Inferring graphical structures

We consider the problem of inferring the underlying graph using samples from a Markov random field defined on the graph. In particular, we consider the special but interesting case when the underlying graph comes from a distribution on sparse graphs. We provide matching upper and lower bounds for the sample-complexity of learning the underlying graph of a hard-core model, when the underlying graph model in G (n,d/n). We also survey some recent results on inferring pairwise Markov random fields from samples on graphs drawn from G (n,d/n) and from random graphs of degree at most d .