Manifold regularization based semisupervised semiparametric regression

Semiparametric regression is an attractive solution for many practical problems. A nonlinear parametric model set, which is frequently encountered in practice, brings difficulties in complexity evaluation and control. On the other hand, it is quite common in practice that a mass of unlabeled samples is available, this fact suggests the possibility of applying a semisupervised regression method. Motivated by these facts, this paper proposes the manifold regularization based semisupervised semiparametric regression (MRBS2R) method, which is characterized by introducing the manifold regularization (MR) technique in determining the parametric model. Generalization performance analysis shows that the generalization performance of the regression will be remarkably improved by introducing MR. Numerical experiments are performed to validate the proposed method.