• 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.

## Figures and Tables from this paper

### A Dual Active-Set Algorithm for Regularized Monotonic Regression

• Computer Science, Mathematics
J. Optim. Theory Appl.
• 2017
This work introduces a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints, and proves that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size.

### A second-order method for convex 1-regularized optimization with active-set prediction

• Mathematics
Optim. Methods Softw.
• 2016
An active-set method for the minimization of an objective function φ that is the sum of a smooth convex function f and an -regularization term is described, and global convergence is established under the assumptions of Lipschitz-continuity and strong-convexity of f.

### Penalized matrix decomposition for denoising, compression, and improved demixing of functional imaging data

• Computer Science
bioRxiv
• 2018
An improved approach to compressing and denoising functional imaging data is introduced, based on a spatially-localized penalized matrix decomposition (PMD) of the data to separate (low-dimensional) signal from (temporally-uncorrelated) noise, which facilitates the process of demixing the observed activity into contributions from individual neurons.

### Regularized monotonic regression

• Mathematics
• 2016
Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that ...

## References

SHOWING 1-10 OF 27 REFERENCES

### Fast Active-set-type Algorithms for L1-regularized Linear Regression

• 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.

### Globally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem Solves

• 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.

### A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization

• 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.

### Nearly-Isotonic Regression

• 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).

### Fast and Flexible ADMM Algorithms for Trend Filtering

• Computer Science
ArXiv
• 2014
This article presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool, that is competitive with the specialized interior point methods that are currently in use, and yet is far more numerically robust.

### The Primal-Dual Active Set Strategy as a Semismooth Newton Method

• Mathematics
SIAM J. Optim.
• 2002
The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept, which leads to new local convergence results of the primal-dual active set strategy.

### Active set algorithms for isotonic regression; A unifying framework

• 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.

### A family of second-order methods for convex $$\ell _1$$ℓ1-regularized optimization

• 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.

### The Isotonic Regression Problem and its Dual

• 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}.

### Reoptimization With the Primal-Dual Interior Point Method

• 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.