Show simple item record

dc.contributor.authorSpantini, Alessio
dc.contributor.authorBigoni, Daniele
dc.contributor.authorMarzouk, Youssef M
dc.date.accessioned2020-08-03T13:59:58Z
dc.date.available2020-08-03T13:59:58Z
dc.date.issued2018-07
dc.date.submitted2017-12
dc.identifier.issn1532-4435
dc.identifier.urihttps://hdl.handle.net/1721.1/126468
dc.description.abstractWe 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.isoen
dc.relation.isversionofhttp://www.jmlr.org/papers/volume19/17-747/17-747.pdfen_US
dc.rightsCreative Commons Attribution 4.0 International licenseen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.sourceJournal of Machine Learning Researchen_US
dc.titleInference via low-dimensional couplingsen_US
dc.typeArticleen_US
dc.identifier.citationSpantini, 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.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.relation.journalJournal of machine learning researchen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2019-10-29T18:40:37Z
dspace.date.submission2019-10-29T18:40:44Z
mit.journal.volume19en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record