Learning a hyperplane regressor by minimizing an exact bound on the VC dimension

TL;DR

This paper introduces the Minimal Complexity Machine (MCM) Regressor, which minimizes an exact VC dimension bound to produce simpler, more generalizable hyperplane regressors with fewer support vectors and lower error rates.

Contribution

It presents a novel linear programming approach to learn hyperplane regressors by directly minimizing an exact VC dimension bound, improving simplicity and generalization over SVMs.

Findings

MCM achieves lower error rates than SVMs on benchmark datasets.

MCM uses significantly fewer support vectors, often less than one-tenth of SVMs.

The approach is computationally simple and effective for regression tasks.

Abstract

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{$\Theta$} 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.