On Characterizing Finite Exchangeability for Relational Data

• Activity Number: 228
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Alexander Volfovsky*+ and Edoardo M. Airoldi
• Companies: Harvard and Harvard
• Keywords: exchangeability ; networks ; array data ; latent variable model

Abstract

Exchangeable structure is an integral part of the study of statistical models. When considering exchangeability, statisticians frequently employ the definition of infinitely exchangeable sequences due to de Finetti (1931) and its' extensions by Aldous (1981) and Hoover (1979) to infinitely exchangeable multidimensional arrays. However, while infinite exchangeability is appealing due to these representation theorems, it is not necessarily appropriate for finite data streams. Diaconis (1977) provides a representation theorem for finitely exchangeable sequences and a signed-measure de Finetti's theorem is showcased in Dellacherie and Meyer (1982). In this talk we extend the results from sequences to relational data that is frequently represented by a square matrix and demonstrate the pitfalls of assumptions of infinite exchangeability in these cases. We provide a representation theorem for weakly exchangeable finite adjacency matrices that represent directed and undirected relational data as well as a signed-measure de Finetti's theorem. To develop these results we build on results from group theory and combinatorics.