A Few Notes on Statistical Learning Theory

摘要

In these notes our aim is to survey recent (and not so recent) results regarding the mathematical foundations of learning theory. The focus in this article is on the theoretical side and not on the applicative one; hence, we shall not present examples which may be interesting from the practical point of view but have little theoretical significance. This survey is far from being complete and it focuses on problems the author finds interesting (an opinion which is not necessarily shared by the majority of the learning community). Relevant books which present a more evenly balanced approach are, for example. The starting point of our discussion is the formulation of the learning problem. Consider a class G, consisting of real valued functions defined on a space Ω, and assume that each g ∈ G maps Ω into. Let T be an unknown function, T : Ω → and set μ to be an unknown probability measure on Ω.