Isotonic Regression via Partitioning

Algorithms are given for determining weighted isotonic regressions satisfying order constraints specified via a directed acyclic graph (DAG). For the L (1) metric a partitioning approach is used which exploits the fact that L (1) regression values can always be chosen to be data values. Extending this approach, algorithms for binary-valued L (1) isotonic regression are used to find L (p) isotonic regressions for 1 < p < a. Algorithms are given for trees, 2-dimensional and multidimensional orderings, and arbitrary DAGs. Algorithms are also given for L (p) isotonic regression with constrained data and weight values, L (1) regression with unweighted data, and L (1) regression for DAGs where there are multiple data values at the vertices.