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A Dual Active-Set Algorithm for Regularized Monotonic Regression

Author

Listed:
  • Oleg Burdakov

    (Linköping University)

  • Oleg Sysoev

    (Linköping University)

Abstract

Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-017-1060-0
    DOI: 10.1007/s10957-017-1060-0
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    References listed on IDEAS

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    1. J. Spouge & H. Wan & W.J. Wilbur, 2003. "Least Squares Isotonic Regression in Two Dimensions," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 585-605, June.
    2. 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.
    3. William L. Maxwell & John A. Muckstadt, 1985. "Establishing Consistent and Realistic Reorder Intervals in Production-Distribution Systems," Operations Research, INFORMS, vol. 33(6), pages 1316-1341, December.
    4. Frank Curtis & Zheng Han & Daniel Robinson, 2015. "A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization," Computational Optimization and Applications, Springer, vol. 60(2), pages 311-341, March.
    5. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    6. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
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