Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data
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Complex network data may be analyzed by constructing statistical models that accurately reproduce structural properties that may be of theoretical relevance or empirical interest. In the context of the efficient fitting of models for large network data, we propose a very efficient algorithm for the maximum likelihood estimation (MLE) of the parameters of complex statistical models. The proposed algorithm is similar to the famous Metropolis algorithm but allows a Monte Carlo simulation to be performed while constraining the desired network properties. We demonstrate the algorithm in the context of exponential random graph models (ERGMs) - a family of statistical models for network data. Thus far, the lack of efficient computational methods has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The proposed approach allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes.
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