Multitask Smoothed Support Vector Machines for High-dimensional Heterogeneous Data

We study high-dimensional binary classification across multiple related but heterogeneous tasks.For each task, the proposed method models the task-specific coefficient vector of a linear support vector machine (SVM) as the sum of a sparse common component and a row-sparse taskspecific deviation, thereby separating features shared across tasks from those that capture cross-task heterogeneity.To handle the nonsmooth hinge loss, we employ a convolution-smoothing technique and estimate the common and deviation components through a composite regularizer that combines an ℓ1 penalty with a row-wise ℓ2,1 penalty.Theoretically, we establish nonasymptotic estimation error bounds under high-dimensional settings, with the rate explicitly decomposing the stochastic error from the smoothing bias.We further prove variable selection consistency for both the shared active set and the heterogeneous active row set under irrepresentability and beta-min conditions.For computation, we develop a projected proximal-gradient algorithm tailored to the constrained composite optimization problem.Simulation studies and an application to PISA data illustrate the finite-sample performance of the proposed method relative to pooled and task-specific alternatives.