Latent Space Model for Higher-Order Networks and Generalized Tensor Decomposition

References

• Arroyo, J., Athreya, A., Cape, J., Chen, G., Priebe, C. E., and Vogelstein, J. T. (2021), “Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace,” Journal of Machine Learning Research, 22, 1–49.
   PubMed Web of Science ®Google Scholar
• Athreya, A., Fishkind, D. E., Tang, M., Priebe, C. E., Park, Y., Vogelstein, J. T., Levin, K., Lyzinski, V., and Qin, Y. (2017), “Statistical Inference on Random Dot Product Graphs: A Survey,” The Journal of Machine Learning Research, 18, 8393–8484.
   Web of Science ®Google Scholar
• Balasubramanian, K. (2021), “Nonparametric Modeling of Higher-Order Interactions via Hypergraphons,” arXiv preprint arXiv:2105.2105.08678.
   Google Scholar
• Benson, A. R., Gleich, D. F., and Leskovec, J. (2016), “Higher-Order Organization of Complex Networks,” Science, 353, 163–166. DOI: 10.1126/science.aad9029.
   PubMed Web of Science ®Google Scholar
• Bhattacharjee, M., Banerjee, M., and Michailidis, G. (2018), “Change Point Estimation in a Dynamic Stochastic Block Model,” arXiv preprint arXiv:1812.03090.
   Google Scholar
• Bick, C., Gross, E., Harrington, H. A., and Schaub, M. T. (2021), “What are Higher-Order Networks?” arXiv preprint arXiv:2104.11329.
   Google Scholar
• Cai, J.-F., Li, J., and Xia, D. (2021), “Generalized Low-Rank Plus Sparse Tensor Estimation by Fast Riemannian Optimization,” arXiv preprint arXiv:2103.08895. DOI: 10.1080/01621459.2022.2063131.
   Google Scholar
• Cai, T. T., and Zhang, A. (2018), “Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics,” The Annals of Statistics, 46, 60–89. DOI: 10.1214/17-AOS1541.
   Web of Science ®Google Scholar
• Cardillo, A., Gómez-Gardenes, J., Zanin, M., Romance, M., Papo, D., Del Pozo, F., and Boccaletti, S. (2013a), “Emergence of Network Features from Multiplexity,” Scientific Reports, 3, 1–6. DOI: 10.1038/srep01344.
   Web of Science ®Google Scholar
• Cardillo, A., Zanin, M., Gómez-Gardenes, J., Romance, M., del Amo, A. J. G., and Boccaletti, S. (2013b), “Modeling the Multi-Layer Nature of the European Air Transport Network: Resilience and Passengers Re-Scheduling Under Random Failures,” The European Physical Journal Special Topics, 215, 23–33. DOI: 10.1140/epjst/e2013-01712-8.
   Web of Science ®Google Scholar
• Chen, H., and Zhang, N. (2015), “Graph-based Change-Point Detection,” Annals of Statistics, 43, 139–176.
   Web of Science ®Google Scholar
• Chen, Y., Li, C., and Xu, G. (2021), “A Note on Statistical Inference for Noisy Incomplete 1-bit Matrix,” arXiv preprint arXiv:2105.01769.
   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, pp. 871–879. PMLR.
   Google Scholar
• Davenport, M. A., Plan, Y., Van Den Berg, E., and Wootters, M. (2014), “1-Bit Matrix Completion,” Information and Inference: A Journal of the IMA, 3, 189–223. DOI: 10.1093/imaiai/iau006.
   Google Scholar
• Dickison, M. E., Magnani, M., and Rossi, L. (2016), Multilayer Social Networks, Cambridge: Cambridge University Press.
   Google Scholar
• Edelman, A., Arias, T. A., and Smith, S. T. (1998), “The Geometry of Algorithms with Orthogonality Constraints,” SIAM journal on Matrix Analysis and Applications, 20, 303–353. DOI: 10.1137/S0895479895290954.
   Web of Science ®Google Scholar
• Ghoshal, G., Zlatić, V., Caldarelli, G., and Newman, M. E. (2009), “Random Hypergraphs and their Applications,” Physical Review E, 79, 066118. DOI: 10.1103/PhysRevE.79.066118.
   Web of Science ®Google Scholar
• Ghoshdastidar, D., and Dukkipati, A. (2014), “Consistency of Spectral Partitioning of Uniform Hypergraphs Under Planted Partition Model,” in Advances in Neural Information Processing Systems (Vol. 27), pp. 397–405.
