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An algorithm for isotonic regression problems
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .ORCID iD: 0000-0003-1836-4200
Linköping University, Department of Computer and Information Science, Statistics.
Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Mathematics, Statistics.
Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Mathematics, Statistics.
2004 (English)In: European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS / [ed] P. Neittaanmäki, T. Rossi, K. Majava and O. Pironneau, Jyväskylä: University of Jyväskylä , 2004, 1-9 p.Conference paper (Refereed)
Abstract [en]

We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraintsof the form   xi  xj Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph.This problem is known as the isotonic regression (IR) problem. It has important applications in statistics, operations research and signal processing. The most of the applied IR problems are characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not rise with n too rapidly.The existing optimization-based algorithms and statistical IR algorithms have either too high computational complexity or too low accuracy of the approximation to the optimal solution they generate. We introduce a new IR algorithm, which can be viewed as a generalization of the Pool-Adjacent-Violator (PAV) algorithm from completely to partially ordered data. Our algorithm combines both low computational complexity O(n2) and high accuracy. This allows us to obtain sufficiently accurate solutions to the IR problems with thousands of observations.

Place, publisher, year, edition, pages
Jyväskylä: University of Jyväskylä , 2004. 1-9 p.
Keyword [en]
Quadratic Programming, Statistical Computing, Numerical Algorithms, Isotonic Regression, Nonparametric Regression, Pool-Adjacent-Violators Algorithm
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-24327Local ID: 3955ISBN: 951-39-1868-8OAI: diva2:244645
The 4th European Congress of Computational Methods in Applied Science and Engineering "ECCOMAS 2004"
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2015-06-02

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