Latent Space Modeling of Hypergraph Data

References

• Balasubramanian, K. (2021), “Nonparametric Modeling of Higher-Order Interactions via Hypergraphons,” Journal of Machine Learning Research, 22, 1–35.
   Web of Science ®Google Scholar
• Banterle, M., Grazian, C., Lee, A., and Robert, C. P. (2019), “Accelerating Metropolis-Hastings Algorithms by Delayed Acceptance,” Foundations of Data Science, 1, 103–128. DOI: 10.3934/fods.2019005.
   Google Scholar
• Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G., and Petri, G. (2020), “Networks Beyond Pairwise Interactions: Structure and Dynamics,” Physics Reports, 874, 1–92. DOI: 10.1016/j.physrep.2020.05.004.
   Web of Science ®Google Scholar
• Bianconi, G., and Rahmede, C. (2017), “Emergent Hyperbolic Network Geometry,” Scientific Reports, 7, 41974. DOI: 10.1038/srep41974.
   PubMed Web of Science ®Google Scholar
• Bobrowski, O., and Kahle, M. (2018), “Topology of Random Geometric Complexes: A Survey,” Journal of Applied and Computational Topology, 1, 331–364. DOI: 10.1007/s41468-017-0010-0.
   Google Scholar
• Bookstein, F. L. (1986), “Size and Shape Spaces for Landmark Data in Two Dimensions,” Statistical Science, 1, 181–222. DOI: 10.1214/ss/1177013696.
   Google Scholar
• Chazal, F., and Michel, B. (2017), “An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists,” Frontiers in Artificial Intelligence, 4, 667963. DOI: 10.3389/frai.2021.667963.
   Google Scholar
• Chien, I., Lin, C.-Y., and Wang, I.-H. (2018), “Community Detection in Hypergraphs: Optimal Statistical Limit and Efficient Algorithms,” in International Conference on Artificial Intelligence and Statistics (Vol. 84), pp. 871–879, PMLR.
   Google Scholar
• Csardi, G., and Nepusz, T. (2006), “The igraph Software Package for Complex Network Research,” InterJournal, complex systems, 1695.5, 1–9.
   Google Scholar
• Doreian, P., Batagelj, V., and Ferligoj, A. (2004), “Generalized Blockmodeling of Two-Mode Network Data,” Social Networks, 26, 29–53. DOI: 10.1016/j.socnet.2004.01.002.
   Web of Science ®Google Scholar
• Dryden, I. L., and Mardia, K. V. (1998), Statistical Shape Analysis, Chichester: Wiley.
   Google Scholar
• Duchesne, P., and de Micheaux, P. L. (2010), “Computing the Distribution of Quadratic Forms: Further Comparisons between the Liu-Tang-Zhang Approximation and Exact Methods,” Computational Statistics and Data Analysis, 54, 858–862. DOI: 10.1016/j.csda.2009.11.025.
   Web of Science ®Google Scholar
• Edelsbrunner, H., and Harer, J. (2010), Computational Topology - an Introduction, Providence, RI: American Mathematical Society.
   Google Scholar
• Friel, N., Rastelli, R., Wyse, J., and Raftery, A. E. (2016), “Interlocking Directorates in Irish Companies Using a Latent Space Model for Bipartite Networks,” Proceedings of the National Academy of Sciences, 113, 6629–6634. DOI: 10.1073/pnas.1606295113.
   PubMed Web of Science ®Google Scholar
• Gamerman, D., and Lopes, H. F. (2006), Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (2nd ed.), London: Chapman and Hall/CRC.
   Google Scholar
• Ghoshdastidar, D., and Dukkipati, A. (2017), “Consistency of Spectral Hypergraph Partitioning Under Planted Partition Model,” The Annals of Statistics, 45, 289–315. DOI: 10.1214/16-AOS1453.
   Web of Science ®Google Scholar
• Gilliland, D. C. (1962), “Integral of the Bivariate Normal Distribution over an Offset Circle,” Journal of the American Statistical Association, 57, 758–768. DOI: 10.1080/01621459.1962.10500813.
   Web of Science ®Google Scholar
• Hahsler, C. B., Buchta, C., Gruen, B., Hornik, K., Borgelt, C., Johnson, I., and Ledmi, M. (2021), arules: Mining Association Rules and Frequent Itemsets, R package version 1.6-8.
   Google Scholar
• Handcock, M. S., Raftery, A. E., and Tantrum, J. M. (2007), “Model-based Clustering for Social Networks,” Journal of the Royal Statistical Society, Series A, 170, 301–354. DOI: 10.1111/j.1467-985X.2007.00471.x.
   Web of Science ®Google Scholar
• Helske, J. (2021), ramcmc: Robust Adaptive Metropolis Algorithm, R package version 0.1.1.
   Google Scholar
• Hoff, P. D., Raftery, A. E., and Handcock, M. S. (2002), “Latent Space Approaches to Social Network Analysis,” Journal of the American Statistical Association, 97, 1090–1098. DOI: 10.1198/016214502388618906.
   Web of Science ®Google Scholar
• Ji, P., and Jin, J. (2016), “Coauthorship and Citation Networks for Statisticians,” The Annals of Applied Statistics, 10, 1779–1812. DOI: 10.1214/15-AOAS896.
