Learning a hyperplane regressor by minimizing an exact bound on the VC dimension
This addresses the issue of generalization in regression for machine learning practitioners by offering a more efficient and accurate alternative to SVMs, though it appears incremental as it builds on existing VC dimension theory.
The paper tackles the problem of high VC dimension in SVM regressors by introducing the Minimal Complexity Machine (MCM) Regressor, which minimizes an exact bound on VC dimension via linear programming, resulting in error rates much lower than SVMs and often using fewer support vectors, with reductions to less than one-tenth on some datasets.
The capacity of a learning machine is measured by its Vapnik-Chervonenkis dimension, and learning machines with a low VC dimension generalize better. It is well known that the VC dimension of SVMs can be very large or unbounded, even though they generally yield state-of-the-art learning performance. In this paper, we show how to learn a hyperplane regressor by minimizing an exact, or \boldmath{$Θ$} bound on its VC dimension. The proposed approach, termed as the Minimal Complexity Machine (MCM) Regressor, 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 less 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.