Quentin Stout– Going Up: Isotonic Regression Algorithms
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Suppose you have data on shirt size, height, and weight, and want to predict weight as a function of shirt size and height. If your only assumptions are that weight is an increasing function of shirt size and of height then you should use an isotonic regression function, rather than a parametric one such as linear regression. Isotonic regressions are also being used in settings where the underlying order is a tree, such as occurs in classification. The talk will survey isotonic regression algorithms for several error metrics and underlying ordered sets. Techniques used include dynamic programming, minimal flows, and parametric search. Several open problems will also be given.