Title: Consistency of Maximum Likelihood for Continuous-Space Network Models,
Abstract: Network analysis needs tools to infer distributions over graphs of arbitrary
size from a single graph. Assuming the distribution is generated by a
continuous latent space model which obeys certain natural symmetry and
smoothness properties, we establish three levels of consistency for
non-parametric maximum likelihood inference as the number of nodes grows: (i)
the estimated locations of all nodes converge in probability on their true
locations; (ii) the distribution over locations in the latent space converges
on the true distribution; and (iii) the distribution over graphs of arbitrary
size converges.