Tikhonov Regularization for Learning as an Inverse Problem
Başak Akteke-Öztürk, Pakize Taylan, Süreyya Özöğür
We discuss a relation between learning theory and regularization of linear ill-posed inverse problems. In fact learning theory is intrinsically probabilistic whereas the theory of inverse problem is mostly deterministic. We explain the mathematical connections between learning theory and inverse problems theory. It is well known that Tikhonov regularization can be used in the context of supervised learning, where its name becomes regularized least-squares algorithm. When a learning problem is ill-posed, regularization approach reformulate and solve this problem as a minimization problem which contain a loss function and a penalization term. As an theoretic example we will use Tikhonov regularization for MARS (Multivariate Adaptive Regression spline) which is a supervised learning method for high dimensional data.