Our paper on Structured nonlinear variable selection has been accepted to the UAI2018 conference.
In the paper we investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. 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 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. The arXiv preprint is available from here.