Spectral Bootstrapping for Networks

• Activity Number: 402
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xinyu Kang*+ and Prakash Balachandran and Eric Kolaczyk
• Companies: Boston University and Boston University and Boston University
• Keywords: Networks ; Network Statistics ; Boostrap

Abstract

Consider an undirected network that has been polluted by both Type I and Type II errors in terms of observing edges. How can we quantify our uncertainty in summarizing network characteristics? In this talk we describe a method that enables us to produce confidence intervals for network summary statistics even with only one realization, using an extension of bootstrap principles. In particular, we use a spectral-based method to separate `signal' from `noise' in the adjacency matrix of an observed network. We then bootstrap the noise and generate bootstrapped networks by adding the noise back to the signals. Based on the resulting bootstrapped adjacency matrices, we are able to compute bootstrap distributions for various network summary statistics. We present theoretical and numerical results describing the performance of our proposed method, and illustrate in the context of various biological networks.