Rkhs representer theorem. Moore–Aronszajn: Any positive definite function $K$ defines an RKHS. (Representer Theorem, adapted from [Sch¨olkopfet al. principle component analysis chapter, we review the RKHS theory and the representer theorem. None of these quite seem like what I need though Edit: Here is a promising cuprit! The nonparametric representor Representer Theorem The representer theorem guarantees that the solution can be written as n = f cjKxj for some c = (c1, . We will consider couple of easy examples to get some intuition. g. || 5. A kernel method (or kernel machine) is a discrimination rule of the form n 1 X bf = arg min L(yi; f(xi)) + kfk2 F The representer theorem assures that ker-nel methods retain optimality under penal-ized empirical risk minimization. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. It also discusses the main properties on kernel functions and their construction, as well as the basic ideas to work with complex objects and reproducing spaces.