# Computing Estimators of Dantzig Selector type via Column and Constraint Generation

arXiv: https://arxiv.org/abs/1908.06515 · HTML: https://mlsanity.com/paper/1908.06515/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [Learning Massive-scale Partial Correlation Networks in Clinical Multi-omics Studies with HP-ACCORD](https://mlsanity.com/paper/2412.11554/) (2024)

## Abstract (arXiv)

We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case in which the measurements contain no errors), and the fused Dantzig selector (for the case in which the underlying signal is piecewise constant). In spite of being estimators central to sparse signal processing and machine learning, solving these linear programming problems for large scale instances remains a challenging task, thereby limiting their usage in practice. We show that classic constraint- and column-generation techniques from large scale linear programming, when used in conjunction with a commercial implementation of the simplex method, and initialized with the solution from a closely-related Lasso formulation, yields solutions with high efficiency in many settings.