Papers › Fast, Provable Algorithms for Isotonic Regression in all ℓₚ-norms

Fast, Provable Algorithms for Isotonic Regression in all ℓₚ-norms

2 Jul 2015arXiv:1507.00710archive 2025-07-28

Rasmus Kyng, Anup Rao, Sushant Sachdeva

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 ||x-y||, for a specified norm. This paper gives improved algorithms for computing the Isotonic Regression for all weighted ℓₚ-norms with rigorous performance guarantees. Our algorithms are quite practical, and their variants can be implemented to run fast in practice.

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