Distributed Learning for Principal Eigenspaces without Moment Constraints

References

• Alimisis, F., Davies, P., and Alistarh, D. (2021), “Communication-Efficient Distributed Optimization with Quantized Preconditioners,” in Proceedings of the 38th International Conference on Machine Learning, Volume 139 of Proceedings of Machine Learning Research, PMLR, pp. 196–206.
   Google Scholar
• Alimisis, F., Davies, P., Vandereycken, B., and Alistarh, D. (2021), “Distributed Principal Component Analysis with Limited Communication,” in Advances in Neural Information Processing Systems (Vol. 34), Curran Associates, Inc., pp. 2823–2834.
   Google Scholar
• Anderson, T. W. (1963), “Asymptotic Theory for Principal Component Analysis,” The Annals of Mathematical Statistics, 34, 122–148. DOI: 10.1214/aoms/1177704248.
   Google Scholar
• Bai, Z., Choi, K. P., and Fujikoshi, Y. (2018), “Consistency of AIC and BIC in Estimating the Number of Significant Components in High-Dimensional Principal Component Analysis,” The Annals of Statistics, 46, 1050–1076. DOI: 10.1214/17-AOS1577.
   Web of Science ®Google Scholar
• Bao, Z., Ding, X., Wang, J., and Wang, K. (2022), “Statistical Inference for Principal Components of Spiked Covariance Matrices,” The Annals of Statistics, 50, 1144–1169. DOI: 10.1214/21-AOS2143.
   Web of Science ®Google Scholar
• Bertrand, A., and Moonen, M. (2014), “Distributed Adaptive Estimation of Covariance Matrix Eigenvectors in Wireless Sensor Networks with Application to Distributed PCA,” Signal Processing, 104, 120–135. DOI: 10.1016/j.sigpro.2014.03.037.
   Web of Science ®Google Scholar
• Birnbaum, A., Johnstone, I. M., Nadler, B., and Paul, D. (2013), “Minimax Bounds for Sparse PCA with Noisy High-Dimensional Data,” Annals of Statistics, 41, 1055. DOI: 10.1214/12-AOS1014.
   PubMed Web of Science ®Google Scholar
• Cai, T. T., and Wei, H. (2022a), “Distributed Adaptive Gaussian Mean Estimation with Unknown Variance: Interactive Protocol Helps Adaptation,” The Annals of Statistics, 50, 1992–2020. DOI: 10.1214/21-AOS2167.
   Web of Science ®Google Scholar
• Cai, T. T., and Wei, H. (2022b), “Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation,” The Annals of Statistics, 50, 698–725.
   Web of Science ®Google Scholar
• Chen, X., Zhang, J., and Zhou, W. (2021), “High-Dimensional Elliptical Sliced Inverse Regression in Non-Gaussian Distributions,” Journal of Business & Economic Statistics, 40, 1204–1215. DOI: 10.1080/07350015.2021.1910041.
   Web of Science ®Google Scholar
• Choi, K., and Marden, J. (1998), “A Multivariate Version of Kendall’s τ,” Journal of Nonparametric Statistics, 9, 261–293. DOI: 10.1080/10485259808832746.
   Web of Science ®Google Scholar
• Davies, P., Gurunanthan, V., Moshrefi, N., Ashkboos, S., and Alistarh, D. (2021), “New Bounds for Distributed Mean Estimation and Variance Reduction,” in International Conference on Learning Representations.
   Google Scholar
• Davies, P., Gurunathan, V., Moshrefi, N., Ashkboos, S., and Alistarh, D. (2020), “New Bounds for Distributed Mean Estimation and Variance Reduction,” arXiv preprint arXiv:2002.09268.
   Google Scholar
• Fan, J., Guo, Y., and Wang, K. (2021), “Communication-Efficient Accurate Statistical Estimation,” Journal of the American Statistical Association, 118, 1000–1010. DOI: 10.1080/01621459.2021.1969238.
