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Recent Advances in Big Data Analytics

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The Palgrave Handbook of Operations Research

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Abstract

Unprecedented advances in digital technology have produced a revolution that is transforming science and society. Big data have been rapidly generated in many disciplines, such as business, sciences, engineering, medicine, biology, and humanities. It is often accompanied by a large number of features and/or a large volume of observations. The value of big data lies in effective analysis using statistical inference and machine learning methods that are computationally scalable and efficient. There have seen many new statistical methods and tools to deal with big data in recent years. In this chapter, we aim to summarize some of these approaches to provide a selective overview of the recent developments of theory, methods, and implementations for big data analytics. We will focus on two types of big data: ultrahigh-dimensional data and massive data, where the former refers to the data in which the number of features may grow exponentially with the number of observations while the latter means that the number of observations is huge and much larger than the number of features.

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References

  1. Ai, M., Yu, J., Zhang, H., and Wang, H. (2021). Optimal subsampling algorithms for Big Data regressions. Stat. Sin. 31, 749–772.

    Google Scholar 

  2. Battey, H., Fan, J., Liu, H., Lu, J., and Zhu, Z. (2018). Distributed testing and estimation under sparse high dimensional models. Ann. Stat. 46, 1352–1382.

    Article  Google Scholar 

  3. Bickel, P. J. and Levina, E. (2008). Regularized estimation of large covariance matrices. Ann. Stat. 36, 199–227.

    Google Scholar 

  4. Bien, J., Taylor, J., and Tibshirani, R. (2013). A lasso for hierarchical interactions. Ann. Stat. 41, 1111–1141.

    Article  Google Scholar 

  5. Bühlmann, P. and Van De Geer, S. (2011). Statistics for high-dimensional data: methods, theory and applications, Springer Science & Business Media.

    Google Scholar 

  6. Cai, T., Liu, W., and Luo, X. (2011). A constrained \(\ell _1\) minimization approach to sparse precision matrix estimation. J. Amer. Statist. Assoc. 106, 594–607.

    Article  Google Scholar 

  7. Candés, E. and Tao, T. (2007). The Dantzig selector: Statistical estimation when \(p\) is much larger than \(n\). Ann. Stat. 35, 2313–2351.

    Google Scholar 

  8. Chen, L. and Zhou, Y. (2021). Quantile regression in big data: A divide and conquer based strategy. Comput. Statist. Data Anal. 144, 106892.

    Article  Google Scholar 

  9. Chen, X., Lee, J. D., Li, H., and Yang, Y. (2021). Distributed estimation for principal component analysis: an enlarged eigenspace analysis. J. Amer. Statist. Assoc., to appear.

    Google Scholar 

  10. Chen, X., Liu, W., and Zhang, Y. (2019). Quantile regression under memory constraint. Ann. Stat. 47, 3244–3273.

    Google Scholar 

  11. Chen, X. and Xie, M. (2014). A split-and-conquer approach for analysis of extraordinarily large data. Stat. Sin. 24, 1655–1684.

    Google Scholar 

  12. Chu, W., Li, R., Liu, J. and Reimherr, M. (2020). Feature screening for generalized varying coefficient mixed effect models with application to obesity GWAS. Ann. Appl. Stat. 14, 276–298.

    Article  Google Scholar 

  13. Cordell, H. J. (2009). Detecting gene-gene interactions that underlie human diseases. Nat. Rev. Genet. 10, 392–404.

    Article  Google Scholar 

  14. Cui, H., Li, R., and Zhong, W. (2015). Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis. J. Amer. Statist. Assoc. 110, 630–641.

    Article  Google Scholar 

  15. Donoho, D. L. (2000). High-dimensional data analysis: The curses and blessings of dimensionality; Aide-Memoire of a Lecture at AMS Conference on Math Challenges of the 21st Century.

    Google Scholar 

  16. Dong, R., Li, D., and Zheng, D. (2021). Parallel integrative learning for large-scale multi-response regression with incomplete outcomes. Comput. Statist. Data Anal. 160, 107243.

    Article  Google Scholar 

  17. Drineas, P., Mahoney, M. W., and Muthukrishnan, S. (2006). Sampling algorithms for \(\ell _2\) regression and applications. In Proceedings of the seventeenth annual ACM-SIAM symposium on discrete algorithm, 1127–1136.

    Google Scholar 

  18. Drineas, P., Magdon-Ismail, M., Mahoney, M. W., and Woodruff, D. P. (2012). Fast approximation of matrix coherence and statistical leverage. J. Mach. Learn. Res. 13, 3475–3506.

