Structured nonlinear variable selection
This addresses variable selection for regression problems with nonlinear dependencies, which is an incremental improvement over existing structured sparsity methods.
The paper tackles variable selection in regression with nonlinear input dependencies by proposing two new regularizers based on partial derivatives as nonlinear equivalents of group lasso and elastic net, and develops an ADMM-based algorithm (NVSD) that shows favorable prediction and variable selection accuracy in experiments.
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.