   PubMed Web of Science ®Google Scholar
• Fan, J., Liu, H., and Wang, W. (2018), “Large Covariance Estimation through Elliptical Factor Models,” Annals of Statistics, 46, 1383–1414.
   PubMed Web of Science ®Google Scholar
• Fan, J., Wang, D., Wang, K., and Zhu, Z. (2019), “Distributed Estimation of Principal Eigenspaces,” Annals of Statistics, 47, 3009–3031.
   PubMed Web of Science ®Google Scholar
• Feng, L., and Liu, B. (2017), “High-Dimensional Rank Tests for Sphericity,” Journal of Multivariate Analysis, 155, 217–233. DOI: 10.1016/j.jmva.2017.01.003.
   Web of Science ®Google Scholar
• Fonseca, R., and Nadler, B. (2023), “Distributed Sparse Linear Regression Under Communication Constraints.”
   Google Scholar
• Hallin, M., Paindaveine, D., and Verdebout, T. (2010), “Optimal Rank-based Testing for Principal Components,” The Annals of Statistics, 38, 3245–3299. DOI: 10.1214/10-AOS810.
   Web of Science ®Google Scholar
• Hallin, M., Paindaveine, D., and Verdebout, T. (2014), “Efficient r-estimation of Principal and Common Principal Components,” Journal of the American Statistical Association, 109, 1071–1083. DOI: 10.1080/01621459.2014.880057.
   Web of Science ®Google Scholar
• Han, F., and Liu, H. (2014), “Scale-Invariant Sparse PCA on High-Dimensional Meta-Elliptical Data,” Journal of the American Statistical Association, 109, 275–287. DOI: 10.1080/01621459.2013.844699.
   PubMed Web of Science ®Google Scholar
• Han, F., and Liu, H. (2018), “Eca: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions,” Journal of the American Statistical Association, 113, 252–268. DOI: 10.1080/01621459.2016.1246366.
   Web of Science ®Google Scholar
• He, Y., Kong, X., Yu, L., and Zhang, X. (2022), “Large-Dimensional Factor Analysis Without Moment Constraints,” Journal of Business & Economic Statistics, 40, 302–312. DOI: 10.1080/07350015.2020.1811101.
   Web of Science ®Google Scholar
• Hu, J., Li, W., Liu, Z., and Zhou, W. (2019), “High-Dimensional Covariance Matrices in Elliptical Distributions with Application to Spherical Test,” The Annals of Statistics, 47, 527–555. DOI: 10.1214/18-AOS1699.
   Web of Science ®Google Scholar
• Hult, H., and Lindskog, F. (2002), “Multivariate Extremes, Aggregation and Dependence in Elliptical Distributions,” Advances in Applied Probability, 34, 587–608. DOI: 10.1239/aap/1033662167.
   Web of Science ®Google Scholar
• Jing, B.-Y., Kong, X.-B., and Liu, Z. (2012), “Modeling High-Frequency Financial Data by Pure Jump Processes,” The Annals of Statistics, 40, 759–784. DOI: 10.1214/12-AOS977.
   Web of Science ®Google Scholar
• Jordan, M. I., Lee, J. D., and Yang, Y. (2018), “Communication-Efficient Distributed Statistical Inference,” Journal of the American Statistical Association, 114, 668–681. DOI: 10.1080/01621459.2018.1429274.
   Web of Science ®Google Scholar
• Kong, X.-B., Lin, J.-G., Liu, C., and Liu, G.-Y. (2021), “Discrepancy between Global and Local Principal Component Analysis on Large-Panel High-Frequency Data,” Journal of the American Statistical Association, 118, 1333–1344. DOI: 10.1080/01621459.2021.1996376.
   Web of Science ®Google Scholar
• Kong, X.-B., Liu, Z., and Jing, B.-Y. (2015), “Testing for Pure-Jump Processes for High-Frequency Data,” The Annals of Statistics, 43, 847–877. DOI: 10.1214/14-AOS1298.