    Google Scholar 

  19. Drineas, P., Mahoney M.W., Muthukrishnan S, and Sarlós, T. (2011). Faster least squares approximation. Numer. Math. 117, 219–249.

    Article  Google Scholar 

  20. Fan, J., Feng, Y., and Xia, L. (2020). A projection-based conditional dependence measure with applications to high-dimensional undirected graphical models. J. Econometrics 218, 119–139.

    Article  Google Scholar 

  21. Fan, J., Feng, Y., and Song, R. (2011). Nonparametric independence screening in sparse ultra-high dimensional additive models. J. Amer. Statist. Assoc. 106, 544–557.

    Article  Google Scholar 

  22. Fan, J., Han, F., and Liu, H. (2014). Challenges of big data analysis. Natl. Sci. Rev. 1, 293-314.

    Article  Google Scholar 

  23. Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96, 1348–1360.

    Article  Google Scholar 

  24. Fan, J. and Li, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. In: Sanz-Sole M, Soria J, Varona JL, Verdera J, editors. Proceedings of the International Congress of Mathematicians, 595–622.

    Google Scholar 

  25. Fan, J., Li, R., Zhang, C.-H., and Zou, H. (2020). Statistical Foundations of Data Science. CRC Press.

    Book  Google Scholar 

  26. Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space (with discussion). J. R. Stat. Soc., Ser. B 70, 849-911.

    Google Scholar 

  27. Fan, J. and Lv, J. (2010). A selective overview of variable selection in high dimensional feature space (invited review article). Stat. Sin. 20, 101–148.

    Google Scholar 

  28. Fan, J. and Lv, J. (2018). Sure independence screening (invited review article). Wiley StatsRef: Statistics Reference Online.

    Google Scholar 

  29. Fan, J., Lv, J., and Qi, L. (2011). Sparse high dimensional models in economics (invited review article). Annu. Rev. Econ. 3, 291–317.

    Article  Google Scholar 

  30. Fan, J., Ma, Y., and Dai, W. (2014). Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models. J. Amer. Statist. Assoc. 109, 1270–1284.

    Article  Google Scholar 

  31. Fan, J. and Song, R. (2010). Sure independence screening in generalized linear models with NP-dimensionality. Ann. Stat. 38, 3567–3604.

    Google Scholar 

  32. Fang, X. and Xu, J. Joint variable screening in accelerated failure time models. Stat. Sin. 30, 467–485.

    Google Scholar 

  33. Fan, Y., Kong, Y., Li, D., and Zheng, Z. (2015). Innovated interaction screening for high-dimensional nonlinear classification. Ann. Stat. 43, 1243–1272.

    Google Scholar 

  34. Fan, Y. and Lv, J. (2016). Innovated scalable efficient estimation in ultra-large Gaussian graphical models. Ann. Stat. 44, 2098–2126.

    Google Scholar 

  35. Friedman, J., Hastie, T, and Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432–441.

    Article  Google Scholar 

  36. Gorst-Rasmussen, A. and Scheike, T. (2013). Independent screening for single-index hazard rate models with ultrahigh dimensional features. J. R. Stat. Soc., Ser. B 75, 217–245.

    Google Scholar 

  37. Gosik, K., Sun, L., Chinchilli, V. M., and Wu, R. (2018). An ultrahigh-dimensional mapping model of high-order epistatic networks for complex traits. Curr. Genomics 19, 384–394.

    Article  Google Scholar 

  38. Hall, P. and Xue, J.-H. (2014). On selecting interacting features from high-dimensional data. Comput. Stat. Data Anal. 71, 694–708.

    Article  Google Scholar 

  39. Hao, N., Feng, Y., and Zhang, H.H. (2018). Model selection for high dimensional quadratic regression via regularization. J. Amer. Statist. Assoc. 113, 615–625.

    Article  Google Scholar 

  40. Hao, N. and Zhang, H.H. (2014). Interaction screening for ultra-high dimensional data. J. Amer. Statist. Assoc. 109, 1285–1301.

    Article  Google Scholar 

  41. Haris, A., Witten, D., and Simon, N. (2016). Convex modeling of interactions with strong heredity. J. Comput. Graph. Stat. 25, 981–1004.

    Article  Google Scholar 

  42. He, X., Wang, L. and Hong, H. G. (2013). Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data. Ann. Stat. 41, 342–369.

