论文标题
Banach空间中强大的SVM优化
Robust SVM Optimization in Banach spaces
论文作者
论文摘要
在存在不确定性的情况下，我们解决了Banach空间中二元分类的问题。我们表明，经典支持向量机理论的许多结果可以适当地概括为其在Banach空间中的强大对应物。这些包括代表定理，相关优化问题的强二元性以及它们的几何解释。此外，我们通过表达NASH均衡问题制定的表达来提出一种游戏理论解释，该问题是在基础空间反身空间时找到两个封闭凸集中最接近的问题的更普遍的问题。
We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation. Furthermore, we propose a game theoretic interpretation by expressing a Nash equilibrium problem formulation for the more general problem of finding the closest points in two closed convex sets when the underlying space is reflexive and smooth.
