Generalized Low-Rank Plus Sparse Tensor Estimation by Fast Riemannian Optimization

References

• Anandkumar, A., Ge, R., Hsu, D., Kakade, S. M., and Telgarsky, M. (2014), “Tensor Decompositions for Learning Latent Variable Models,” Journal of Machine Learning Research, 15, 2773–2832.
   Web of Science ®Google Scholar
• Bi, X., Qu, A., and Shen, X. (2018), “Multilayer Tensor Factorization with Applications to Recommender Systems,” Annals of Statistics, 46, 3308–3333.
   Web of Science ®Google Scholar
• Bi, X., Tang, X., Yuan, Y., Zhang, Y., and Qu, A. (2020), “Tensors in Statistics,” Annual Review of Statistics and Its Application, 8, 345–368. DOI: 10.1146/annurev-statistics-042720-020816.
   Web of Science ®Google Scholar
• Cai, C., Li, G., Vincent Poor, H., and Chen, Y. (2019), “Nonconvex Low-rank Tensor Completion from Noisy Data,” in Advances in Neural Information Processing Systems, pp. 1863–1874.
   Google Scholar
• Cai, J.-F., Miao, L., Wang, Y., and Xian, Y. (2020), “Provable Near-Optimal Low-Multilinear-Rank Tensor Recovery,” arXiv preprint arXiv:2007.08904.
   Google Scholar
• Candès, E. J., Li, K., Ma, Y., and Wright, J. (2011), “Robust Principal Component Analysis?” Journal of the ACM, 58, 1–37. DOI: 10.1145/1970392.1970395.
   Web of Science ®Google Scholar
• Cattell, R. B. (1966), “The Scree Test for the Number of Factors,” Multivariate Behavioral Research, 1, 245–276. DOI: 10.1207/s15327906mbr0102_10.
   PubMed Web of Science ®Google Scholar
• Chen, H., Raskutti, G., and Yuan, M. (2019), “Non-convex Projected Gradient Descent for Generalized Low-Rank Tensor Regression,” The Journal of Machine Learning Research, 20, 172–208.
   Web of Science ®Google Scholar
• Chen, Y., Fan, J., Ma, C., and Yan, Y. (2020), “Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data,” arXiv preprint arXiv:2001.05484.
   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
• Edelman, A., Arias, T., 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
• Fan, X., Pensky, M., Yu, F., and Zhang, T. (2021), “Alma: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network,” arXiv preprint arXiv:2102.10226.
   Google Scholar
• Gu, Q., Gui, H., and Han, J. (2014), “Robust Tensor Decomposition with Gross Corruption,” Advances in Neural Information Processing Systems, 27, 1422–1430.
   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
• Hao, B., Zhang, A., and Cheng, G. (2020), “Sparse and Low-Rank Tensor Estimation via Cubic Sketchings,” IEEE Transactions on Information Theory, 66, 5927–5964. DOI: 10.1109/tit.2020.2982499.
   PubMed 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
• Jin, J. (2015), “Fast Community Detection by Score,” Annals of Statistics, 43, 57–89.
   Web of Science ®Google Scholar
• Jing, B.Y., Li, T., Lyu, Z., and Xia, D. (2020), “Community Detection on Mixture Multi-Layer Networks via Regularized Tensor Decomposition,” arXiv preprint arXiv:2002.04457.
   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
• 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
• Kressner, D., Steinlechner, M., and Vandereycken, B. (2014), “Low-Rank Tensor Completion by Riemannian Optimization,” BIT Numerical Mathematics, 54, 447–468. DOI: 10.1007/s10543-013-0455-z.
   Web of Science ®Google Scholar
• Li, X., Xu, D., Zhou, H., and Li, L. (2018), “Tucker Tensor Regression and Neuroimaging Analysis,” Statistics in Biosciences, 10, 520–545. DOI: 10.1007/s12561-018-9215-6.
   PubMed Web of Science ®Google Scholar
• Liu, T., Yuan, M., and Zhao, H. (2017), “Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition,” arXiv preprint arXiv:1702.07449.
   Google Scholar
• Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z., and Yan, S. (2016), “Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5249–5257.
   Google Scholar
• Luo, Y., and Zhang, A. R. (2020), “Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits,” arXiv preprint arXiv:2005.10743.
   Google Scholar
• Pan, Y., Mai, Q., and Zhang, X. (2018), “Covariate-Adjusted Tensor Classification in High Dimensions,” Journal of the American Statistical Association, 114, 1305–1319. DOI: 10.1080/01621459.2018.1497500.