   Web of Science ®Google Scholar
• Kahle, M. (2017), “Random Simplicial Complexes,” in Handbook of Discrete and Computational Geometry, eds. J. E. Goodman, J. O’Rourke, and C. D. Tóth, pp. 581–604, Boca Raton, FL: CRC Press.
   Google Scholar
• Kahle, M. (2014), “Topology of Random Simplicial Complexes: A Survey,” AMS Contemporary Mathematics, 620, 201–222.
   Google Scholar
• Kolaczyk, E. D. (2009), Statistical Analysis of Network Data: Methods and Models (1st ed.), New York: Springer.
   Google Scholar
• Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., and Boguñá, M. (2010), “Hyperbolic Geometry of Complex Networks,” Physical Review E, 82, 036106. DOI: 10.1103/PhysRevE.82.036106.
   Web of Science ®Google Scholar
• Lunagómez, S., Mukherjee, S., Wolpert, R. L., and Airoldi, E. M. (2017), “Geometric Representations of Random Hypergraphs,” Journal of the American Statistical Association, 112, 363–383. DOI: 10.1080/01621459.2016.1141686.
   Web of Science ®Google Scholar
• Lunagómez, S., Olhede, S. C., and Wolfe, P. J. (2020), “Modeling Network Populations via Graph Distances,” Journal of the American Statistical Association, 116, 2023–2040. DOI: 10.1080/01621459.2020.1763803.
   Web of Science ®Google Scholar
• Mao, X., Sarkar, P., and Chakrabarti, D. (2020), “Estimating Mixed Memberships with Sharp Eigenvector Deviations,” Journal of the American Statistical Association, 116, 1928–1940. DOI: 10.1080/01621459.2020.1751645.
   Web of Science ®Google Scholar
• Marchette. (2021), HyperG: Hypergraphs in R, R package version 1.0.0.
   Google Scholar
• Ng, T. L. J., and Murphy, T. B. (2021), “Model-based Clustering for Random Hypergraphs,” Advances in Data Analysis and Classification, 16, 691–723. DOI: 10.1007/s11634-021-00454-7.
   PubMed Web of Science ®Google Scholar
• Penrose, M. (2003), Random Geometric Graphs. Oxford Studies in Probability. Oxford: Oxford University Press.
   Google Scholar
• Raftery, A. E., Niu, X., Hoff, P. D., and Yeung, K. Y. (2012), “Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood,” Journal of Computational and Graphical Statistics, 21, 901–919. DOI: 10.1080/10618600.2012.679240.
   PubMed Web of Science ®Google Scholar
• Rastelli, R., Friel, N., and Raftery, A. E. (2016), “Properties of Latent Variable Network Models,” Network Science, 4, 407–432. DOI: 10.1017/nws.2016.23.
   Web of Science ®Google Scholar
• Salter-Townshend, M., and Murphy, T. B. (2013), “Variational Bayesian Inference for the Latent Position Cluster Model for Network Data,” Computational Statistics & Data Analysis, 57, 661–671. DOI: 10.1016/j.csda.2012.08.004.
   Web of Science ®Google Scholar
• Stasi, D., Sadeghi, K., Rinaldo, A., Petrović, S., and Fienberg, S. E. (2014), “β Models for Random Hypergraphs with a Given Degree Sequence,” ArXiv e-prints.
   Google Scholar
• Teerapabolarn, K. (2014), “An Improvement of Poisson Approximation for Sums of Dependent Bernoulli Random Variables,” Communications in Statistics - Theory and Methods, 43, 1758–1777. DOI: 10.1080/03610926.2012.674606.
   Web of Science ®Google Scholar
• The GUDHI Project (2021), GUDHI User and Reference Manual. GUDHI Editorial Board, 3.4.1 edition.
   Google Scholar
• Vihola, M. (2012), “Robust Adaptive Metropolis Algorithm with Coerced Acceptance Rate,” Statistics and Computing, 22, 997–1008. DOI: 10.1007/s11222-011-9269-5.
   Web of Science ®Google Scholar
• Wang, J.-W., Rong, L.-L., Deng, Q.-H., and Zhang, J.-Y. (2010), “Evolving Hypernetwork Model,” The European Physical Journal B, 77, 493–498. DOI: 10.1140/epjb/e2010-00297-8.
   Web of Science ®Google Scholar
• Wang, P., Pattison, P., and Robins, G. (2013), “Exponential Random Graph Model Specifications for Bipartite Networks—A Dependence Hierarchy,” Social Networks, 35, 211–222. DOI: 10.1016/j.socnet.2011.12.004.
   Web of Science ®Google Scholar
• Young, J.-G., Petri, G., Vaccarino, F., and Patania, A. (2017), “Construction of and Efficient Sampling from the Simplicial Configuration Model,” Physical Review E, 96, 032312. DOI: 10.1103/PhysRevE.96.032312.
   PubMed Web of Science ®Google Scholar
• Zhong, Y., Arandjelovic, R., and Zisserman, A. (2018), “Compact Deep Aggregation for Set Retrieval,” in Proceedings of the European Conference on Computer Vision Workshops.
   Google Scholar
• Zuev, K., Eisenberg, O., and Krioukov, D. (2015), “Exponential Random Simplicial Complexes,” Journal of Physics A: Mathematical and Theoretical, 48, 465002. DOI: 10.1088/1751-8113/48/46/465002.
   Web of Science ®Google Scholar