Extendability for Exchangeable Network Models

• Activity Number: 79 - Statistical Analysis for Networks
• Type: Contributed
• Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Jiaqi Yin* and Thomas Richardson
• Companies: University of Washington and University of Washington
• Keywords: network model; exchangeability; extendability; polyhedral geometry

Abstract

We consider exchangeable distributions over finite random networks. In particular, we consider the question of when an exchangeable distribution over networks of size p is the marginal of an exchangeable distribution over networks of size q, where p < q. In this case, the distribution over networks of size p is said to be extendable to networks of size q. We use polyhedral geometry to provide characterizations of the set of exchangeable distributions on p nodes that are extendable to distributions on q nodes for p < q  < = 7. For the case where p = 3 we give 3d plots of the polytopes for q = 4, 5, 6, and compute their volumes. Finally, we provide some results and a conjecture concerning the the set of distribution space on three-node networks that are extendable to networks of arbitrary size.