Fast, Provable Algorithms for Isotonic Regression in all $\ell_{p}$norms
Abstract
Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $xy,$ for a specified norm. This paper gives improved algorithms for computing the Isotonic Regression for all weighted $\ell_{p}$norms with rigorous performance guarantees. Our algorithms are quite practical, and their variants can be implemented to run fast in practice.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.00710
 Bibcode:
 2015arXiv150700710K
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Statistics Theory