Functional learning through kernels

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.

• Publication year

  2003

• Venue

  arXiv: Machine Learning

• Publication date

  2003-10-06

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 0910.1013
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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