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A Dual Active-Set Algorithm for Regularized Slope-Constrained Monotonic Regression
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-1836-4200
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
2017 (English)In: Iranian Journal of Operations Research, ISSN 2008-1189, Vol. 8, no 2, p. 40-47Article in journal (Refereed) Published
Abstract [en]

In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is o(n2) its running time is growing in our computational experiments almost linearly with n. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.

Place, publisher, year, edition, pages
Tehran, 2017. Vol. 8, no 2, p. 40-47
Keywords [en]
Monotonic regression, Regularization, Quadratic penalty, Convex quadratic optimization, Dual active-set method, Large-scale optimization
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-148061DOI: 10.29252/iors.8.2.40OAI: oai:DiVA.org:liu-148061DiVA, id: diva2:1210896
Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2018-06-07Bibliographically approved

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Burdakov, OlegSysoev, Oleg

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