Distributed Feature Selection for High-dimensional Additive Models

Distributed statistical learning is a common strategy for handling massive data where we divide the learning task into multiple local machines and aggregate the results afterward. However, most existing work considers the case where the samples are divided. In this work, we propose a new algorithm, DDAC-SpAM, that divides features under the high-dimensional sparse additive model. The new algorithm contains three steps: divide, decorrelate, and conquer. We show that after the decorrelation operation, every local estimator can recover the sparsity pattern for each additive component consistently without imposing strict constraints to the correlation structure among variables. Theoretical analysis of the aggregated estimator and empirical results on synthetic and real data illustrate that the DDAC-SpAM algorithm is effective and competitive in fitting sparse additive models.