    Google Scholar 

  43. Hector, E. and Song, P. (2021). A distributed and integrated method of moments for high-dimensional correlated data analysis. J. Amer. Statist. Assoc. 116, 805–818.

    Article  Google Scholar 

  44. Huang, D., Zhu, X., Li, R., and Wang, H. (2021). Feature screening for network autoregression model. Stat. Sin. 31, 1–21.

    Google Scholar 

  45. Huo, X. and Székely, G. J. (2016). Fast Computing for Distance Covariance. Technometrics 58, 435–447.

    Article  Google Scholar 

  46. Jiang, B. and Liu, J. S. (2014). Variable selection for general index models via sliced inverse regression. Ann. Stat. 42, 1751–1786.

    Google Scholar 

  47. Jordan, M. I., Lee, J. D., and Yang, Y. (2019). Communication-efficient distributed statistical learning. J. Amer. Statist. Assoc. 114, 668–681.

    Article  Google Scholar 

  48. Kong, Y., Li, D., Fan, Y., and Lv, J. (2017). Interaction pursuit in high-dimensional multi-response regression via distance correlation. Ann. Stat. 45, 897–922.

    Google Scholar 

  49. Lee, J. D., Liu, Q., Sun, Y., and Taylor, J. E. (2017). Communication-efficient sparse regression. J. Mach. Learn. Res. 18, 1–30.

    Google Scholar 

  50. Lee, J., Wang, H., and Schifano, E. (2020). Online updating method to correct for measurement error in big data streams. Comput. Statist. Data Anal. 149, 106976

    Article  Google Scholar 

  51. Li, D., Kong, Y., Fan, Y., and Lv, J. (2021). High-dimensional interaction detection with false sign rate control. J. Bus. Econom. Statist., in press.

    Google Scholar 

  52. Li, G., Peng, H., Zhang, J., and Zhu, L-X. (2012). Robust rank correlation based screening. Ann. Stat. 40, 1846–1877.

    Google Scholar 

  53. Li, J., Zhong, W., Li, R. and Wu, R. (2014). A fast algorithm for detecting gene-gene interactions in genome-wide association studies. Ann. Appl. Stat. 8, 2292–2318.

    Article  Google Scholar 

  54. Li, R., Zhong, W., and Zhu, L.P. (2012). Feature screening via distance correlation Learning. J. Amer. Statist. Assoc. 107, 1129–1139.

    Article  Google Scholar 

  55. Li, X., Li, R., Xia, Z., and Xu, C. (2020). Distributed feature screening via componentwise debiasing. J. Mach. Learn. Res. 21, 1–32.

    Google Scholar 

  56. Lin, N. and Xi, R. (2011). Aggregated estimating equation estimation. Stat. Interface 4, 73–83.

    Google Scholar 

  57. Liu, J., Li, R., and Wu, R. (2014). Feature selection for varying coefficient models with ultrahigh-dimensional covariates. J. Amer. Statist. Assoc. 109, 266–274.

    Article  Google Scholar 

  58. Liu, J., Zhong, W., and Li, R. (2015). A selective overview of feature screening for ultrahigh-dimensional data. Sci. China Math. 58, 1–22.

    Article  Google Scholar 

  59. Liu, W., Ke, Y., Liu, J., and Li, R. (2020). Model-free feature screening and FDR control with Knockoff features. J. Amer. Statist. Assoc., in press.

    Google Scholar 

  60. Liu, W. and Li, R. (2020). Variable Selection and Feature Screening. Macroeconomic Forecasting in the Era of Big Data, 293–326.

    Google Scholar 

  61. Lv, J., and Fan, Y. (2009). A unified approach to model selection and sparse recovery using regularized least squares. Ann. Stat., 37, 3498–3528.

    Article  Google Scholar 

  62. Ma, P., Mahoney, M. W., and Yu, B. (2015). A statistical perspective on algorithmic leveraging. J. Mach. Learn. Res. 16, 861–911.

    Google Scholar 

  63. Ma, P. and Sun, X. (2015). Leveraging for big data regression. Wiley Interdisciplinary Reviews: Computational Statistics 7, 70–76.

    Article  Google Scholar 

  64. Ma, P. , Zhang, X., Xing, X., Ma, J., and Mahoney, M. (2020). Asymptotic analysis of sampling estimators for randomized linear algebra algorithms, AISTATS, 1026–1035.

    Google Scholar 

  65. Ma, S., Li, R. and Tsai, C.L. (2017). Variable Screening via quantile partial correlation. J. Amer. Statist. Assoc. 112, 650–663.

    Article  Google Scholar 

  66. Mai, Q. and Zou, H. (2011). The Kolmogorov filter for variable screening in high-dimensional binary classification. Biometrika 100, 229–234.

    Article  Google Scholar 

  67. Mai, Q. and Zou, H. (2015). The fused Kolmogorov filter: A nonparametric model-free screening method. Ann. Stat. 43, 1471–1497.

    Article  Google Scholar 

  68. Musani, S. K., Shriner, D., Liu, N., Feng, R., Coffey, C. S., Yi, N., Tiwari, H. K., and Allison, D. B. (2007). Detection of gene\(\times\)gene interactions in genome-wide association studies of human population data. Human Heredity 63, 67–84.

    Article  Google Scholar 

  69. Nandy, D., Chiaromonte, F., and Li, R. (2021). Covariate information number for feature screening in ultrahigh-dimensional supervised problems. J. Amer. Statist. Assoc., in press.

    Google Scholar 

  70. Niu, Y. S., Hao, N. and Zhang, H.H. (2018). Interaction screening by partial correlation. Stat. Interface 11, 317–325.

    Article  Google Scholar 

  71. Pan, W., Wang, X., Xiao, W., and Zhu, H. (2019). A generic sure independence screening procedure. J. Amer. Statist. Assoc. 114, 928–937.

    Article  Google Scholar 

  72. Ren, Z., Kang, Y., Fan, Y., and Lv, J. (2019). Tuning-free heterogeneous inference in massive networks. J. Amer. Statist. Assoc., 114, 1908–1925.

    Article  Google Scholar 

  73. Sheng, Y. and Wang, Q. (2020). Model-free feature screening for ultrahigh dimensional classification. J. Multivariate Anal. 178, 104618.

    Article  Google Scholar 

  74. Székely, G. J., Rizzo, M. L., and Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances.Ann. Stat. 35, 2769-2794.

    Article  Google Scholar 

  75. Song, R., Lu, W., Ma, S., and Jeng, J. (2014). Censored rank independence screening for high-dimensional survival data. Biometrika 101, 799–814.

    Article  Google Scholar 

  76. Tang, L., Zhou, L., and Song, P. (2020). Distributed simultaneous inference in generalized linear models via confidence distribution. J. Multivariate Anal. 176, 104567.

    Article  Google Scholar 

  77. Tian, Y. and Feng, Y. (2021). RaSE: A Variable Screening Framework via Random Subspace Ensembles. J. Amer. Statist. Assoc., in press.

    Google Scholar 

  78. Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. J. R. Stat. Soc., Ser. B 58, 267–288.

    Google Scholar 

  79. Wang, H. (2019). Divide-and-conquer information-based optimal subdata selection algorithm. J. Stat. Theory Pract. 13, 46.

    Article  Google Scholar 

  80. Wang, H. (2019). More efficient estimation for logistic regression with optimal subsamples. J. Mach. Learn. Res. 20, 1–59.

    Google Scholar 

  81. Wang, H. and Ma, Y. (2021). Optimal subsampling for quantile regression in big data, Biometrika, 108, 99–112.

    Article  Google Scholar 

  82. Wang, H., Yang, M., and Stufken, J. (2019). Information-based optimal subdata selection for big data linear regression. J. Amer. Statist. Assoc. 114, 26393–405.

    Google Scholar 

  83. Wang, H., Zhu, R., and Ma, P. (2018). Optimal subsampling for large sample logistic regression. J. Amer. Statist. Assoc. 113, 829-844.

    Article  Google Scholar 

  84. Wang, L., Chen, Z., Wang, C.D., and Li, R. (2020). Ultrahigh dimensional precision matrix estimation via refitted cross validation. J. Econometrics 215, 118–130.

    Article  Google Scholar 

  85. Wang, W., Lu, S.-E., Cheng, J. Q., Xie, M., and Kostis, J. (2021). Multivariate survival analysis in big data: A divide-and-combine approach. Biometrics, to appear.

    Google Scholar 

  86. Wang, X., Yang, Z., Chen, X., and Liu, W. (2019). Distributed inference for linear support vector machine. J. Mach. Learn. Res. 20, 1–41.

    Google Scholar 

  87. Wang, Y., Hong, C., Palmer, N., Di, Q., Schwartz, J., Ko-hane, I., and Cai, T. (2021). A fast divide-and-conquer sparse Cox regression. Biostatistics 22, 381–401.

