Question: Does anyone know of any textbooks introducing machine learning (for the first time) via the reproducing kernel Hilbert space approach? I.e., which assume functional analysis as a prerequisite, but do not assume prior knowledge of machine learning?

Any survey articles would be a close second. No research papers please -- I want to learn the theory first before trying to put it into practice.

Background: There is a course which will be taught at my university this semester which promises to use methods from functional analysis to introduce machine learning, specifically Hilbert spaces with reproducing kernels. This would be really good for me, since I know functional analysis, do not know machine learning, and want to learn machine learning for the first time.

Course Description (in German) -- no references to literature
Course Home Page -- again no references to literature
Course Page for a similar course at another university -- all of the references are research papers

However, I am not sure if I will have the space in my schedule to take this course, or if it will conflict with a course which I have to take this semester. Thus, I would like to be able to study this subject on my own in my free time in the future if I cannot take this course this semester.


1 Answer 1


The best and standard reference will be

Aronszajn, Nachman. "Theory of reproducing kernels." Transactions of the American mathematical society 68.3 (1950): 337-404.

I am not sure how deep you know about functional analysis, different levels of functional analysis has great difference. So I will say another standard is:

Smola, Alex J., and Bernhard Schölkopf. Learning with kernels. GMD-Forschungszentrum Informationstechnik, 1998.

I am also not sure about your general math background, more or less you may be interested in:

Lafferty, John, and Guy Lebanon. "Diffusion kernels on statistical manifolds." Journal of Machine Learning Research 6.Jan (2005): 129-163.

  • 1
    $\begingroup$ These all look like very good and interesting references -- especially the last one, since I will probably be able to use what I am learning in my differential geometry course to try to understand it. I appreciate you taking the time to answer this -- enjoy the rest of your week! $\endgroup$ Dec 20, 2016 at 14:13

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