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Adaptively refined dynamic program for linear spline regression

Author

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  • Noam Goldberg
  • Youngdae Kim
  • Sven Leyffer
  • Thomas Veselka

Abstract

The linear spline regression problem is to determine a piecewise linear function for estimating a set of given points while minimizing a given measure of misfit or error. This is a classical problem in computational statistics and operations research; dynamic programming was proposed as a solution technique more than 40 years ago by Bellman and Roth (J Am Stat Assoc 64:1079–1084, 1969 ). The algorithm requires a discretization of the solution space to define a grid of candidate breakpoints. This paper proposes an adaptive refinement scheme for the grid of candidate breakpoints in order to allow the dynamic programming method to scale for larger instances of the problem. We evaluate the quality of solutions found on small instances compared with optimal solutions determined by a novel integer programming formulation of the problem. We also consider a generalization of the linear spline regression problem to fit multiple curves that share breakpoint horizontal coordinates, and we extend our method to solve the generalized problem. Computational experiments verify that our nonuniform grid construction schemes are useful for computing high-quality solutions for both the single-curve and two-curve linear spline regression problem. Copyright Springer Science+Business Media New York (outside the USA) 2014

Suggested Citation

  • Noam Goldberg & Youngdae Kim & Sven Leyffer & Thomas Veselka, 2014. "Adaptively refined dynamic program for linear spline regression," Computational Optimization and Applications, Springer, vol. 58(3), pages 523-541, July.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:3:p:523-541
    DOI: 10.1007/s10589-014-9647-y
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    References listed on IDEAS

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    1. Toriello, Alejandro & Vielma, Juan Pablo, 2012. "Fitting piecewise linear continuous functions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 86-95.
    2. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
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    Cited by:

    1. John Alasdair Warwicker & Steffen Rebennack, 2022. "A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1042-1047, March.
    2. Noam Goldberg & Steffen Rebennack & Youngdae Kim & Vitaliy Krasko & Sven Leyffer, 2021. "MINLP formulations for continuous piecewise linear function fitting," Computational Optimization and Applications, Springer, vol. 79(1), pages 223-233, May.
    3. Steffen Rebennack & Vitaliy Krasko, 2020. "Piecewise Linear Function Fitting via Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 507-530, April.

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