On the Precise Error Analysis of Support Vector Machines

This paper investigates the asymptotic behavior of soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional numerous data (large n large p with n/p→ δ) drawn from a Gaussian mixture distribution. Sharp predictions classification error rate SVM are provided, as well limits such important parameters margin bias. As further outcome, analysis allows identification maximum number training samples that is able to separate. The precise nature our results an accurate performance comparison better understanding involved (such measurements parameter) on performance. Our analysis, confirmed by set numerical experiments, builds upon convex min-max Theorem, extends its scope new problems never studied before this framework.