Stochastic Support Vector Machine for Classifying and Regression of Random Variables

Support vector machine (SVM) is a supervised machine learning method which can be used for both classification and regression models. In this paper, we introduce a new model of SVM and support vector regression which any of training samples containing inputs and outputs are considered the random variables with known or unknown probability functions. In this new models, we need the mathematical expectation for any of training samples but when these are unknown we apply nonparametric statistical methods. Also constraints occurrence have probability function which helps obtain maximum margin and achieve robustness. We obtain the optimal separating hyperplane and the optimal hyperplane regression by solving the quadratic optimization problems. Finally the proposed methods are illustrated by several experiments.