# Generalized Linear Model Regression under Distance-to-set Penalties

arXiv: https://arxiv.org/abs/1711.01341 · HTML: https://mlsanity.com/paper/1711.01341/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [The Stochastic Proximal Distance Algorithm](https://mlsanity.com/paper/2210.12277/) (2022)
- [Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification](https://mlsanity.com/paper/2201.01973/) (2022)

## Abstract (arXiv)

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distance to constraint sets. Distance penalties are more flexible than algebraic and regularization penalties, and avoid the drawback of shrinkage. To optimize distance penalized objectives, we make use of the majorization-minimization principle. Resulting algorithms constructed within this framework are amenable to acceleration and come with global convergence guarantees. Applications to shape constraints, sparse regression, and rank-restricted matrix regression on synthetic and real data showcase strong empirical performance, even under non-convex constraints.