   Web of Science ®Google Scholar
• Paul, S., and Chen, Y. (2020), “Spectral and Matrix Factorization Methods for Consistent Community Detection in Multi-Layer Networks,” The Annals of Statistics, 48, 230–250. DOI: 10.1214/18-AOS1800.
   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
• Raskutti, G., Yuan, M., and Chen, H. (2019), “Convex Regularization for High-Dimensional Multiresponse Tensor Regression,” The Annals of Statistics, 47, 1554–1584. DOI: 10.1214/18-AOS1725.
   Web of Science ®Google Scholar
• Richard, E., and Montanari, A. (2014), “A Statistical Model for Tensor PCA,” Advances in Neural Information Processing Systems, 27, 2897–2905.
   Google Scholar
• Robin, G., Klopp, O., Josse, J., Moulines, E., and Tibshirani, R. (2020), “Main Effects and Interactions in Mixed and Incomplete Data Frames,” Journal of the American Statistical Association, 115, 1292–1303. DOI: 10.1080/01621459.2019.1623041.
   Web of Science ®Google Scholar
• Sun, W. W., and Li, L. (2019), “Dynamic Tensor Clustering,” Journal of the American Statistical Association, 114, 1894–1907. DOI: 10.1080/01621459.2018.1527701.
   Web of Science ®Google Scholar
• Sun, W. W., Lu, J., Liu, H., and Cheng, G. (2017), “Provable Sparse Tensor Decomposition,” Journal of the Royal Statistical Society, Series B, 79, 899–916. DOI: 10.1111/rssb.12190.
   Google Scholar
• Vershynin, R. (2011), “Spectral Norm of Products of Random and Deterministic Matrices,” Probability Theory and Related Fields, 150, 471–509. DOI: 10.1007/s00440-010-0281-z.
   Web of Science ®Google Scholar
• Vershynin, R. (2018), High-Dimensional Probability: An Introduction with Applications in Data Science (Vol. 47), Cambridge: Cambridge University Press.
   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, M., and Zeng, Y. (2019), “Multiway Clustering via Tensor Block Models,” arXiv preprint arXiv:1906.03807.
   Google Scholar
• Xia, D. (2019), “Normal Approximation and Confidence Region of Singular Subspaces,” Electronic Journal of Statistics, 15, 3798–3851.
   Web of Science ®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
• Xia, D., Yuan, M., and Zhang, C-H. (2021), “Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries,” Annals of Statistics, 49, 76–99.
   Web of Science ®Google Scholar
• Xia, D., Zhang, A. R., and Zhou, Y. (2020), “Inference for Low-Rank Tensors–No Need to Debias,” arXiv preprint arXiv:2012.14844.
   Google Scholar
• Xia, D., and Zhou, F. (2019), “The Sup-norm Perturbation of HOSVD and Low Rank Tensor Denoising,” Journal of Machine Learning Research, 20, 1–42.
   Web of Science ®Google Scholar
• Yu, R., and Liu, Y. (2016), “Learning from Multiway Data: Simple and Efficient Tensor Regression,” in International Conference on Machine Learning, pp. 373–381.
   Google Scholar
• Yuan, M., and Zhang, C.-H. (2017), “Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion,” IEEE Transactions on Information Theory, 63, 6753–6766. DOI: 10.1109/TIT.2017.2724549.
   Web of Science ®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, A. R., Luo, Y., Raskutti, G., and Yuan, M. (2020), “Islet: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching,” SIAM Journal on Mathematics of Data Science, 2, 444–479. DOI: 10.1137/19M126476X.
   Google Scholar
• Zhang, C., Han, R., Zhang, A. R., and Voyles, P. M. (2020), “Denoising Atomic Resolution 4D Scanning Transmission Electron Microscopy Data with Tensor Singular Value Decomposition,” Ultramicroscopy, 219, 113123. DOI: 10.1016/j.ultramic.2020.113123.
   PubMed Web of Science ®Google Scholar
• Zhang, X., Wang, L., and Gu, Q. (2018), “A Unified Framework for Nonconvex Low-Rank Plus Sparse Matrix Recovery,” in International Conference on Artificial Intelligence and Statistics, pp. 1097–1107. PMLR.
   Google Scholar
• Zhou, H., Li, L., and Zhu, H. (2013), “Tensor Regression with Applications in Neuroimaging Data Analysis,” Journal of the American Statistical Association, 108, 540–552. DOI: 10.1080/01621459.2013.776499.
   PubMed Web of Science ®Google Scholar
• Zhou, P., and Feng, J. (2017), “Outlier-Robust Tensor PCA,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2263–2271.
   Google Scholar