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Algorithms for Sparse k-Monotone Regression

  • Sergei P. Sidorov
  • Alexey R. Faizliev
  • Alexander A. Gudkov
  • Sergei V. Mironov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)

Abstract

The problem of constructing k-monotone regression is to find a vector \(z\in \mathbb {R}^n\) with the lowest square error of approximation to a given vector \(y\in \mathbb {R}^n\) (not necessary k-monotone) under condition of k-monotonicity of z. The problem can be rewritten in the form of a convex programming problem with linear constraints. The paper proposes two different approaches for finding a sparse k-monotone regression (Frank-Wolfe-type algorithm and k-monotone pool adjacent violators algorithm). A software package for this problem is developed and implemented in R. The proposed algorithms are compared using simulated data.

Keywords

Greedy algorithms Pool-adjacent-violators algorithm Isotonic regression Monotone regression Frank-Wolfe type algorithm 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sergei P. Sidorov
    • 1
  • Alexey R. Faizliev
    • 1
  • Alexander A. Gudkov
    • 1
  • Sergei V. Mironov
    • 1
  1. 1.Saratov State UniversitySaratovRussian Federation

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