Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but mos...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Curran Associates, Inc.
2020
|
| Online Access: | https://hdl.handle.net/1721.1/126537 |
| _version_ | 1811071063866474496 |
|---|---|
| author | Morrison, Rebecca E. Baptista, Ricardo Miguel Marzouk, Youssef M |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Morrison, Rebecca E. Baptista, Ricardo Miguel Marzouk, Youssef M |
| author_sort | Morrison, Rebecca E. |
| collection | MIT |
| description | We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another. |
| first_indexed | 2024-09-23T08:45:30Z |
| format | Article |
| id | mit-1721.1/126537 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:45:30Z |
| publishDate | 2020 |
| publisher | Curran Associates, Inc. |
| record_format | dspace |
| spelling | mit-1721.1/1265372022-09-30T11:02:47Z Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting Morrison, Rebecca E. Baptista, Ricardo Miguel Marzouk, Youssef M Massachusetts Institute of Technology. Department of Aeronautics and Astronautics We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another. United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award FA9550-15-1-0038) 2020-08-12T14:00:31Z 2020-08-12T14:00:31Z 2017-12 2019-10-29T18:02:03Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/126537 Morrison, Rebecca E., Ricardo Baptista and Youssef Marzouk. “Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting.” Paper presented at the 31st Conference on Neural Information Processing Systems (NIPS 2017, Long Beach, CA, Dec. 4-9 2017, Curran Associates, Inc. © 2017 The Author(s) en 31st Conference on Neural Information Processing Systems (NIPS 2017) 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 Curran Associates, Inc. Neural Information Processing Systems (NIPS) |
| spellingShingle | Morrison, Rebecca E. Baptista, Ricardo Miguel Marzouk, Youssef M Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title | Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title_full | Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title_fullStr | Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title_full_unstemmed | Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title_short | Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting |
| title_sort | beyond normality learning sparse probabilistic graphical models in the non gaussian setting |
| url | https://hdl.handle.net/1721.1/126537 |
| work_keys_str_mv | AT morrisonrebeccae beyondnormalitylearningsparseprobabilisticgraphicalmodelsinthenongaussiansetting AT baptistaricardomiguel beyondnormalitylearningsparseprobabilisticgraphicalmodelsinthenongaussiansetting AT marzoukyoussefm beyondnormalitylearningsparseprobabilisticgraphicalmodelsinthenongaussiansetting |