Abstract
In this paper, we present two new stochastic approximation algorithms for the problem of quantile estimation. The algorithms uses the characterization of the quantile provided in terms of an optimization problem in [1]. The algorithms take the shape of a stochastic gradient descent which minimizes the optimization problem. Asymptotic convergence of the algorithms to the true quantile is proven using the ODE method. The theoretical results are also supplemented through empirical evidence. The algorithms are shown to provide significant improvement in terms of memory requirement and accuracy.
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References
Hu, J., Hu, P., Chang, H.S.: A stochastic approximation framework for a class of randomized optimization algorithms. IEEE Trans. Autom. Control 57(1), 165–178 (2012)
Kushner, H.J., Clark, D.S.: Stochastic Approximation Methods for Constrained and Unconstrained Systems, vol. 26. Springer Science & Business Media, New York (2012)
Yu, K., Zudi, L., Stander, J.: Quantile regression: applications and current research areas. J. Royal Stat. Soc. Ser. D (Stat.) 52(3), 331–350 (2003)
Chen, E.J., Kelton, W.D.: Simulation-based estimation of quantiles. In: Simulation Conference Proceedings, 1999 Winter, vol. 1. IEEE (1999)
Glynn, P.W.: Importance sampling for Monte Carlo estimation of quantiles. In: Mathematical Methods in Stochastic Simulation and Experimental Design: Proceedings of the 2nd St. Petersburg Workshop on Simulation (1996)
Borkar, V.S.: Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press, Cambridge (2008)
Avramidis, A.N., Wilson, J.R.: Correlation-induction techniques for estimating quantiles in simulation experiments. Oper. Res. 46(4), 574–591 (1998)
Cannamela, C., Garnier, J., Iooss, B.: Controlled stratification for quantile estimation. Ann. Appl. Stat. 2, 1554–1580 (2008)
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Joseph, A.G., Bhatnagar, S. (2015). A Stochastic Approximation Algorithm for Quantile Estimation. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9490. Springer, Cham. https://doi.org/10.1007/978-3-319-26535-3_36
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DOI: https://doi.org/10.1007/978-3-319-26535-3_36
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