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A segmentation-based algorithm for large-scale partially ordered monotonic regression

Author

Listed:
  • Sysoev, O.
  • Burdakov, O.
  • Grimvall, A.

Abstract

Monotonic regression (MR) is an efficient tool for estimating functions that are monotonic with respect to input variables. A fast and highly accurate approximate algorithm called the GPAV was recently developed for efficient solving large-scale multivariate MR problems. When such problems are too large, the GPAV becomes too demanding in terms of computational time and memory. An approach, that extends the application area of the GPAV to encompass much larger MR problems, is presented. It is based on segmentation of a large-scale MR problem into a set of moderate-scale MR problems, each solved by the GPAV. The major contribution is the development of a computationally efficient strategy that produces a monotonic response using the local solutions. A theoretically motivated trend-following technique is introduced to ensure higher accuracy of the solution. The presented results of extensive simulations on very large data sets demonstrate the high efficiency of the new algorithm.

Suggested Citation

  • Sysoev, O. & Burdakov, O. & Grimvall, A., 2011. "A segmentation-based algorithm for large-scale partially ordered monotonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2463-2476, August.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:8:p:2463-2476
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    References listed on IDEAS

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    1. Oh, Man-Suk & Shin, Dong Wan, 2011. "A unified Bayesian inference on treatment means with order constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 924-934, January.
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    Cited by:

    1. Oleg Burdakov & Oleg Sysoev, 2017. "A Dual Active-Set Algorithm for Regularized Monotonic Regression," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 929-949, March.
    2. Alexander I. Jordan & Anja Mühlemann & Johanna F. Ziegel, 2022. "Characterizing the optimal solutions to the isotonic regression problem for identifiable functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 489-514, June.

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