   Google Scholar
• Ghoshdastidar, D., and Dukkipati, A. (2015), “A Provable Generalized Tensor Spectral Method for Uniform Hypergraph Partitioning,” in International Conference on Machine Learning, pp. 400–409. PMLR.
   Google Scholar
• Ghoshdastidar, D., and Dukkipati, A. (2017), “Consistency of Spectral Hypergraph Partitioning Under Planted Partition Model,” Annals of Statistics, 45, 289–315.
   Web of Science ®Google Scholar
• Goldenberg, A., Zheng, A. X., Fienberg, S. E., and Airoldi, E. M. (2010), “A Survey of Statistical Network Models.” Foundations and Trends® in Machine Learning, 2, 129–233. DOI: 10.1561/2200000005.
   Google Scholar
• Han, R., Willett, R., and Zhang, A. (2020), “An Optimal Statistical and Computational Framework for Generalized Tensor Estimation,” arXiv preprint arXiv:2002.11255.
   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
• Holland, P. W., Laskey, K. B., and Leinhardt, S. (1983), “Stochastic Blockmodels: First Steps,” Social Networks, 5, 109–137. DOI: 10.1016/0378-8733(83)90021-7.
   Web of Science ®Google Scholar
• Hore, V., Viñuela, A., Buil, A., Knight, J., McCarthy, M. I., Small, K., and Marchini, J. (2016), “Tensor Decomposition for Multiple-Tissue Gene Expression Experiments,” Nature Genetics, 48, 1094–1100. DOI: 10.1038/ng.3624.
   PubMed Web of Science ®Google Scholar
• Hu, J., Lee, C., and Wang, M. (2019), “Supervised Tensor Decomposition with Features on Multiple Modes,” arXiv e-prints, pp. arXiv–1910.
   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
• Jing, B.-Y., Li, T., Lyu, Z., and Xia, D. (2021), “Community Detection on Mixture Multi-Layer Networks via Regularized Tensor Decomposition,” The Annals of Statistics, 49, 3181–3205. DOI: 10.1214/21-AOS2079.
   Web of Science ®Google Scholar
• Ke, Z. T., Shi, F., and Xia, D. (2019), “Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration,” arXiv preprint arXiv:1909.06503.
   Google Scholar
• Keshavan, R. H., Montanari, A., and Oh, S. (2010), “Matrix Completion from a Few Entries,” IEEE Transactions on Information Theory, 56, 2980–2998. DOI: 10.1109/TIT.2010.2046205.
   Web of Science ®Google Scholar
• Kim, C., Bandeira, A. S., and Goemans, M. X. (2018), “Stochastic Block Model for Hypergraphs: Statistical Limits and a Semidefinite Programming Approach,” arXiv preprint arXiv:1807.02884.
   Google Scholar
• Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., and Porter, M. A. (2014), “Multilayer Networks,” Journal of Complex Networks, 2, 203–271. DOI: 10.1093/comnet/cnu016.
   Google Scholar
• Kolda, T. G. (2006), “Multilinear Operators for Higher-Order Decompositions,” Technical Report, Citeseer.
   Google Scholar
• Kolda, T. G., and Bader, B. W. (2009), “Tensor Decompositions and Applications,” SIAM Review, 51, 455–500. DOI: 10.1137/07070111X.
   Web of Science ®Google Scholar
• Larremore, D. B., Clauset, A., and Buckee, C. O. (2013), “A Network Approach to Analyzing Highly Recombinant Malaria Parasite Genes,” PLOS Computational Biology, 9, e1003268. DOI: 10.1371/journal.pcbi.1003268.
   PubMed Web of Science ®Google Scholar
• Le, C. M., Levin, K., and Levina, E. (2018), “Estimating a Network from Multiple Noisy Realizations,” Electronic Journal of Statistics, 12, 4697–4740. DOI: 10.1214/18-EJS1521.
   Web of Science ®Google Scholar
• Lee, S. H., Magallanes, J. M., and Porter, M. A. (2017), “Time-Dependent Community Structure in Legislation Cosponsorship Networks in the Congress of the Republic of Peru,” Journal of Complex Networks, 5, 127–144. DOI: 10.1093/comnet/cnw004.
