Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Introduction to Algorithms
Dual algorithm for l(1) isotonic optimization on a partially ordered set
Dual algorithm for l(1) isotonic optimization on a partially ordered set
Clustering short time series gene expression data
Bioinformatics
Page-level template detection via isotonic smoothing
Proceedings of the 16th international conference on World Wide Web
Enhanced hierarchical classification via isotonic smoothing
Proceedings of the 17th international conference on World Wide Web
Nonparametric combinatorial regression for shape constrained modeling
IEEE Transactions on Signal Processing
Lipschitz unimodal and isotonic regression on paths and trees
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
A two-dimensional Poisson equation formulation of non-parametric statistical non-linear modeling
Computers & Mathematics with Applications
| Hi-index | 0.00 |
Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n3) when there are n observations. The analysis of large-scale microarray data, which is one of the important tools in biology, using isotonic regression is hence expensive. This is because in microarray analysis, the same procedure is used for studying the fit of tens of thousands of genes to a given partial order. Fast estimation for the fitting error is therefore highly desired to reduce the number of regression instances through pruning. In this paper, we present approximation algorithms to the isotonic regression problem under the L1 error measure. We relate the problem to an edge packing problem and in the special case when the observations are not weighted, we relate it to a weighted matching problem.