Structured nonlinear variable selection

TL;DR

This paper introduces structured sparsity methods for nonlinear variable selection using derivative-based regularizers within kernel methods, proposing a new algorithm that improves prediction and selection accuracy.

Contribution

It presents two novel regularizers based on partial derivatives, reformulates the problem in RKHS, and develops an ADMM-based algorithm for efficient nonlinear variable selection.

Findings

Favorable prediction accuracy demonstrated in experiments.

Effective variable selection with structured sparsity models.

Algorithm relies on closed-form proximal operators for efficiency.

Abstract

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.