Efficient structured support vector regression

Support Vector Regression (SVR) has been a long standing problem in machine learning, and gains its popularity on various computer vision tasks. In this paper, we propose a structured support vector regression framework by extending the max-margin principle to incorporate spatial correlations among neighboring pixels. The objective function in our framework considers both label information and pairwise features, helping to achieve better cross-smoothing over neighboring nodes. With the bundle method, we effectively reduce the number of constraints and alleviate the adverse effect of outliers, leading to an efficient and robust learning algorithm. Moreover, we conduct a thorough analysis for the loss function used in structured regression, and provide a principled approach for defining proper loss functions and deriving the corresponding solvers to find the most violated constraint. We demonstrate that our method outperforms the state-of-the-art regression approaches on various testbeds of synthetic images and real-world scenes.