Nonparametric Regression and Classification with Joint Sparsity Constraints

We propose new families of models and algorithms for high-dimensional nonpara- metric learning with joint sparsity constraints. Our approach is based on a regular- ization method that enforces common sparsity patterns across different function components in a nonparametric additive model. The algorithms employ a coor- dinate descent approach that is based on a functional soft-thresholding operator. The framework yields several new models, including multi-task sparse additive models, multi-response sparse additive models, and sparse additive multi-category logistic regression. The methods are illustrated with experiments on synthetic data and gene microarray data.