Learning a hyperplane regressor through a tight bound on the VC dimension

In this paper, we show how to learn a hyperplane regressor by minimizing a tight or Theta bound on its VC dimension. While minimizing the VC dimension with respect to the defining variables is an ill posed and intractable problem, we propose a smooth, continuous, and differentiable function for a tight bound. Minimizing a tight bound yields the Minimal Complexity Machine (MCM) Regressor, and involves solving a simple linear programming problem. Experimental results show that on a number of benchmark datasets, the proposed approach yields regressors with error rates much lower than those obtained with conventional SVM regresssors, while often using fewer support vectors. On some benchmark datasets, the number of support vectors is less than one-tenth the number used by SVMs, indicating that the MCM does indeed learn simpler representations. (C) 2015 Elsevier B.V. All rights reserved.