Year: 2017
Type: preprint
Abstract: Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating randomized subsampling to distributional invariance: Assuming an invariance holds is tantamount to assuming the sample has been generated by a specific algorithm. That in turn yields a notion of ergodicity. Sampling algorithms induce model classes---graphon models, sparse generalizations of exchangeable graphs, and random multigraphs with exchangeable edges can all be obtained in this manner, and we specialize our results to a number of examples. One class of sampling algorithms emerges as special: Roughly speaking, those defined as limits of random transformations drawn uniformly from certain sequences of groups. Some known pathologies of network models based on graphons are explained as a form of selection bias.
Source: arXiv (Cornell University)
Author: Orbanz, Peter
Institution: Columbia University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, G2964764773, G7142813775
OpenAlex ID: W2763811754