Rate-optimal graphon estimation

Gao, Chao; Lu, Yu; Zhou, Harrison H.

doi:10.1214/15-aos1354

Cited by 179 publications

(308 citation statements)

References 48 publications

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“…Of note, SBM hybrids have also been considered in the analysis of dynamic connectivity (Matias and Miele, 2017) and in neuroimaging (Robinson et al, 2015). Theoretical properties of the SBMs have additionally been studied in the work of Bickel et al (2013), Choi et al (2012, Ambroise and Matias (2012), Wolfe and Olhede (2013), Olhede and Wolfe (2014) and Gao et al (2015) to mention a few.…”

Section: Introductionmentioning

confidence: 99%

Multi-Subject Stochastic Blockmodels for Adaptive Analysis of Individual Differences in Human Brain Network Cluster Structure

Pavlović

Guillaume

Towlson

et al. 2019

Preprint

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There is great interest in elucidating the cluster structure of brain networks in terms of modules, blocks or clusters of similar nodes. However, it is currently challenging to handle data on multiple subjects since most of the existing methods are applicable only on a subject-by-subject basis or for analysis of a group average network. The main limitation of per-subject models is that there is no obvious way to combine the results for group comparisons, and of groupaveraged models that they do not reflect the variability between subjects. Here, we propose two novel extensions of the classical Stochastic Blockmodel (SBM) that use a mixture model to estimate blocks or clusters of connected nodes, combined with a regression model to capture the effects on cluster structure of individual differences on subject-level covariates. Multi-subject Stochastic Blockmodels (MS-SBM) can flexibly account for between-subject variability in terms of a homogenous or heterogeneous effect on connectivity of covariates such as age or diagnostic status. Using synthetic data, representing a range of block sizes and cluster structures, we investigate the accuracy of the estimated MS-SBM parameters as well as the validity of inference procedures based on Wald, likelihood ratio and Monte Carlo permutation tests. We show that multi-subject SBMs recover the true cluster structure of synthetic networks more accurately and adaptively than standard methods for modular decomposition. Permutation tests of MS-SBM parameters were more robustly valid for statistical inference and Type I error control than tests based on standard asymptotic assumptions. Applied to analysis of multi-subject resting state fMRI networks (13 healthy volunteers; 12 people with schizophrenia; N = 268 brain regions), we show that the Heterogeneous Stochastic Blockmodel estimates 'core-on-modules' architecture. The intra-block and inter-block connection weights vary between individual participants and can be modelled as a logistic function of subject-level covariates like age or diagnostic status. Multi-subject Stochastic Blockmodels are likely to be useful tools for statistical analysis of individual differences in human brain graphs and other networks whose prior cluster structure needs to be estimated from the data.

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Section: Introductionmentioning

confidence: 99%

Multi-Subject Stochastic Blockmodels for Adaptive Analysis of Individual Differences in Human Brain Network Cluster Structure

Pavlović

Guillaume

Towlson

et al. 2019

Preprint

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“…However, in order to estimate them, computationally intensive MCMC algorithms are needed. Most recently, graphon-based methods have been proposed for network modeling (Wolfe and Olhede, 2013;Olhede and Wolfe, 2014;Gao et al, 2015). A graphon is a nonnegative symmetric function f , measurable and bounded, which is used to model the probability for two nodes to be connected such…”

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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“…We consider problems in network analysis where the observed data constitute a single graph. Tools that have been developed for such problems include, for example, graphon models (Borgs et al, 2008;Hoff et al, 2002;Bickel et al, 2011;Ambroise and Matias, 2012;Wolfe and Olhede, 2013;Gao et al, 2015), the subfamily of stochastic block models (e.g. Goldenberg et al (2010)), preferential attachment graphs (Barabási and Albert, 1999) and interacting particle models (Liggett, 2005).…”

Section: Introductionmentioning

confidence: 99%

Random-Walk Models of Network Formation and Sequential Monte Carlo Methods for Graphs

Bloem-Reddy

Orbanz

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by permitting the location of a new edge to depend explicitly on the structure of the graph, but being nonetheless statistically and computationally tractable. In the limit of infinite walk length, the model converges to an extension of the preferential attachment model—in this sense, it can be motivated alternatively by asking what preferential attachment is an approximation to. Theoretical properties, including the limiting degree sequence, are studied analytically. If the entire history of the graph is observed, parameters can be estimated by maximum likelihood. If only the final graph is available, its history can be imputed by using Markov chain Monte Carlo methods. We develop a class of sequential Monte Carlo algorithms that are more generally applicable to sequential network models and may be of interest in their own right. The model parameters can be recovered from a single graph generated by the model. Applications to data clarify the role of the random‐walk length as a length scale of interactions within the graph.

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Rate-optimal graphon estimation

Cited by 179 publications

References 48 publications

Multi-Subject Stochastic Blockmodels for Adaptive Analysis of Individual Differences in Human Brain Network Cluster Structure

Multi-Subject Stochastic Blockmodels for Adaptive Analysis of Individual Differences in Human Brain Network Cluster Structure

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

Random-Walk Models of Network Formation and Sequential Monte Carlo Methods for Graphs

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