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.
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