通过最小化VC维数上的精确界学习超平面回归量
Learning a hyperplane regressor by minimizing an exact bound on the VC dimension
摘要：
学习机的能力是通过其Vapnik-Chervonenkis维数来衡量的，VC维数低的学习机泛化能力更好。众所周知，支持向量机的VC维可以非常大或无界，即使它们通常产生最先进的学习性能。在本文中，我们展示了如何学习一个超平面回归最小化一个确切的，或\boldmath{$Θ$}约束的VC维。所提出的方法，称为最小复杂性机（MCM）回归，涉及解决一个简单的线性规划问题。实验结果表明，在一些基准数据集上，所提出的方法产生的回归与出错率远低于传统的SVM回归，而往往使用更少的支持向量。在一些基准数据集上，支持向量的数量不到SVM使用的数量的十分之一，这表明MCM确实学习了更简单的表示。
英文摘要：
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.
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