Abstract
Sparse additive machines (SAMs) have attracted increasing attention in high dimensional classification due to their representation flexibility and interpretability. However, most of existing methods are formulated under Tikhonov regularization scheme with the hinge loss, which are susceptible to outliers. To circumvent this problem, we propose a sparse additive machine with ramp loss (called ramp-SAM) to tackle classification and variable selection simultaneously. Misclassification error bound is established for ramp-SAM with the help of detailed error decomposition and constructive hypothesis error analysis. To solve the nonsmooth and nonconvex ramp-SAM, a proximal block coordinate descent method is presented with convergence guarantees. The empirical effectiveness of our model is confirmed on simulated and benchmark datasets.
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