An iterativeframework based on finding point correspondences and estimating the transformation function is widely adopted for nonrigid point set registration. However, correspondences established based on feature descriptors are likely to be inaccurate. In this paper, we propose a novel transformation model that can learn from such correspondences. The model is built by means of weighted support vector (SV) regression with a quadratic ε-insensitive loss and manifold regularization. The loss is insensitive to noise, and the regularization forces the transformation function to preserve the intrinsic geometry of the input data. To assess the confidences of correspondences, we introduce a probabilistic model that is solved using the expectation maximization (EM) algorithm. Then, we input the confidences into the transformation model as instance weights to guide model training. We use the coordinate descent method to solve the transformation model in a reproducing kernel Hilbert space and accelerate its speed by means of sparse approximation. Extensive experiments show that our approach is efficient and outperforms other state-of-the-art methods.