  The methods of statistical physics are widely used for modelling complex
networks. Building on the recently proposed Equilibrium Expectation approach,
we derive a simple and efficient algorithm for maximum likelihood estimation
(MLE) of parameters of exponential family distributions - a family of
statistical models, that includes Ising model, Markov Random Field and
Exponential Random Graph models. Computational experiments and analysis of
empirical data demonstrate that the algorithm increases by orders of magnitude
the size of network data amenable to Monte Carlo based inference. We report
results suggesting that the applicability of the algorithm may readily be
extended to the analysis of large samples of dependent observations commonly
found in biology, sociology, astrophysics, and ecology.
