Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Highly Scalable Maximum Likelihood and Conjugate Bayesian Inference for
  ERGMs on Graph Sets with Equivalent Vertices   The exponential family random graph modeling (ERGM) framework provides a
flexible approach for the statistical analysis of networks. As ERGMs typically
involve normalizing factors that are costly to compute, practical inference
relies on a variety of approximations or other workarounds. Markov Chain Monte
Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the
MLE of ERGM parameters, and is feasible for typical models on single networks
with as many as a few thousand nodes. MCMC-based algorithms for Bayesian
analysis are more expensive, and high-quality answers are challenging to obtain
on large graphs. For both strategies, extension to the pooled case - in which
we observe multiple networks from a common generative process - adds further
computational cost, with both time and memory scaling linearly in the number of
graphs. This becomes prohibitive for large networks, or where large numbers of
graph observations are available. Here, we exploit some basic properties of the
discrete exponential families to develop an approach for ERGM inference in the
pooled case that (where applicable) allows an arbitrarily large number of graph
observations to be fit at no additional computational cost beyond preprocessing
the data itself. Moreover, a variant of our approach can also be used to
perform Bayesian inference under conjugate priors, again with no additional
computational cost in the estimation phase. As we show, the conjugate prior is
easily specified, and is well-suited to applications such as regularization.
Simulation studies show that the pooled method leads to estimates with good
frequentist properties, and posterior estimates under the conjugate prior are
well-behaved. We demonstrate our approach with applications to pooled analysis
of brain functional connectivity networks and to replicated x-ray crystal
structures of hen egg-white lysozyme.

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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph