Beta Diffusion Trees. Heaukulani, C., <b>Knowles</b>, 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 <b>Knowles</b>, David A. and Ghahramani, Zoubin},
booktitle = {Proceedings of The 31st International Conference on Machine Learning},
eprint = {1408.3378},
isbn = {9781634393973},
number = {2011},
pages = {1809--1817},
title = {{Beta Diffusion Trees}},
url = {http://proceedings.mlr.press/v32/heaukulani14.pdf},
keywords = {Machine Learning/Statistics},
year = {2014}
}
Downloads: 0
{"_id":"CmaCLdwuTP8GBthMo","bibbaseid":"heaukulani-bknowlesb-ghahramani-betadiffusiontrees-2014","downloads":0,"creationDate":"2017-05-18T03:55:31.753Z","title":"Beta Diffusion Trees","author_short":["Heaukulani, C.","<b>Knowles</b>, D. A.","Ghahramani, Z."],"year":2014,"bibtype":"inproceedings","biburl":"http://cs.stanford.edu/people/davidknowles/my_publications.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":["<b>Knowles</b>"],"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","number":"2011","pages":"1809--1817","title":"Beta Diffusion Trees","url":"http://proceedings.mlr.press/v32/heaukulani14.pdf","keywords":"Machine Learning/Statistics","year":"2014","bibtex":"@inproceedings{Heaukulani2014beta,\nabstract = {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.},\narchivePrefix = {arXiv},\narxivId = {1408.3378},\nauthor = {Heaukulani, Creighton and <b>Knowles</b>, David A. and Ghahramani, Zoubin},\nbooktitle = {Proceedings of The 31st International Conference on Machine Learning},\neprint = {1408.3378},\nisbn = {9781634393973},\nnumber = {2011},\npages = {1809--1817},\ntitle = {{Beta Diffusion Trees}},\nurl = {http://proceedings.mlr.press/v32/heaukulani14.pdf},\nkeywords = {Machine Learning/Statistics},\nyear = {2014}\n}\n","author_short":["Heaukulani, C.","<b>Knowles</b>, D. A.","Ghahramani, Z."],"key":"Heaukulani2014beta","id":"Heaukulani2014beta","bibbaseid":"heaukulani-bknowlesb-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","<b>knowles</b>","ghahramani"],"keywords":["machine learning/statistics"],"authorIDs":[],"dataSources":["hxiRh73hmfi3m787q"]}