Divide-and-Conquer for Debiased $l_1$-norm Support Vector Machine in Ultra-high Dimensions; Heng Lian, Zengyan Fan

$1$-norm support vector machine (SVM) generally has competitive
performance compared to standard $2$-norm support vector machine
in classification problems, with the advantage of automatically
selecting relevant features. We propose a divide-and-conquer
approach in the large sample size and high-dimensional setting
by splitting the data set across multiple machines, and then
averaging the debiased estimators. Extension of existing
theoretical studies to SVM is challenging in estimation of the
inverse Hessian matrix that requires approximating the Dirac
delta function via smoothing. We show that under appropriate
conditions the aggregated estimator can obtain the same
convergence rate as the central estimator utilizing all
observations.

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