标题： 支持向量机的统计性能 显示英文标题

标题： Statistical performance of support vector machines

摘要： 支持向量机（SVM）算法因其非常出色的实践成果而闻名于计算机学习社区。 本文的目标是从统计学的角度研究这一算法，并使用集中理论和经验过程的工具。 我们的主要结果基于其他作者的观察，即SVM可以被视为一种统计正则化程序。 从这个角度来看，它也可以被解释为一种利用惩罚准则进行模型选择的原则。 然后，在这种框架下可以适应与模型选择相关的通用方法来研究两个重要问题：(1) 最小惩罚是什么？它与SVM算法中实际使用的惩罚相比如何？(2) 在SVM算法所用的具体损失函数的情况下，在这种设置下是否可以获得“oracle不等式”？ 我们证明了后一个问题的答案是肯定的，并且对前一个问题提供了相关见解。 我们的结果表明，对于SVM来说，获得快速收敛率是可能的。 显示英文摘要

摘要： The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of concentration theory and empirical processes. Our main result builds on the observation made by other authors that the SVM can be viewed as a statistical regularization procedure. From this point of view, it can also be interpreted as a model selection principle using a penalized criterion. It is then possible to adapt general methods related to model selection in this framework to study two important points: (1) what is the minimum penalty and how does it compare to the penalty actually used in the SVM algorithm; (2) is it possible to obtain ``oracle inequalities'' in that setting, for the specific loss function used in the SVM algorithm? We show that the answer to the latter question is positive and provides relevant insight to the former. Our result shows that it is possible to obtain fast rates of convergence for SVMs.