   Web of Science ®Google Scholar
• Li, L., Scaglione, A., and Manton, J. H. (2011), “Distributed Principal Subspace Estimation in Wireless Sensor Networks,” IEEE Journal of Selected Topics in Signal Processing, 5, 725–738. DOI: 10.1109/JSTSP.2011.2118742.
   Web of Science ®Google Scholar
• Li, Z., He, Y., Kong, X., and Zhang, X. (2022), “Manifold Principle Component Analysis for Large-Dimensional Matrix Elliptical Factor Model,” arXiv preprint arXiv:2203.14063.
   Google Scholar
• Onatski, A. (2012), “Asymptotics of the Principal Components Estimator of Large Factor Models with Weakly Influential Factors,” Journal of Econometrics, 168, 244–258. DOI: 10.1016/j.jeconom.2012.01.034.
   Web of Science ®Google Scholar
• Qu, Y., Ostrouchov, G., Samatova, N., and Geist, A. (2002), “Principal Component Analysis for Dimension Reduction in Massive Distributed Data Sets,” in Proceedings of IEEE International Conference on Data Mining (ICDM) (Vol. 1318), p. 1788.
   Google Scholar
• Schizas, I. D., and Aduroja, A. (2015), “A Distributed Framework for Dimensionality Reduction and Denoising,” IEEE Transactions on Signal Processing, 63, 6379–6394. DOI: 10.1109/TSP.2015.2465300.
   Web of Science ®Google Scholar
• Shen, D., Shen, H., Zhu, H., and Marron, J. (2016), “The Statistics and Mathematics of High Dimension Low Sample Size Asymptotics,” Statistica Sinica, 26, 1747–1770. DOI: 10.5705/ss.202015.0088.
   PubMed Web of Science ®Google Scholar
• Stock, J. H., and Watson, M. W. (2002), “Macroeconomic Forecasting Using Diffusion Indexes,” Journal of Business & Economic Statistics, 20, 147–162. DOI: 10.1198/073500102317351921.
   Web of Science ®Google Scholar
• Szabó, B., Vuursteen, L., and van Zanten, H. (2022), “Optimal High-Dimensional and Nonparametric Distributed Testing under Communication Constraints,” arXiv preprint arXiv:2202.00968.
   Google Scholar
• Taskinen, S., Koch, I., and Oja, H. (2012), “Robustifying Principal Component Analysis with Spatial Sign Vectors,” Statistics & Probability Letters, 82, 765–774. DOI: 10.1016/j.spl.2012.01.001.
   Web of Science ®Google Scholar
• Visuri, S., Koivunen, V., and Oja, H. (2000), “Sign and Rank Covariance Matrices,” Journal of Statistical Planning and Inference, 91, 557–575. DOI: 10.1016/S0378-3758(00)00199-3.
   Web of Science ®Google Scholar
• Wang, W., and Fan, J. (2017), “Asymptotics of Empirical Eigenstructure for High Dimensional Spiked Covariance,” Annals of Statistics, 45, 1342–1374.
   PubMed Web of Science ®Google Scholar
• Wang, W., and Fan, J. (2017b), “Asymptotics of Empirical Eigenstructure for High Dimensional Spiked Covariance,” Annals of statistics, 45, 1342.
   PubMed Web of Science ®Google Scholar
• Yu, L., He, Y., and Zhang, X. (2019), “Robust Factor Number Specification for Large-Dimensional Elliptical Factor Model,” Journal of Multivariate analysis, 174, 104543. DOI: 10.1016/j.jmva.2019.104543.
   Web of Science ®Google Scholar
• Zhang, Y., Wainwright, M. J., and Duchi, J. C. (2012), “Communication-Efficient Algorithms for Statistical Optimization,” in Advances in Neural Information Processing Systems (Vol. 25).
   PubMedGoogle Scholar