Lipschitz Unimodal and Isotonic Regression on Paths and Trees

Abstract. 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, for exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each we describe near-linear time algorithms.

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Pankaj K. Agarwal, Jeff M. Phillips, Bardia Sadri
• Keywords: Closest Sequence, Information Retrieval, LATIN 2010, Mean Squared Error, Unimodular Constraint