A local structure model for network analysis

Casleton, Emily; Nordman, Daniel J.; Kaiser, Mark J.

doi:10.4310/sii.2017.v10.n2.a15

Cited by 13 publications

(23 citation statements)

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“…Markov structures may arise with exponential random graph models (e.g., Kolaczyk 2009) and latent variable models (Hoff, Raftery, and Handcock 2002) as two common types of probabilistic models for networks; see Hunter, Krivitsky, and Schweinberger (2012) and references therein. Local structure graph models provide another MRF modeling approach for random graphs, whereby each graph edge has a formulated conditional distribution that depends on neighborhoods of other graph edges; see Casleton, Nordman, and Kaiser (2017). We next examine conclique-based simulation from one such model.…”

Section: Simulation Of a Large Networkmentioning

confidence: 99%

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

Kaplan

Kaiser

Lahiri

et al. 2019

Journal of Computational and Graphical Statistics

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For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. At issue, fast simulation from such MRF models is often an important consideration, particularly when repeated generation of large numbers of data sets is required (e.g., for approximating sampling distributions). However, a standard Gibbs strategy for simulating from MRF models involves single-updates, performed with the conditional distribution of each observation in a sequential manner, whereby a Gibbs iteration may become computationally involved even for relatively small samples. As an alternative, we describe a general way to simulate from MRF models using Gibbs sampling with "concliques" (i.e., groups of non-neighboring observations). Compared to standard Gibbs sampling, this simulation scheme can be much faster by reducing Gibbs steps and by independently updating all observations per conclique at once. We detail the simulation method, establish its validity, and assess its computational performance through numerical studies, where speed advantages are shown for several spatial and network examples. arXiv:1808.04739v1 [stat.CO]

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Section: Simulation Of a Large Networkmentioning

confidence: 99%

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

Kaplan

Kaiser

Lahiri

et al. 2019

Journal of Computational and Graphical Statistics

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“…As shown in Casleton et al (2014b), a correspondence between ERGMs and LSGMs is demonstrated through the negpotential function. The joint distribution for both is that of a Gibbs distribution, which can be specified through the negpotential function, up to a constant.…”

Section: Higher-order Dependencementioning

confidence: 89%

“…Network science as a field is sizable, diverse, and rapidly growing. Both the traditional formulations of ERGMs and LSGMs have joint distributions in Gibbsian form (Casleton et al, 2014b), but these joint distributions must be constructed for a LSGM from the set of specified conditional distributions (Kaiser and Cressie, 2000), which may be accomplished under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

A local structure graph model for network analysis

Casleton

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“…For even a graph with a small number of nodes, there can be many edges, meaning that the single-site (sequential) Gibbs sampler would be computationally time demanding but the conclique-based approach could be applied to reduce the number of computations in each iteration. For example, in the graph models of (Casleton, Nordman, and Kaiser 2017), there is a geographic notion (a radius of influence) whereby nodes in the graph which are far apart in distance (or other covariates) will not share an edge. It follows that collections of nodes which are separated by a distance under the MRF model can be used to define concliques for edges in the graph (observations as edges which do not neighbor other edges in the graph).…”

Section: Discussionmentioning

confidence: 99%

“…Such MRF models have become popular for modeling temporally-or spatially-dependent areal data (Cressie 1993), image segmentation (Zhang, Brady, and Smith 2001), computer vision (S. Z. Li 2012), and positron emission tomography (Higdon 1998), among other challenging applications including the analysis of networks (cf. Strauss and Ikeda 1990;Hoff, Raftery, and Handcock 2002;Casleton, Nordman, and Kaiser 2017). In addition to providing a route for model formulation, another reason for the popularity of MRF specifications is that observation-wise conditional distributions fit naturally with the Gibbs sampler (S. Geman and Geman 1984) for generating data realizations via Markov chain Monte Carlo (MCMC) methods (Gelfand and Smith 1990).…”

Section: Introductionmentioning

confidence: 99%

On advancing MCMC-based methods for Markovian data structures with applications to deep learning, simulation, and resampling

Kaplan¹

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Markov chain Monte Carlo (MCMC) is a computational statistical approach for numerically approximating distributional quantities useful for inference that might otherwise be intractable to directly calculate. A challenge with MCMC methods is developing implementations which are both statistically rigorous and computationally scalable to large data sets. This work generally aims to bridge these aspects by exploiting conditional independence, or Markov structures, in data models. Chapter 2 investigates the model properties and Bayesian fitting of a graph model with Markovian dependence used in deep machine learning and image classification, called a restricted Bolzmann machine (RBM), and Chapter 3 presents a framework for describing inherent instability in a general class of models which includes RBMs. Chapters 4 and 5 introduce a fast method for simulating data from a Markov Random Field (MRF) by exploiting conditional independence specified in the model and a flexible R package that implements the approach in C++.

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A local structure model for network analysis

Cited by 13 publications

References 0 publications

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

A local structure graph model for network analysis

On advancing MCMC-based methods for Markovian data structures with applications to deep learning, simulation, and resampling

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