$L_p$ Isotonic Regression Algorithms Using an $L_0$ Approach
Abstract
Significant advances in flow algorithms have changed the relative performance of various approaches to algorithms for isotonic regression. We show a simple plug-in method to systematically incorporate such advances, and advances in determining violator dags, with no assumptions about the algorithms' structures. The method is based on the standard algorithm for (Hamming distance) isotonic regression (by finding anti-chains in a violator dag), coupled with partitioning based on binary isotonic regression. For several important classes of graphs the algorithms are already faster (in O-notation) than previously published ones, close to or at the lower bound, and significantly faster than those implemented in statistical packages. We consider exact and approximate results for regressions, and , and a variety of orderings.
Keywords
Cite
@article{arxiv.2107.00251,
title = {$L_p$ Isotonic Regression Algorithms Using an $L_0$ Approach},
author = {Quentin F. Stout},
journal= {arXiv preprint arXiv:2107.00251},
year = {2023}
}
Comments
Remove mistaken mistaken in abstract about unweighted points in $d$-dimensional space. Added references, revised paper to make it more readable Revised material to make some sections clearer. Replaced Gau, Liu, Peng paper with van den Brend, Lee, Liu, Saranurak, Sidford, Song, Wang, D (i.e., did exactly what paper shows, namely plug and play, replace flow algorithm when better one appears)