Optimal Subsampling for Large Sample Logistic Regression

References

• Atkinson, A., Donev, A., and Tobias, R. (2007), Optimum Experimental Designs, With SAS (Vol. 34), Oxford: Oxford University Press.
   Google Scholar
• Baldi, P., Sadowski, P., and Whiteson, D. (2014), “Searching for Exotic Particles in High-Energy Physics With Deep Learning,” Nature Communications 5, 1–9, available at https://doi.org/10.1038/ncomms5308.
   Web of Science ®Google Scholar
• Buldygin, V., and Kozachenko, Y. V. (1980), “Sub-Gaussian Random Variables,” Ukrainian Mathematical Journal, 32, 483–489.
   Google Scholar
• Clarkson, K. L., and Woodruff, D. P. (2013), “Low Rank Approximation and Regression in Input Sparsity Time,” in Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, ACM, pp. 81–90.
   Google Scholar
• Dhillon, P., Lu, Y., Foster, D. P., and Ungar, L. (2013), “New Subsampling Algorithms for Fast Least Squares Regression,” in Advances in Neural Information Processing Systems, pp. 360–368.
   Google Scholar
• Dines, L. L. (1926), “Note on Certain Associated Systems of Linear Equalities and Inequalities,” Annals of Mathematics, 28, 41–42.
   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, Philadelphia, PA: Society for Industrial and Applied Mathematics, pp. 1127–1136.
   Google Scholar
• Efron, B. (1979), “Bootstrap Methods: Another Look at the Jackknife,” The Annals of Statistics, 7, 1–26.
   Web of Science ®Google Scholar
• Efron, B., and Tibshirani, R. J. (1994), An Introduction to the Bootstrap, Boca Raton, FL: CRC Press.
   Google Scholar
• Fithian, W., and Hastie, T. (2014), “Local Case-Control Sampling: Efficient Subsampling in Imbalanced Data Sets,” Annals of Statistics, 42, 1693–1724.
   PubMed Web of Science ®Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2014), Bayesian Data Analysis (3rd ed.), Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Hosmer Jr, D. W., Lemeshow, S., and Sturdivant, R. X. (2013), Applied Logistic Regression (Vol. 398), New York: Wiley.
   Google Scholar
• Kiefer, J. (1959), “Optimum Experimental Designs,” Journal of the Royal Statistical Society, Series B, 21, 272–319.
   Google Scholar
• King, G., and Zeng, L. (2001), “Logistic Regression in Rare Events Data,” Political Analysis, 9, 137–163.
   Google Scholar
• Kohavi, R. (1996), “Scaling up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid,” in Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, pp. 202–207.
   Google Scholar
• Lichman, M. (2013), UCI Machine Learning Repository, Irvine, CA: University of California, School of Information and Computer Science. Available at http://archive.ics.uci.edu/ml
   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
• Mahoney, M. W., and Drineas, P. (2009), “CUR Matrix Decompositions for Improved Data Analysis,” Proceedings of the National Academy of Sciences, 106, 697–702.
   PubMed Web of Science ®Google Scholar
• McWilliams, B., Krummenacher, G., Lucic, M., and Buhmann, J. M. (2014), “Fast and Robust Least Squares Estimation in Corrupted Linear Models,” in Advances in Neural Information Processing Systems, pp. 415–423.
   Google Scholar
• Owen, A. B. (2007), “Infinitely Imbalanced Logistic Regression,” The Journal of Machine Learning Research, 8, 761–773.
   Web of Science ®Google Scholar
• R Core Team (2015), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing, Available at https://www.R-project.org/
   Google Scholar
• Rokhlin, V., and Tygert, M. (2008), “A Fast Randomized Algorithm for Overdetermined Linear Least-Squares Regression,” Proceedings of the National Academy of Sciences, 105, 13212–13217.
   PubMed Web of Science ®Google Scholar
• Scott, A. J., and Wild, C. J. (1986), “Fitting Logistic Models Under Case-Control or Choice Based Sampling,” Journal of the Royal Statistical Society, Series B, 48, 170–182.
   Google Scholar
• Silvapulle, M. (1981), “On the Existence of Maximum Likelihood Estimators for the Binomial Response Models,” Journal of the Royal Statistical Society, Series B, 43, 310–313.
   Google Scholar