   Web of Science ®Google Scholar
• Lei, J., Chen, K., and Lynch, B. (2020), “Consistent Community Detection in Multi-Layer Network Data,” Biometrika, 107, 61–73. DOI: 10.1093/biomet/asz068.
   Web of Science ®Google Scholar
• Lei, J., and Rinaldo, A. (2015), “Consistency of Spectral Clustering in Stochastic Block Models,” Annals of Statistics, 43, 215–237.
   Web of Science ®Google Scholar
• Levin, K., Athreya, A., Tang, M., Lyzinski, V., Park, Y., and Priebe, C. E. (2017), “A Central Limit Theorem for An Omnibus Embedding of Multiple Random Graphs and Implications for Multiscale Network Inference,” arXiv preprint arXiv:1705.09355.
   Google Scholar
• Ma, Z., Ma, Z., and Yuan, H. (2020). Universal latent space model fitting for large networks with edge covariates. Journal of Machine Learning Research, 21(4):1–67.
   PubMedGoogle Scholar
• MacDonald, P. W., Levina, E., and Zhu, J. (2020), “Latent Space Models for Multiplex Networks with Shared Structure,” arXiv preprint arXiv:2012.14409.
   Google Scholar
• Matias, C., and Miele, V. (2017), “Statistical Clustering of Temporal Networks through a Dynamic Stochastic Block Model,” Journal of the Royal Statistical Society, Series B, 79, 1119–1141. DOI: 10.1111/rssb.12200.
   Google Scholar
• Newman, M. (2018), Networks, Oxford: Oxford University Press.
   Google Scholar
• Newman, M. E. (2011), “The Structure of Scientific Collaboration Networks,” in The Structure and Dynamics of Networks, pp. 221–226, Princeton: Princeton University Press.
   Google Scholar
• Pal, S., and Zhu, Y. (2019), “Community Detection in the Sparse Hypergraph Stochastic Block Model,” arXiv preprint arXiv:1904.05981.
   Google Scholar
• Park, Y., Priebe, C. E., and Youssef, A. (2012), “Anomaly Detection in Time Series of Graphs Using Fusion of Graph Invariants,” IEEE Journal of Selected Topics in Signal Processing, 7, 67–75. DOI: 10.1109/JSTSP.2012.2233712.
   Web of Science ®Google Scholar
• Paul, S., and Chen, Y. (2020a), “A Random Effects Stochastic Block Model for Joint Community Detection in Multiple Networks with Applications to Neuroimaging,” Annals of Applied Statistics, 14, 993–1029.
   Web of Science ®Google Scholar
• Paul, S., and Chen, Y. (2020b), “Spectral and Matrix Factorization Methods for Consistent Community Detection in Multi-Layer Networks,” The Annals of Statistics, 48, 230–250.
   Web of Science ®Google Scholar
• Pensky, M. (2019), “Dynamic Network Models and Graphon Estimation,” Annals of Statistics, 47, 2378–2403.
   Web of Science ®Google Scholar
• Pensky, M., and Zhang, T. (2019), “Spectral Clustering in the Dynamic Stochastic Block Model,” Electronic Journal of Statistics, 13, 678–709. DOI: 10.1214/19-EJS1533.
   Web of Science ®Google Scholar
• Rohe, K., Chatterjee, S., and Yu, B. (2011). Spectral clustering and the high-dimensional stochastic blockmodel. Annals of Statistics, 39(4):1878–1915.
   Web of Science ®Google Scholar
• Sarkar, P., and Moore, A. W. (2005), “Dynamic Social Network Analysis using Latent Space Models,” Acm Sigkdd Explorations Newsletter, 7, 31–40. DOI: 10.1145/1117454.1117459.
   Google Scholar
• Sewell, D. K., and Chen, Y. (2015), “Latent Space Models for Dynamic Networks,” Journal of the American Statistical Association, 110, 1646–1657. DOI: 10.1080/01621459.2014.988214.
   Web of Science ®Google Scholar
• Tang, R., Tang, M., Vogelstein, J. T., and Priebe, C. E. (2017), “Robust Estimation from Multiple Graphs Under Gross Error Contamination,” arXiv preprint arXiv:1707.03487.
   Google Scholar
• Wang, D., Yu, Y., and Rinaldo, A. (2018), “Optimal Change Point Detection and Localization in Sparse Dynamic Networks,” arXiv preprint arXiv:1809.09602.
