# Group selection and shrinkage: Structured sparsity for semiparametric additive models

arXiv: https://arxiv.org/abs/2105.12081 · HTML: https://mlsanity.com/paper/2105.12081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 9 of 9)

- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives](https://mlsanity.com/paper/2001.06471/) (2020)
- [Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is low](https://mlsanity.com/paper/1708.03288/) (2017)
- [Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectives](https://mlsanity.com/paper/2104.07084/) (2021)
- [Best subset selection is robust against design dependence](https://mlsanity.com/paper/2007.01478/) (2020)
- [Sparse Partially Linear Additive Models](https://mlsanity.com/paper/1407.4729/) (2014)
- [Generalized Additive Model Selection](https://mlsanity.com/paper/1506.03850/) (2015)
- [A Splicing Approach to Best Subset of Groups Selection](https://mlsanity.com/paper/2104.12576/) (2021)
- [Overlapping group logistic regression with applications to genetic pathway selection](https://mlsanity.com/paper/1510.05144/) (2015)

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

- [Scalable Subset Selection in Linear Mixed Models](https://mlsanity.com/paper/2506.20425/) (2025)

## Abstract (arXiv)

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconvex regularization surface and present finite-sample error bounds for estimation of the regression function. As an application requiring structure, we study sparse semiparametric additive modeling, a procedure that allows the effect of each predictor to be zero, linear, or nonlinear. For this task, the new estimators improve across several metrics on synthetic data compared to alternatives. Finally, we demonstrate their efficacy in modeling supermarket foot traffic and economic recessions using many predictors. These demonstrations suggest sparse semiparametric additive models, fit using the new estimators, are an excellent compromise between fully linear and fully nonparametric alternatives. All of our algorithms are made available in the scalable implementation grpsel.