Adaptively refined dynamic program for linear spline regression

Noam Goldberg (), Youngdae Kim (), Sven Leyffer () and Thomas Veselka ()

Computational Optimization and Applications, 2014, vol. 58, issue 3, 523-541

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

Keywords: Piecewise regression; Least squares; Change point detection; Dynamic programming; Mixed-integer programming (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-014-9647-y (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:58:y:2014:i:3:p:523-541

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-014-9647-y

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().