","keywords":"Machine Learning/Statistics","number":"2011","pages":"1809–1817","title":"Beta Diffusion Trees","url":"http://proceedings.mlr.press/v32/heaukulani14.pdf","year":"2014","bibtex":"@inproceedings{Heaukulani2014beta,\n\tAbstract = {We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogously to the Dirichlet diffusion tree (Neal, 2003b), which defines a tree structure over partitions (i.e., non-overlapping subsets) of the objects. Unlike in the Dirichlet diffusion tree, multiple copies of a particle may exist and diffuse along multiple branches in the beta diffusion tree, and an object may therefore belong to multiple subsets of particles. We demonstrate how to build a hierarchically-clustered factor analysis model with the beta diffusion tree and how to perform inference over the random tree structures with a Markov chain Monte Carlo algorithm. We conclude with several numerical experiments on missing data problems with data sets of gene expression microarrays, international development statistics, and intranational socioeconomic measurements.},\n\tArchiveprefix = {arXiv},\n\tArxivid = {1408.3378},\n\tAuthor = {Heaukulani, Creighton and Knowles, David A. and Ghahramani, Zoubin},\n\tBooktitle = {Proceedings of The 31st International Conference on Machine Learning},\n\tEprint = {1408.3378},\n\tIsbn = {9781634393973},\n\tKeywords = {Machine Learning/Statistics},\n\tNumber = {2011},\n\tPages = {1809--1817},\n\tTitle = {{Beta Diffusion Trees}},\n\tUrl = {http://proceedings.mlr.press/v32/heaukulani14.pdf},\n\tYear = {2014}}\n\n","author_short":["Heaukulani, C.","Knowles, D. A.","Ghahramani, Z."],"key":"Heaukulani2014beta","id":"Heaukulani2014beta","bibbaseid":"heaukulani-knowles-ghahramani-betadiffusiontrees-2014","role":"author","urls":{"Paper":"http://proceedings.mlr.press/v32/heaukulani14.pdf"},"keyword":["Machine Learning/Statistics"],"downloads":0},"search_terms":["beta","diffusion","trees","heaukulani","knowles","ghahramani"],"keywords":["machine learning","statistics","biology","genetics","machine learning/statistics"],"authorIDs":["591d0fffd87d7fe574000007"],"dataSources":["E5kTWRuqMhy8QxJbW"]}