Lipschitz Unimodal and Isotonic Regression on Paths and Trees

Details Lipschitz Unimodal and Isotonic Regression on Paths and Trees Lipschitz Unimodal and Isotonic Regression on Paths and Trees

2009-12-28

arxiv.org/abs/0912.5182v1

Computer Science

Data Structures and Algorithms

18 pages, 5 figures

Scientific paper

We describe algorithms for finding the regression of t, a sequence of values, to the closest sequence s by mean squared error, so that s is always increasing (isotonicity) and so the values of two consecutive points do not increase by too much (Lipschitz). The isotonicity constraint can be replaced with a unimodular constraint, where there is exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each scenario we describe near-linear time algorithms.

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