Linear time isotonic and unimodal regression in the L1 and L∞ norms

Authors:
Victor Boyarshinov;Malik Magdon-Ismail
Affiliations:
Rm 207 Lally Building, CS, RPI, 110 8th Street, Troy, NY 12180, USA;Rm 207 Lally Building, CS, RPI, 110 8th Street, Troy, NY 12180, USA
Venue:
Journal of Discrete Algorithms
Year:
2006

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Abstract

We consider L"1-isotonic regression and L"~ isotonic and unimodal regression. For L"1-isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L"~ isotonic and unimodal regression.