Inverse Problems in Learning from Data

Abstrakt

It is shown that application of methods from theory of inverse problems to learning from data leads to simple proofs of characterization of minima of empirical and expected error functionals and their regularized versions. The reformulation of learning in terms of inverse problems also enables comparison of regularized and non regularized case showing that regularization achieves stability by merely modifying output weights of global minima. Methods of theory of inverse problems lead to choice of reproducing kernel Hilbert spaces as suitable ambient function spaces.