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2018 Exchangeable trait allocations
Trevor Campbell, Diana Cai, Tamara Broderick
Electron. J. Statist. 12(2): 2290-2322 (2018). DOI: 10.1214/18-EJS1455

Abstract

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.

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Trevor Campbell. Diana Cai. Tamara Broderick. "Exchangeable trait allocations." Electron. J. Statist. 12 (2) 2290 - 2322, 2018. https://doi.org/10.1214/18-EJS1455

Information

Received: 1 September 2016; Published: 2018
First available in Project Euclid: 25 July 2018

zbMATH: 06917477
MathSciNet: MR3832093
Digital Object Identifier: 10.1214/18-EJS1455

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Vol.12 • No. 2 • 2018
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