Distributionally robust joint chance-constrained support vector machines

In this paper, we investigate the chance-constrained support vector machine (SVM) problem in which the data points are virtually uncertain although some properties of distributions are available. Thus the robust joint chance-constrained SVM is applied to consider the probability of any existing misclassification in the uncertain data. We transform the chance-constrained SVM into a semidefinite programming problem and a deterministic problem of second-order cone programming.We present new techniques for handling these problems. By assuming the fact that the rows related to the separation constraint matrix of the chance-constrained SVM model are dependent, it is possible to present a new approach for connecting copulas to a stochastic separation constrained support vector machine. Hence, we can use a marginal distribution of the archimedean copula functions, instead of the distribution functions. The experimental results indicate that the stochastic separation constrained support vector machine with copula theory is able to achieve an efficient performance.