Information-Based Optimal Subdata Selection for Big Data Linear Regression

References

• Candes, E., and Tao, T. (2007), “The Dantzig Selector: Statistical Estimation When p is Much Larger Than n,” The Annals of Statistics, 35, 2313–2351.
   Web of Science ®Google Scholar
• Drineas, P., Magdon-Ismail, M., Mahoney, M., and Woodruff, D. (2012), “Faster Approximation of Matrix Coherence and Statistical Leverage,” Journal of Machine Learning Research, 13, 3475–3506.
   Web of Science ®Google Scholar
• Drineas, P., Mahoney, M., Muthukrishnan, S., and Sarlos, T. (2011), “Faster Least Squares Approximation,” Numerische Mathematik, 117, 219–249.
   Web of Science ®Google Scholar
• Drineas, P., Mahoney, M. W., and Muthukrishnan, S. (2006), “Sampling Algorithms for l2 Regression and Applications,” in Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, Society for Industrial and Applied Mathematics, pp. 1127–1136.
   Google Scholar
• Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911.
   Google Scholar
• Fonollosa, J., Sheik, S., Huerta, R., and Marco, S. (2015), “Reservoir Computing Compensates Slow Response of Chemosensor Arrays Exposed to Fast Varying Gas Concentrations in Continuous Monitoring,” Sensors and Actuators B: Chemical, 215, 618–629.
   Web of Science ®Google Scholar
• Galambos, J. (1987), The Asymptotic Theory of Extreme Order Statistics, Florida: Robert E. Krieger.
   Google Scholar
• Goodson, D. Z. (2011), Mathematical Methods for Physical and Analytical Chemistry, New York: Wiley.
   Google Scholar
• Hadamard, J. (1893), “Résolution d’une Question Relative aux Déterminants,” Bulletin des Sciences Mathmatiques, 17, 240–246.
   Google Scholar
• Hall, P. (1979), “On the Relative Stability of Large Order Statistics,” in Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 86), Cambridge: Cambridge University Press, pp. 467–475.
   Web of Science ®Google Scholar
• Kiefer, J. (1959), “Optimum Experimental Designs,” Journal of the Royal Statistical Society, Series B, 21, 272–319.
   Google Scholar
• Lin, N., and Xie, R. (2011), “Aggregated Estimating Equation Estimation,” Statistics and Its Interface, 4, 73–83.
   Web of Science ®Google Scholar
• Ma, P., Mahoney, M., and Yu, B. (2014), “A Statistical Perspective on Algorithmic Leveraging,” in Proceedings of the 31st International Conference on Machine Learning (ICML-14), pp. 91–99.
   Google Scholar
• ——— (2015), “A Statistical Perspective on Algorithmic Leveraging,” Journal of Machine Learning Research, 16, 861–911.
   Web of Science ®Google Scholar
• Ma, P., and Sun, X. (2015), “Leveraging for Big Data Regression,” Wiley Interdisciplinary Reviews: Computational Statistics, 7, 70–76.
   Google Scholar
• Martínez, C. (2004), “Partial Quicksort,” in Proc. 6th ACMSIAM Workshop on Algorithm Engineering and Experiments and 1st ACM-SIAM Workshop on Analytic Algorithmics and Combinatorics, pp. 224–228.
   Google Scholar
• Meinshausen, N., and Yu, B. (2009), “Lasso-Type Recovery of Sparse Representations for High-Dimensional Data,” The Annals of Statistics, 37, 246–270.
   Web of Science ®Google Scholar
• Musser, D. R. (1997), “Introspective Sorting and Selection Algorithms,” Software: Practice and Experience, 27, 983–993.
   Web of Science ®Google Scholar
• R Core Team (2015), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Schifano, E. D., Wu, J., Wang, C., Yan, J., and Chen, M.-H. (2016), “Online Updating of Statistical Inference in the Big Data Setting,” Technometrics, 58, 393–403.
   PubMed Web of Science ®Google Scholar
• Stroustrup, B. (1986), The C++ Programming Language, India: Pearson Education.
   Google Scholar
• Thompson, E. E., Sowers, M., Frongillo, E., and Parpia, B. (1992), “Sources of Fiber and Fat in Diets of U.S. Women Aged 19 to 50: Implications for Nutrition Education and Policy,” American Journal of Public Health, 82, 695–702.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Wang, H., Zhu, R., and Ma, P. (2017), “Optimal Subsampling for Large Sample Logistic Regression,” Journal of the American Statistical Association.
   Web of Science ®Google Scholar