   Google Scholar
• Wang, H., Tang, M., Park, Y., and Priebe, C. E. (2013), “Locality Statistics for Anomaly Detection in Time Series of Graphs,” IEEE Transactions on Signal Processing, 62, 703–717. DOI: 10.1109/TSP.2013.2294594.
   Web of Science ®Google Scholar
• Wang, L., Zhang, Z., and Dunson, D. (2019), “Common and Individual Structure of Brain Networks,” The Annals of Applied Statistics, 13, 85–112. DOI: 10.1214/18-AOAS1193.
   Web of Science ®Google Scholar
• Wang, M., and Li, L. (2020), “Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality,” Journal of Machine Learning Research, 21, 1–38.
   PubMed Web of Science ®Google Scholar
• Wang, Y., Chakrabarti, A., Sivakoff, D., and Parthasarathy, S. (2017), “Fast Change Point Detection on Dynamic Social Networks,” arXiv preprint arXiv:1705.07325.
   Google Scholar
• Wilson, J. D., Stevens, N. T., and Woodall, W. H. (2019), “Modeling and Detecting Change in Temporal Networks via the Degree Corrected Stochastic Block Model,” Quality and Reliability Engineering International, 35, 1363–1378. DOI: 10.1002/qre.2520.
   Web of Science ®Google Scholar
• Xia, D. (2019), “Normal Approximation and Confidence Region of Singular Subspaces,” arXiv preprint arXiv:1901.00304.
   Google Scholar
• Xia, D., and Yuan, M. (2019), “On Polynomial Time Methods for Exact Low-Rank Tensor Completion,” Foundations of Computational Mathematics, 19, 1265–1313. DOI: 10.1007/s10208-018-09408-6.
   Web of Science ®Google Scholar
• Xu, K. (2015), “Stochastic Block Transition Models for Dynamic Networks,” in Artificial Intelligence and Statistics, pp. 1079–1087, PMLR.
   Google Scholar
• Yuan, M., Liu, R., Feng, Y., and Shang, Z. (2018), “Testing Community Structures for Hypergraphs,” arXiv preprint arXiv:1810.04617.
   Google Scholar
• Zhang, A., and Xia, D. (2018), “Tensor SVD: Statistical and Computational Limits,” IEEE Transactions on Information Theory, 64, 7311–7338. DOI: 10.1109/TIT.2018.2841377.
   Web of Science ®Google Scholar
• Zhang, J., and Cao, J. (2017), “Finding Common Modules in a Time-Varying Network with Application to the Drosophila Melanogaster Gene Regulation Network,” Journal of the American Statistical Association, 112, 994–1008. DOI: 10.1080/01621459.2016.1260465.
   Web of Science ®Google Scholar
• Zhang, X., Xu, G., and Zhu, J. (2021), “Joint Latent Space Models for Network Data with High-Dimensional Node Variables,” Biometrika, 109, 707–720. DOI: 10.1093/biomet/asab063.
   Web of Science ®Google Scholar
• Zhang, X., Xue, S., and Zhu, J. (2020), “A Flexible Latent Space Model for Multilayer Networks,” in International Conference on Machine Learning, pp. 11288–11297. PMLR.
   Google Scholar
• Zhang, Y., Levina, E., and Zhu, J. (2016), “Community Detection in Networks with Node Features,” Electronic Journal of Statistics, 10, 3153–3178. DOI: 10.1214/16-EJS1206.
   Web of Science ®Google Scholar
• Zhang, Y., Levina, E., and Zhu, J. (2020), “Detecting Overlapping Communities in Networks using Spectral Methods,” SIAM Journal on Mathematics of Data Science, 2, 265–283.
   Google Scholar
• Zhao, Y., Wu, Y.-J., Levina, E., and Zhu, J. (2017), “Link Prediction for Partially Observed Networks,” Journal of Computational and Graphical Statistics, 26, 725–733. DOI: 10.1080/10618600.2017.1286243.
   Web of Science ®Google Scholar
• Zhao, Z., Chen, L., and Lin, L. (2019), “Change-Point Detection in Dynamic Networks via Graphon Estimation,” arXiv preprint arXiv:1908.01823.
   Google Scholar
• Zhen, Y., and Wang, J. (2021), “Community Detection in General Hypergraph via Graph Embedding,” arXiv preprint arXiv:2103.15035. DOI: 10.1080/01621459.2021.2002157.
   Google Scholar