# Structured nonlinear variable selection

arXiv: https://arxiv.org/abs/1805.06258 · HTML: https://mlsanity.com/paper/1805.06258/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2018.

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

- [Grouped Feature Importance and Combined Features Effect Plot](https://mlsanity.com/paper/2104.11688/) (2021)
- [Kernel-Based Sparse Additive Nonlinear Model Structure Detection through a Linearization Approach](https://mlsanity.com/paper/2508.01453/) (2025)

## Abstract (arXiv)

We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive models. We propose two new regularizers based on partial derivatives as nonlinear equivalents of group lasso and elastic net. We formulate the problem within the framework of learning in reproducing kernel Hilbert spaces and show how the variational problem can be reformulated into a more practical finite dimensional equivalent. We develop a new algorithm derived from the ADMM principles that relies solely on closed forms of the proximal operators. We explore the empirical properties of our new algorithm for Nonlinear Variable Selection based on Derivatives (NVSD) on a set of experiments and confirm favourable properties of our structured-sparsity models and the algorithm in terms of both prediction and variable selection accuracy.