K.C.S.Pillai Memorial Lecture

Nonparametric Inference for Unlabeled Graphs (Joint work with Patrick Wolfe and Sharmo Bhattacharyya)

Chancellor's Distinguished Professor Peter J. Bickel
Department of Statistics, Professor Emeritus
University of California-Berkeley

Start Date and Time: Fri, 25 Apr 2014, 10:30 AM

End Date and Time: Fri, 25 Apr 2014, 11:30 AM

Venue: Stanley Coulter (SC) Hall 239

Refreshments: Refreshments will be served in HAAS 111 at 9:45 prior to the lecture

Abstract:

In a 2009 Proceedings of the National Academy of Sciences article based on work of Aldous and Hoover (1981), Bickel and Chen proposed a general nonparametric framework which could be related to the graphons of Lovasz et al. (2006), and large degree asymptotics for unlabeled random graphs. They studied fitting of block models viewable as "histogram approximations" in this framework.

Recently, Airoldi, Costa and Chan (2013), and independently Olhede and Wolfe (2013), showed how to construct block model approximations to the density of a pair of latent variables corresponding to a pair of nodes, given that the nodes are the endpoints of an edge. We discuss these results and argue that while they are hard to interpret, statistically they imply statistically meaningful approximation. Moreover, we argue that computationally efficient block model fitting procedures such as spectral and local methods can also be used for such approximation.

Finally, we propose a principled cross validation method for choosing the "bandwidth" implicit in all such approximation procedures, give some specific theory in this direction, and an application to a proteomics network.