Title: From which world is your graph?,
Abstract: Discovering statistical structure from links is a fundamental problem in the
analysis of social networks. Choosing a misspecified model, or equivalently, an
incorrect inference algorithm will result in an invalid analysis or even
falsely uncover patterns that are in fact artifacts of the model. This work
focuses on unifying two of the most widely used link-formation models: the
stochastic blockmodel (SBM) and the small world (or latent space) model (SWM).
Integrating techniques from kernel learning, spectral graph theory, and
nonlinear dimensionality reduction, we develop the first statistically sound
polynomial-time algorithm to discover latent patterns in sparse graphs for both
models. When the network comes from an SBM, the algorithm outputs a block
structure. When it is from an SWM, the algorithm outputs estimates of each
node's latent position.