# 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} }

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.

## 5 Citations

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

- Computer Science, MathematicsJ. 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

- MathematicsOptim. 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 SciencebioRxiv
- 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 ...

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