A generalized lasso formulation of weighted and regularized (nearly-)isotonic regression on graphs

Abstract

In this paper we study a regularized version of nearly-isotonic regression with respect to a general partial order. In this estimator the sum of squares is weighted, with some of the weights allowed to be zero, and an additional quadratic penalty is imposed. The only assumption we make is that the quadratic part of the objective function is strictly convex, and we show that this assumption is mild. First, we show that for all sufficiently large values of the penalty parameter the estimator coincides with the regularized isotonic regression, in which the penalty is replaced by the isotonic constraint. Further, we prove that the resulting problem can be written as a generalized lasso problem with a design matrix of full column rank and with the penalty matrix unchanged. Next, we derive the dual problem, which is a quadratic program with box constraints, and write it in a sparse form that can be solved by standard quadratic programming solvers for sparse problems.

On the Calibration of Isotonic Distributional Regression
Tobias Biegert, Johannes Resin, Alexander Jordan +1
arXiv22 Oct 2026PreprintarXiv licenceFull textStatisticsarXiv
Fixed-Point Formulation and Parallel Averaged Operator Algorithms for Generalized Variational Inclusion Problems
Arifuzzaman, Syed Shakaib Irfan, Ahmad Almutlg +1
Axioms11 Oct 2026Peer-reviewedCC BY 4.0General mathematicsCrossref
Weighted persistence intensity regression
Matteo Pegoraro, Mario Beraha
arXiv1 Sep 2026PreprintarXiv licenceFull textGeometry & topology StatisticsarXiv
Generalized Stević–Sharma operators on weighted Dirichlet spaces
Guo Zhitao
Demonstratio Mathematica26 Oct 2026Peer-reviewedCC BYFull textGeneral mathematicsDOAJ
Component-weighted sparse group LASSO for finite mixture regression models
Vinay Joshy, Zeny Feng, Grace Stelter +2
arXiv12 Sep 2026PreprintCC BY 4.0Full textStatisticsarXiv

Cite

BibTeX RIS

BibTeX

@misc{pastukhov2026generalized,
  title = {{A generalized lasso formulation of weighted and regularized (nearly-)isotonic regression on graphs}},
  author = {Vladimir Pastukhov},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04018},
  eprint = {2611.04018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04018},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - A generalized lasso formulation of weighted and regularized (nearly-)isotonic regression on graphs
AU  - Vladimir Pastukhov
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.04018
UR  - https://arxiv.org/abs/2611.04018
AB  - In this paper we study a regularized version of nearly-isotonic regression with respect to a general partial order. In this estimator the sum of squares is weighted, with some of the weights allowed to be zero, and an additional quadratic penalty is imposed. The only assumption we make is that the quadratic part of the objective function is strictly convex, and we show that this assumption is mild. First, we show that for all sufficiently large values of the penalty parameter the estimator coincides with the regularized isotonic regression, in which the penalty is replaced by the isotonic constraint. Further, we prove that the resulting problem can be written as a generalized lasso problem with a design matrix of full column rank and with the penalty matrix unchanged. Next, we derive the dual problem, which is a quadratic program with box constraints, and write it in a sparse form that can be solved by standard quadratic programming solvers for sparse problems.
ER  -

Abstract

Related

Cite