Learning latent structure of large random graphs
  In this paper, we estimate the distribution of hidden nodes weights in large
random graphs from the observation of very few edges weights. In this very
sparse setting, the first non-asymptotic risk bounds for maximum likelihood
estimators (MLE) are established. The proof relies on the construction of a
graphical model encoding conditional dependencies that is extremely efficient
to study n-regular graphs obtained using a round-robin scheduling. This
graphical model allows to prove geometric loss of memory properties and deduce
the asymp-totic behavior of the likelihood function. Following a classical
construction in learning theory, the asymptotic likelihood is used to define a
measure of performance for the MLE. Risk bounds for the MLE are finally
obtained by subgaussian deviation results derived from concentration
inequalities for Markov chains applied to our graphical model.
