  We propose a penalized pseudo-likelihood criterion to estimate the graph of
conditional dependencies in a discrete Markov random field that can be
partially observed. We prove the convergence of the estimator in the case of a
finite or countable infinite set of nodes. In the finite case, the underlying
graph can be recovered with probability one, while in the countable infinite
case, we can recover any finite sub-graph with probability one by allowing the
candidate neighborhoods to grow as a function o(log n), with n the sample size.
Our method requires minimal assumptions on the probability distribution, and
contrary to other approaches in the literature, the usual positivity condition
is not needed. We evaluate the performance of the estimator on simulated data,
and we apply the methodology to a real dataset of stock index markets in
different countries.
