  In this work, we propose a global model selection criterion to estimate the
graph of conditional dependencies of a random vector based on a finite sample.
By global criterion, we mean optimizing a function over the entire set of
possible graphs, eliminating the need to estimate the individual neighborhoods
and subsequently combine them to estimate the graph. We prove the almost sure
convergence of the graph estimator. This convergence holds provided the data is
a realization of a multivariate stochastic process that satisfies a mixing
condition. To the best of our knowledge, these are the first results to show
the consistency of a model selection criterion for Markov random fields on
graphs under non-independent data.
