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Bayesian inference for exponential family random graph models (ERGMs) is adoubly-intractable problem because of the intractability of both the likelihoodand posterior normalizing factor. Auxiliary variable based Markov Chain MonteCarlo (MCMC) methods for this problem are asymptotically exact butcomputationally demanding, and are difficult to extend to modified ERGMfamilies. In this work, we propose a kernel-based approximate Bayesiancomputation algorithm for fitting ERGMs. By employing an adaptive importancesampling technique, we greatly improve the efficiency of the sampling step.Though approximate, our easily parallelizable approach is yields comparableaccuracy to state-of-the-art methods with substantial improvements in computetime on multi-core hardware. Our approach also flexibly accommodates bothalgorithmic enhancements (including improved learning algorithms for estimatingconditional expectations) and extensions to non-standard cases such asinference from non-sufficient statistics. We demonstrate the performance ofthis approach on two well-known network data sets, comparing its accuracy andefficiency with results obtained using the approximate exchange algorithm. Ourtests show a wallclock time advantage of up to 50% with five cores, and theability to fit models in 1/5th the time at 30 cores; further speed enhancementsare possible when more cores are available.

Kernel-based Approximate Bayesian Inference for Exponential Family Random Graph Models