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Abstract:
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We consider the problem of estimating isotonic regression functions under partial order constraints. When the loss function is square error, this problem becomes a quadratic programming problem, and an efficient algorithm using a recursive partitioning method is known (Spouge, Wan, and Wilbur 2003; Luss, Rosset, and Shahar 2012). Generalization of the recursive partitioning approach is considered by Luss and Rosset (2014) for general differentiable convex loss functions, termed the generalized isotonic recursive partitioning (GIRP) algorithm. In this work, we show that the GIRP algorithm may fail to produce a correct solution for some important differentiable convex losses. We study the reason for this incorrect behavior, and seek ways to resolve this problem.
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