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

TL;DR

This paper introduces the Minimal Complexity Machine (MCM), a linear programming-based method for learning hyperplane classifiers that minimizes an exact VC dimension bound, leading to simpler models with better generalization.

Contribution

The paper proposes a novel approach to hyperplane classification by directly minimizing an exact VC dimension bound, resulting in simpler models with fewer support vectors and improved generalization.

Findings

MCM achieves lower error rates than SVMs on benchmark datasets.

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

MCM learns simpler classifiers with better generalization performance.

Abstract

The VC dimension measures the capacity of a learning machine, and a low VC dimension leads to good generalization. While SVMs produce state-of-the-art learning performance, it is well known that the VC dimension of a SVM can be unbounded; despite good results in practice, there is no guarantee of good generalization. In this paper, we show how to learn a hyperplane classifier by minimizing an exact, or \boldmath{$\Theta$} bound on its VC dimension. The proposed approach, termed as the Minimal Complexity Machine (MCM), involves solving a simple linear programming problem. Experimental results show, that on a number of benchmark datasets, the proposed approach learns classifiers with error rates much less than conventional SVMs, while often using fewer support vectors. On many 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.