    Article  Google Scholar 

  88. Wu, Y. and Yin, G. (2015). Conditional quantile screening in ultrahigh-dimensional heterogeneous data. Biometrika 102, 65–76.

    Article  Google Scholar 

  89. Xue, L. and Zou, H. (2011). Sure independence screening and compressed random sensing. Biometrika 98, 371–380.

    Article  Google Scholar 

  90. Yao, Y. and Wang, H. (2019). Optimal subsampling for softmax regression. Stat. Papers 60, 235–249.

    Article  Google Scholar 

  91. Yan, X. and Bien, J. (2017). Hierarchical sparse modeling: A choice of two group lasso formulations Stat. Sci. 32, 531–560.

    Google Scholar 

  92. Yang, G., Yang, S. and Li, R. (2020). Feature screening in ultrahigh dimensional generalized varying-coefficient models. Stat. Sin., 30, 1049–1067.

    Google Scholar 

  93. Yuan, M. (2010). High dimensional inverse covariance matrix estimation via linear programming. J. Mach. Learn. Res. 11, 2261–2286.

    Google Scholar 

  94. Zhang, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38, 894–942.

    Article  Google Scholar 

  95. Zhang, Y., Duchi, J., and Wainwright, M. (2015). Divide and conquer kernel ridge regression: A distributed algorithm with minimax optimal rates. J. Mach. Learn. Res. 16, 3299–3340.

    Google Scholar 

  96. Zhao, S.D. and Li, Y. (2012). Principled sure independence screening for Cox models with ultra-high-dimensional covariates. J. Multivariate Anal. 105, 397–411.

    Article  Google Scholar 

  97. Zhao, S. D. and Li, Y. (2014). Score test variable screening. Biometrics 70, 862–871.

    Article  Google Scholar 

  98. Zheng, Z., Zhang, J., Kong, Y., and Wu, Y. (2018). Scalable inference for massive data. Procedia Comput. Sci. 129, 81–87.

    Article  Google Scholar 

  99. Zhou, T., Zhu, L, Xu, C., and Li, R. (2020). Model-free forward screening via cumulative divergence. J. Amer. Statist. Assoc. 115, 1393–1405.

    Article  Google Scholar 

  100. Zhou, Y. and Zhu, L.P. (2018). Model-free feature screening for ultrahigh dimensional data through a modified BLUM-KIEFER-ROSENBLATT correlation. Stat. Sin. 28, 1351–1370.

    Google Scholar 

  101. Zhong, W. and Zhu, L. (2015). An iterative approach to distance correlation-based sure independence screening. J. Stat. Comput. Simul. 85, 2331–2345.

    Article  Google Scholar 

  102. Zhu, L.-P., Li, L., Li, R., and Zhu, L.-X. (2011). Model-free feature screening for ultrahigh-dimensional data. J. Amer. Statist. Assoc. 106, 1464–1475.

    Article  Google Scholar 

  103. Zhu, X., Li, F., and Wang, H. (2021). Least squares approximation for a distributed system. J. Comput. Graph. Statist., to appear.

    Google Scholar 

  104. Zou, H. (2006). The adaptive Lasso and its oracle properties. J. Amer. Statist. Assoc. 101, 1418–1429.

    Article  Google Scholar 

  105. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J. R. Stat. Soc., Ser. B 67, 301–320.

    Google Scholar 

  106. Zuo, L., Zhang, H., Wang, H., and Liu, L. (2021). Sampling-based estimation for massive survival data with additive hazards model. Stat. Med. 40, 441–450.

    Article  Google Scholar 

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Acknowledgements

We sincerely thank Professors Zvi Drezner and Saïd Salhi for their kind invitation to write this article.

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Authors and Affiliations

  1. Department of Information Systems and Decision Sciences, California State University, Fullerton, CA, USA

    Daoji Li & Yinfei Kong

  2. International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, China

    Zemin Zheng

  3. School of Mathematics, The University of Manchester, Manchester, UK

    Jianxin Pan

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  1. Daoji Li
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Correspondence to Yinfei Kong .

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Editors and Affiliations

  1. Kent Business School, University of Kent, Canterbury, UK

    Saïd Salhi

  2. Lancaster University, Lancaster, UK

    John Boylan

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Li, D., Kong, Y., Zheng, Z., Pan, J. (2022). Recent Advances in Big Data Analytics. In: Salhi, S., Boylan, J. (eds) The Palgrave Handbook of Operations Research . Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-96935-6_25

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