Stochastic blockmodels with a growing number of classes

Choi, David; Wolfe, Patrick J.; Airoldi, Edoardo M.

doi:10.1093/biomet/asr053

Cited by 191 publications

(204 citation statements)

References 24 publications

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“…As a result, α generally suffers from an incidental parameter bias and is inconsistent. Nevertheless, (15) implies that the group misclassification probability tends to zero at an exponential rate, which intuitively means that the incidental parameter problem vanishes very rapidly as T increases.…”

Section: The Setupmentioning

confidence: 99%

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Grouped Patterns of Heterogeneity in Panel Data

Bonhomme¹,

2015

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This paper introduces time-varying grouped patterns of heterogeneity in linear panel data models. A distinctive feature of our approach is that group membership is left unrestricted. We estimate the parameters of the model using a "grouped fixed-effects" estimator that minimizes a least-squares criterion with respect to all possible groupings of the cross-sectional units. Recent advances in the clustering literature allow for fast and efficient computation. We provide conditions under which our estimator is consistent as both dimensions of the panel tend to infinity, and we develop inference methods. Finally, we allow for grouped patterns of unobserved heterogeneity in the study of the link between income and democracy across countries.JEL codes: C23.

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Section: The Setupmentioning

confidence: 99%

“…Given the interactive structure of model (12) . 15 Lastly, when using interactive fixed-effects the 14 Equation (21) holds if: …”

Section: Assumptionmentioning

confidence: 99%

Grouped Patterns of Heterogeneity in Panel Data

Bonhomme¹,

2015

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“…, K}. Following Rohe et al (2011) and Choi et al (2012), throughout this paper we assume each Z i is fixed and unknown, thus yielding P(…”

Section: Standard Stochastic Blockmodelmentioning

confidence: 99%

“…Under this framework, Choi et al (2012) showed that the fraction of misclustered nodes converges in probability to zero under maximum likelihood fitting when K is allowed to grow no faster than √ N . By means of a regularized maximum likelihood estimation approach, Rohe et al (2014) further proved that this weak convergence can be achieved for K = O(N/ log 5 N ).…”

Section: Standard Stochastic Blockmodelmentioning

confidence: 99%

How Many Communities Are There?

Saldana

Feng

2017

Journal of Computational and Graphical Statistics

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Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.

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“…Later, Wang and Wong (1987) and Nowicki and Snijders (2001) further extended the model so that stochastic block structures can be accommodated. See also Airoldi et al (2008), Bickel andChen (2009), Choi et al (2012), and Bickel et al (2013) for some relevant discussions. Because all these models are based on certain independence assumptions about either edges or dyads, they cannot describe more complicated higher order dependence structures.…”

Section: Introductionmentioning

confidence: 99%

A Popularity Scaled Latent Space Model for Large-Scale Directed Social Network

Chang¹,

Huang²,

Wang³

2019

STAT SINICA

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Large-scale directed social network data often involve degree heterogeneity, reciprocity, and transitivity properties. A sensible network generating model should take these features into consideration. To this end, we propose a popularity scaled latent space model for the large-scale directed network structure formulation. It assumes for each node a position in a hypothetically assumed latent space. Then, the nodes close (far away) to each other should have larger (less) probability to be connected. As a consequence, the reciprocity and transitivity properties can be analytically derived. In addition to that, we assume for each node a popularity parameter. Those nodes with larger (smaller) popularity are more (less) likely to be followed by other nodes. By assuming different distributions for popularity parameters, different types of degree heterogeneity can be modeled. Furthermore, based on the proposed model, a comprehensive probabilistic index is constructed for link prediction. Its finite sample performance is demonstrated by extensive simulation studies and a Sina Weibo (a Twitter-type social network in China) dataset. The performances are competitive.

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Stochastic blockmodels with a growing number of classes

Cited by 191 publications

References 24 publications

Grouped Patterns of Heterogeneity in Panel Data

Grouped Patterns of Heterogeneity in Panel Data

How Many Communities Are There?

A Popularity Scaled Latent Space Model for Large-Scale Directed Social Network

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