Correlation, independance and inverse modeling

Abstract

Learning from examples has a wide number of forms depending on what is to be learned from which available information. One of these form is y = f(x) where the input-output pair (x,y) is the available information and f represents the process mapping x ∈ X to y ∈ Y. In general and for real world problems, it is not reasonnable to expect having the exact representation of f. A fortiori when the dimension of x is large and the number of examples is little. In this paper, we introduce a new model, capable to reduce the complexity of many ill-posed problems without loss of generality. The underlying Bayesian artifice is presented as an alternative to the currently used frequency approaches which does not offer a compelling criterion in the case of high dimensional problems. © 2008 Springer-Verlag.