Statistical Inference in Heterogeneous Block Model

There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions, treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing to see which block model is really true.

[1]  Venkatesh Saligrama,et al.  Testing Changes in Communities for the Stochastic Block Model , 2018, ArXiv.

[2]  Marina Meila,et al.  A Comparison of Spectral Clustering Algorithms , 2003 .

[3]  Yuguo Chen,et al.  A block model for node popularity in networks with community structure , 2018 .

[4]  Chao Gao,et al.  Community Detection in Degree-Corrected Block Models , 2016, The Annals of Statistics.

[5]  Ken Wakita,et al.  Finding community structure in mega-scale social networks: [extended abstract] , 2007, WWW '07.

[6]  Zongming Ma,et al.  Optimal hypothesis testing for stochastic block models with growing degrees , 2017, ArXiv.

[7]  René Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications , 2012, IEEE transactions on pattern analysis and machine intelligence.

[8]  Jiashun Jin,et al.  Estimating network memberships by simplex vertex hunting , 2017 .

[9]  Subhabrata Sen,et al.  Testing degree corrections in stochastic block models , 2017, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[10]  Jiashun Jin,et al.  Network Global Testing by Counting Graphlets , 2018, ICML.

[11]  Jing Lei.  A goodness-of-fit test for stochastic block models , 2014, 1412.4857.

[12]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Bo Wang,et al.  Network enhancement as a general method to denoise weighted biological networks , 2018, Nature Communications.

[14]  Emmanuel Abbe,et al.  Community detection and stochastic block models: recent developments , 2017, Found. Trends Commun. Inf. Theory.

[15]  Purnamrita Sarkar,et al.  Hierarchical community detection by recursive bi-partitioning , 2018 .

[16]  H. White,et al.  “Structural Equivalence of Individuals in Social Networks” , 2022, The SAGE Encyclopedia of Research Design.

[17]  Angelo Bifone,et al.  Community detection in weighted brain connectivity networks beyond the resolution limit , 2016, NeuroImage.

[18]  A. Rinaldo,et al.  Consistency of spectral clustering in stochastic block models , 2013, 1312.2050.

[19]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[20]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  M. Pensky,et al.  Estimation and Clustering in Popularity Adjusted Stochastic Block Model , 2019, 1902.00431.

[22]  Emmanuel J. Candès,et al.  Robust Subspace Clustering , 2013, ArXiv.

[23]  Harrison H. Zhou,et al.  Structured matrix estimation and completion , 2017, Bernoulli.

[24]  Chao Gao,et al.  Testing for Global Network Structure Using Small Subgraph Statistics , 2017, ArXiv.

[25]  René Vidal,et al.  A closed form solution to robust subspace estimation and clustering , 2011, CVPR 2011.

[26]  Chao Gao,et al.  Achieving Optimal Misclassification Proportion in Stochastic Block Models , 2015, J. Mach. Learn. Res..

[27]  Edoardo M. Airoldi,et al.  Mixed Membership Stochastic Blockmodels , 2007, NIPS.