Edge-exchangeable graphs and sparsity
Name
NIPS-2016-edge-exchangeable-graphs-and-sparsity-Paper.pdf
Description
Published version
Size
543.44 KB
Format
Adobe PDF
Checksum (MD5)
503c01ceb23e762df14016d2d8806238
Author(s)
Campbell, Trevor David
Broderick, Tamara A
Date Issued
February 2017
Journal
Advances in Neural Information Processing Systems
Publisher
Morgan Kaufmann Publishers
Citation
Cai, Diana, Trevor Campbell and Tamara Broderick. “Edge-exchangeable graphs and sparsity.” Advances in Neural Information Processing Systems, 29 (February 2017) © 2017 The Author(s)
Version
Final published version
Abstract
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We present an alternative notion of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges. We demonstrate that edge-exchangeable models, unlike models that are traditionally vertex exchangeable, can exhibit sparsity. To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox [12], models within our framework are stationary across steps of the graph sequence. In particular, our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
