Multivariate convex support vector regression with semidefinite programming

As one of important nonparametric regression method, support vector regression can achieve nonlinear capability by kernel trick. This paper discusses multivariate support vector regression when its regression function is restricted to be convex. This paper approximates this convex shape restriction with a series of linear matrix inequality constraints and transforms its training to a semidefinite programming problem, which is computationally tractable. Extensions to multivariate concave case, ℓ2-norm Regularization, ℓ1 and ℓ2-norm loss functions, are also studied in this paper. Experimental results on both toy data sets and a real data set clearly show that, by exploiting this prior shape knowledge, this method can achieve better performance than the classical support vector regression.