Sadeghi, K;
(2020)
On finite exchangeability and conditional independence.
Electronic Journal of Statistics
, 14
(2)
pp. 2773-2797.
10.1214/20-EJS1730.
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Abstract
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent or completely dependent. We also provide a sufficient condition for an exchangeable vector so that its elements are marginally independent. We then generalize these results and conditions for exchangeable random networks. In this case, it is demon-strated that the situation is more complex. We show that the independence structure of exchangeable random networks lies in one of six regimes that are two-fold dual to one another, represented by undirected and bidirected independence graphs in graphical model sense with graphs that are com-plement of each other. In addition, under certain additional assumptions, we provide necessary and sufficient conditions for the exchangeable network distributions to be faithful to each of these graphs.
| Type: | Article |
|---|---|
| Title: | On finite exchangeability and conditional independence |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/20-EJS1730 |
| Publisher version: | https://doi.org/10.1214/20-EJS1730 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10111151 |
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