Isotonic Regression for Multiple Independent Variables

Quentin F. Stout
2013 Algorithmica  
This paper gives algorithms for determining isotonic regressions for weighted data at a set of points P in multidimensional space with the standard componentwise ordering. The approach is based on an orderpreserving embedding of P into a slightly larger directed acyclic graph (dag) G, where the transitive closure of the ordering on P is represented by paths of length 2 in G. Algorithms are given which, compared to previous results, improve the time by a factor ofΘ(|P |) for the L 1 , L 2 , and
more » ... ∞ metrics. A yet faster algorithm is given for L 1 isotonic regression with unweighted data. L ∞ isotonic regression is not unique, and algorithms are given for finding L ∞ regressions with desirable properties such as minimizing the number of large regression errors.
doi:10.1007/s00453-013-9814-z fatcat:bounfvm5zjfcjmb3txh3v5ysbi