Functional learning through kernels
Functional learning through kernels
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发表时间：
2003-10
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通讯作者：
S. Canu;X. Mary;A. Rakotomamonjy
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作者：
S. Canu;X. Mary;A. Rakotomamonjy
本文回顾了统计学习理论的功能方面。考虑的要点是当没有先验信息但有数据可用时假设集的性质。在这个框架内，我们首先讨论假设集：它是一个向量空间，它是一组逐点定义的函数，并且该集合上的评估函数是连续映射。基于这些原理，开发了一种原始理论，将再生核希尔伯特空间的概念推广到非希尔伯特集。然后证明任何学习机的假设集都必须是广义再现集。因此，得益于通用的“表示定理”，学习问题的解决方案仍然是核的线性组合。此外，还给出了设计这些内核的方法。为了说明该框架，给出了此类再现集和内核的一些示例。
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions, and the evaluation functional on this set is a continuous mapping. Based on these principles an original theory is developed generalizing the notion of reproduction kernel Hilbert space to non hilbertian sets. Then it is shown that the hypothesis set of any learning machine has to be a generalized reproducing set. Therefore, thanks to a general “representer theorem”, the solution of the learning problem is still a linear combination of a kernel. Furthermore, a way to design these kernels is given. To illustrate this framework some examples of such reproducing sets and kernels are given.