Exchangeable trait allocations
Name
euclid.ejs.1532484331.pdf
Description
Published version
Size
418.49 KB
Format
Adobe PDF
Checksum (MD5)
bb746e2db4bb474b7db50500c2699acd
Author(s)
Campbell, Trevor
Cai, Diana
Broderick, Tamara
Date Issued
2018
Journal
Electronic Journal of Statistics
Publisher
Institute of Mathematical Statistics
Version
Final published version
Abstract
© 2018 Institute of Mathematical Statistics. All rights reserved. Trait allocations are a class of combinatorial structures in which data may belong to multiple groups and may have different levels of belonging in each group. Often the data are also exchangeable, i.e., their joint distribution is invariant to reordering. In clustering—a special case of trait allocation—exchangeability implies the existence of both a de Finetti representation and an exchangeable partition probability function (EPPF), distributional representations useful for computational and theoretical purposes. In this work, we develop the analogous de Finetti representation and exchangeable trait probability function (ETPF) for trait allocations, along with a characterization of all trait allocations with an ETPF. Unlike previous feature allocation characterizations, our proofs fully capture single-occurrence “dust” groups. We further introduce a novel constrained version of the ETPF that we use to establish an intuitive connection between the probability functions for clustering, feature allocations, and trait allocations. As an application of our general theory, we characterize the distribution of all edge-exchangeable graphs, a class of recently-developed models that captures realistic sparse graph sequences.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/18-EJS1455
