dc.contributor.author | Spantini, Alessio | |
dc.contributor.author | Bigoni, Daniele | |
dc.contributor.author | Marzouk, Youssef M | |
dc.date.accessioned | 2020-08-03T13:59:58Z | |
dc.date.available | 2020-08-03T13:59:58Z | |
dc.date.issued | 2018-07 | |
dc.date.submitted | 2017-12 | |
dc.identifier.issn | 1532-4435 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/126468 | |
dc.description.abstract | We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable “reference” measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map—e.g., representing and evaluating it—grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization—to the non-Gaussian case—of the square-root Rauch–Tung–Striebel Gaussian smoother. | en_US |
dc.language.iso | en | |
dc.relation.isversionof | http://www.jmlr.org/papers/volume19/17-747/17-747.pdf | en_US |
dc.rights | Creative Commons Attribution 4.0 International license | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_US |
dc.source | Journal of Machine Learning Research | en_US |
dc.title | Inference via low-dimensional couplings | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Spantini, Alessio, Daniele Bigoni and Youssef Marzouk. “Inference via low-dimensional couplings.” Journal of machine learning research, vol. 19, 2018, pp. 1-71 © 2018 The Author(s) | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics | en_US |
dc.relation.journal | Journal of machine learning research | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2019-10-29T18:40:37Z | |
dspace.date.submission | 2019-10-29T18:40:44Z | |
mit.journal.volume | 19 | en_US |
mit.metadata.status | Complete | |