On the Precise Error Analysis of Support Vector Machines

03/29/2020
by   Abla Kammoun, et al.
0

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

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset