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Title: A noisy MCMC sampler for latent position network models Authors:  Riccardo Rastelli - University College Dublin (Ireland) [presenting]
Florian Maire - University College Dublin (Ireland)
Nial Friel - University College Dublin (Ireland)
Abstract: Latent position models are widely used for the statistical analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, algorithms that can fit these models generally require a computational cost which grows with the square of the number of nodes in the graph. This makes the analysis of large social networks impractical. We will show a new algorithm characterized by a linear computational complexity, which may be used to fit latent position models on networks of several tens of thousands nodes. The approach relies on an approximation of the likelihood function, where the amount of noise introduced can be arbitrarily reduced at the expense of computational efficiency. We will illustrate some theoretical results that show how the likelihood error propagates to the invariant distribution of the Markov chain Monte Carlo sampler. Finally, we will show some applications of the method to simulated networks and to a large network of co-authorships, demonstrating that one can achieve a substantial reduction in computing time and still obtain a reasonably good estimation of the latent structure.