• Corpus ID: 1650609

# Primal-Dual Active-Set Methods for Isotonic Regression and Trend Filtering

@article{Han2015PrimalDualAM,
title={Primal-Dual Active-Set Methods for Isotonic Regression and Trend Filtering},
author={Zheng Han and Frank E. Curtis},
journal={ArXiv},
year={2015},
volume={abs/1508.02452}
}
• Published 10 August 2015
• Computer Science
• ArXiv
Isotonic regression (IR) is a non-parametric calibration method used in supervised learning. [] Key Result In addition, we propose PDAS variants (with safeguarding to ensure convergence) for solving related trend filtering (TF) problems, providing the results of experiments to illustrate their effectiveness.

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## References

SHOWING 1-10 OF 27 REFERENCES

• Computer Science
AISTATS
• 2010
A fast active-set-type method, called block principal pivoting, that accelerates computation by allowing exchanges of several variables among working sets by showing a relationship between l1-regularized linear regression and the linear complementarity problem with bounds.
• Mathematics
SIAM J. Optim.
• 2016
Three primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs) that allow inexactness in the (reduced) linear system solves at all partitions except optimal ones.
• Mathematics, Computer Science
Comput. Optim. Appl.
• 2015
This work presents a primal-dual active-set framework for solving large-scale convex quadratic optimization problems (QPs) and explains the relationship between this framework and semi-smooth Newton techniques, finding that this approach is globally convergent for strictly convex QPs.
• Computer Science
Technometrics
• 2011
A simple algorithm is devised to solve for the path of solutions, which can be viewed as a modified version of the well-known pool adjacent violators algorithm, and computes the entire path in O(n) operations (n being the number of data points).
• Computer Science
Math. Program.
• 1990
The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms, including a new O(n) primal feasible active set algorithm.
• Mathematics
Math. Program.
• 2016
A new active set method is proposed that performs multiple changes in the active manifold estimate at every iteration, and employs a mechanism for correcting these estimates, when needed.
• Mathematics
• 1972
Abstract The isotonic regression problem is to minimize Σt i = 1 [gi − xi]2wi subject to xi ≤ xj when where wi>0 and gi (i= 1, 2, …, k) are given and is a specified partial ordering on {1, 2, …, k}.
• Physics
SIAM J. Optim.
• 2002
Reoptimization techniques for an interior point method applied to solving a sequence of linear programming problems are discussed and numerical results with OOPS, a new object-oriented parallel solver, demonstrate the efficiency of the approach.
• Mathematics
• 1984
AbstractIsotonic regression techniques are reinterpreted and extended to include upper and lower bounds on the ordered sequences in question. This amounts to solving the shortest distance problem for
• Computer Science, Mathematics
Technometrics
• 2016
An order-constrained version of ℓ1-regularized regression (Lasso) is proposed, and it is shown how to solve it efficiently using the well-known pool adjacent violators algorithm as its proximal operator.