  Bayesian inference for exponential family random graph models (ERGMs) is a
doubly-intractable problem because of the intractability of both the likelihood
and posterior normalizing factor. Auxiliary variable based Markov Chain Monte
Carlo (MCMC) methods for this problem are asymptotically exact but
computationally demanding, and are difficult to extend to modified ERGM
families. In this work, we propose a kernel-based approximate Bayesian
computation algorithm for fitting ERGMs. By employing an adaptive importance
sampling technique, we greatly improve the efficiency of the sampling step.
Though approximate, our easily parallelizable approach is yields comparable
accuracy to state-of-the-art methods with substantial improvements in compute
time on multi-core hardware. Our approach also flexibly accommodates both
algorithmic enhancements (including improved learning algorithms for estimating
conditional expectations) and extensions to non-standard cases such as
inference from non-sufficient statistics. We demonstrate the performance of
this approach on two well-known network data sets, comparing its accuracy and
efficiency with results obtained using the approximate exchange algorithm. Our
tests show a wallclock time advantage of up to 50% with five cores, and the
ability to fit models in 1/5th the time at 30 cores; further speed enhancements
are possible when more cores are available.
