Inference of Network Summary Statistics Through Network Denoising

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Prakash Balachandran*+ and Edoardo M Airoldi and Eric D Kolaczyk
• Companies: Boston University and Harvard University and Boston University
• Keywords: Spectral Theory ; Signal Processing ; Statistical Inference ; Edge Noise ; Concentration Inequalities

Abstract

Consider observing an undirected network that is "noisy," in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics or functional connectivity networks in neuroscience. In such circumstances, given a single observed network, to what extent are summary statistics for that network representative of their analogues for the true underlying network? Can we infer such statistics more accurately by taking into account the noise in the observed network edges? Using spectral theory, we answer both of these questions. In particular, we develop a spectral-based methodology to `denoise' the observed network data and produce more accurate inference of the summary statistics of the true network. We provide examples, both synthetic and real, and present concentration type inequalities for confidence of the reconstruction in a particular basis.