Gaussian determinantal processes: A new model for directionality in data
© 2020 National Academy of Sciences. All rights reserved. Determinantal point processes (DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory is rathe...
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| Format: | Article |
| Language: | English |
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Proceedings of the National Academy of Sciences
2021
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| Online Access: | https://hdl.handle.net/1721.1/133340 |
| _version_ | 1826201264090775552 |
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| author | Ghosh, Subhroshekhar Rigollet, Philippe |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ghosh, Subhroshekhar Rigollet, Philippe |
| author_sort | Ghosh, Subhroshekhar |
| collection | MIT |
| description | © 2020 National Academy of Sciences. All rights reserved. Determinantal point processes (DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory is rather limited for this class of models. In this work, we investigate a parametric family of Gaussian DPPs with a clearly interpretable effect of parametric modulation on the observed points. We show that parameter modulation impacts the observed points by introducing directionality in their repulsion structure, and the principal directions correspond to the directions of maximal (i.e., the most longranged) dependency. This model readily yields a viable alternative to principal component analysis (PCA) as a dimension reduction tool that favors directions along which the data are most spread out. This methodological contribution is complemented by a statistical analysis of a spiked model similar to that employed for covariance matrices as a framework to study PCA. These theoretical investigations unveil intriguing questions for further examination in random matrix theory, stochastic geometry, and related topics. |
| first_indexed | 2024-09-23T11:48:54Z |
| format | Article |
| id | mit-1721.1/133340 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:48:54Z |
| publishDate | 2021 |
| publisher | Proceedings of the National Academy of Sciences |
| record_format | dspace |
| spelling | mit-1721.1/1333402023-02-17T17:31:30Z Gaussian determinantal processes: A new model for directionality in data Ghosh, Subhroshekhar Rigollet, Philippe Massachusetts Institute of Technology. Department of Mathematics © 2020 National Academy of Sciences. All rights reserved. Determinantal point processes (DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory is rather limited for this class of models. In this work, we investigate a parametric family of Gaussian DPPs with a clearly interpretable effect of parametric modulation on the observed points. We show that parameter modulation impacts the observed points by introducing directionality in their repulsion structure, and the principal directions correspond to the directions of maximal (i.e., the most longranged) dependency. This model readily yields a viable alternative to principal component analysis (PCA) as a dimension reduction tool that favors directions along which the data are most spread out. This methodological contribution is complemented by a statistical analysis of a spiked model similar to that employed for covariance matrices as a framework to study PCA. These theoretical investigations unveil intriguing questions for further examination in random matrix theory, stochastic geometry, and related topics. 2021-10-27T19:52:13Z 2021-10-27T19:52:13Z 2020 2021-05-26T12:19:26Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133340 en 10.1073/pnas.1917151117 Proceedings of the National Academy of Sciences of the United States of America Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Proceedings of the National Academy of Sciences PNAS |
| spellingShingle | Ghosh, Subhroshekhar Rigollet, Philippe Gaussian determinantal processes: A new model for directionality in data |
| title | Gaussian determinantal processes: A new model for directionality in data |
| title_full | Gaussian determinantal processes: A new model for directionality in data |
| title_fullStr | Gaussian determinantal processes: A new model for directionality in data |
| title_full_unstemmed | Gaussian determinantal processes: A new model for directionality in data |
| title_short | Gaussian determinantal processes: A new model for directionality in data |
| title_sort | gaussian determinantal processes a new model for directionality in data |
| url | https://hdl.handle.net/1721.1/133340 |
| work_keys_str_mv | AT ghoshsubhroshekhar gaussiandeterminantalprocessesanewmodelfordirectionalityindata AT rigolletphilippe gaussiandeterminantalprocessesanewmodelfordirectionalityindata |