Isotonic Regression via Partitioning

• Published in: Algorithmica Vol. 66; no. 1; pp. 93 - 112
• Main Author: Stout, Quentin F.
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.05.2013; Springer
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Applied sciences; Computer Science; Computer science; control theory; systems; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Exact sciences and technology; Information retrieval. Graph; Linear inference, regression; Mathematics; Mathematics of Computing; Probability and statistics; Sciences and techniques of general use; Statistics; Theoretical computing; Theory of Computation; Multidimensional; Nonparametric; Isotonic regression; Tree; DAG; Monotonic; Median regression; Nonparametric · Tree; Tree(graph); Regression analysis; Partitioning; Monolonic; Ordering; Metric; Digraph; Acyclic graph; Quantile; Directed graph
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-012-9628-4

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 <∞. 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.